id	sid	tid	token	lemma	pos
ejpam-811	1	1	5_811_huang.dvi	5_811_huang.dvi	NUM
ejpam-811	1	2	european	european	PROPN
ejpam-811	1	3	journal	journal	PROPN
ejpam-811	1	4	of	of	ADP
ejpam-811	1	5	pure	pure	ADJ
ejpam-811	1	6	and	and	CCONJ
ejpam-811	1	7	applied	apply	VERB
ejpam-811	1	8	mathematics	mathematic	NOUN
ejpam-811	1	9	vol	vol	NOUN
ejpam-811	1	10	.	.	PUNCT
ejpam-811	2	1	3	3	NUM
ejpam-811	2	2	,	,	PUNCT
ejpam-811	2	3	no	no	INTJ
ejpam-811	2	4	.	.	NOUN
ejpam-811	2	5	6	6	NUM
ejpam-811	2	6	,	,	PUNCT
ejpam-811	2	7	2010	2010	NUM
ejpam-811	2	8	,	,	PUNCT
ejpam-811	2	9	989	989	NUM
ejpam-811	2	10	-	-	PUNCT
ejpam-811	2	11	1005	1005	NUM
ejpam-811	2	12	issn	issn	PROPN
ejpam-811	2	13	1307	1307	NUM
ejpam-811	2	14	-	-	SYM
ejpam-811	2	15	5543	5543	NUM
ejpam-811	2	16	–	–	PUNCT
ejpam-811	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-811	2	18	special	special	ADJ
ejpam-811	2	19	issue	issue	NOUN
ejpam-811	2	20	on	on	ADP
ejpam-811	2	21	complex	complex	ADJ
ejpam-811	2	22	analysis	analysis	NOUN
ejpam-811	2	23	:	:	PUNCT
ejpam-811	2	24	theory	theory	NOUN
ejpam-811	2	25	and	and	CCONJ
ejpam-811	2	26	applications	application	NOUN
ejpam-811	2	27	dedicated	dedicate	VERB
ejpam-811	2	28	to	to	ADP
ejpam-811	2	29	professor	professor	PROPN
ejpam-811	2	30	hari	hari	PROPN
ejpam-811	2	31	m.	m.	PROPN
ejpam-811	2	32	srivastava	srivastava	PROPN
ejpam-811	2	33	,	,	PUNCT
ejpam-811	2	34	on	on	ADP
ejpam-811	2	35	the	the	DET
ejpam-811	2	36	occasion	occasion	NOUN
ejpam-811	2	37	of	of	ADP
ejpam-811	2	38	his	his	PRON
ejpam-811	2	39	70th	70th	ADJ
ejpam-811	2	40	birthday	birthday	NOUN
ejpam-811	2	41	complex	complex	ADJ
ejpam-811	2	42	analysis	analysis	NOUN
ejpam-811	2	43	methods	method	NOUN
ejpam-811	2	44	related	relate	VERB
ejpam-811	2	45	an	an	DET
ejpam-811	2	46	optimization	optimization	NOUN
ejpam-811	2	47	problem	problem	NOUN
ejpam-811	2	48	with	with	ADP
ejpam-811	2	49	complex	complex	ADJ
ejpam-811	2	50	variables	variable	NOUN
ejpam-811	2	51	hang	hang	PROPN
ejpam-811	2	52	-	-	PUNCT
ejpam-811	2	53	chin	chin	NOUN
ejpam-811	2	54	lai	lai	PROPN
ejpam-811	2	55	1,∗	1,∗	PROPN
ejpam-811	2	56	,	,	PUNCT
ejpam-811	2	57	tone	tone	NOUN
ejpam-811	2	58	-	-	PUNCT
ejpam-811	2	59	yau	yau	PROPN
ejpam-811	2	60	huang	huang	PROPN
ejpam-811	2	61	2	2	NUM
ejpam-811	2	62	1	1	NUM
ejpam-811	2	63	department	department	NOUN
ejpam-811	2	64	of	of	ADP
ejpam-811	2	65	applied	apply	VERB
ejpam-811	2	66	mathematics	mathematic	NOUN
ejpam-811	2	67	,	,	PUNCT
ejpam-811	2	68	chung	chung	PROPN
ejpam-811	2	69	yuan	yuan	PROPN
ejpam-811	2	70	christian	christian	PROPN
ejpam-811	2	71	university	university	PROPN
ejpam-811	2	72	,	,	PUNCT
ejpam-811	2	73	taiwan	taiwan	PROPN
ejpam-811	2	74	2	2	NUM
ejpam-811	2	75	niigata	niigata	PROPN
ejpam-811	2	76	university	university	PROPN
ejpam-811	2	77	,	,	PUNCT
ejpam-811	2	78	japan	japan	PROPN
ejpam-811	2	79	abstract	abstract	PROPN
ejpam-811	2	80	.	.	PUNCT
ejpam-811	3	1	in	in	ADP
ejpam-811	3	2	this	this	DET
ejpam-811	3	3	paper	paper	NOUN
ejpam-811	3	4	,	,	PUNCT
ejpam-811	3	5	we	we	PRON
ejpam-811	3	6	consider	consider	VERB
ejpam-811	3	7	a	a	DET
ejpam-811	3	8	nondifferentiable	nondifferentiable	ADJ
ejpam-811	3	9	minimax	minimax	NOUN
ejpam-811	3	10	fractional	fractional	ADJ
ejpam-811	3	11	programming	programming	NOUN
ejpam-811	3	12	problem	problem	NOUN
ejpam-811	3	13	treated	treat	VERB
ejpam-811	3	14	with	with	ADP
ejpam-811	3	15	complex	complex	ADJ
ejpam-811	3	16	variables	variable	NOUN
ejpam-811	3	17	.	.	PUNCT
ejpam-811	4	1	duality	duality	NOUN
ejpam-811	4	2	problem	problem	NOUN
ejpam-811	4	3	in	in	ADP
ejpam-811	4	4	optimization	optimization	NOUN
ejpam-811	4	5	theory	theory	NOUN
ejpam-811	4	6	plays	play	VERB
ejpam-811	4	7	an	an	DET
ejpam-811	4	8	important	important	ADJ
ejpam-811	4	9	role	role	NOUN
ejpam-811	4	10	.	.	PUNCT
ejpam-811	5	1	the	the	DET
ejpam-811	5	2	goal	goal	NOUN
ejpam-811	5	3	of	of	ADP
ejpam-811	5	4	this	this	DET
ejpam-811	5	5	paper	paper	NOUN
ejpam-811	5	6	is	be	AUX
ejpam-811	5	7	to	to	PART
ejpam-811	5	8	formulate	formulate	VERB
ejpam-811	5	9	the	the	DET
ejpam-811	5	10	wolfe	wolfe	PROPN
ejpam-811	5	11	type	type	NOUN
ejpam-811	5	12	dual	dual	ADJ
ejpam-811	5	13	and	and	CCONJ
ejpam-811	5	14	mond	mond	NOUN
ejpam-811	5	15	-	-	PUNCT
ejpam-811	5	16	weir	weir	PROPN
ejpam-811	5	17	type	type	NOUN
ejpam-811	5	18	dual	dual	ADJ
ejpam-811	5	19	problems	problem	NOUN
ejpam-811	5	20	.	.	PUNCT
ejpam-811	6	1	we	we	PRON
ejpam-811	6	2	aim	aim	VERB
ejpam-811	6	3	to	to	PART
ejpam-811	6	4	establish	establish	VERB
ejpam-811	6	5	the	the	DET
ejpam-811	6	6	duality	duality	NOUN
ejpam-811	6	7	problems	problem	NOUN
ejpam-811	6	8	,	,	PUNCT
ejpam-811	6	9	and	and	CCONJ
ejpam-811	6	10	prove	prove	VERB
ejpam-811	6	11	that	that	SCONJ
ejpam-811	6	12	the	the	DET
ejpam-811	6	13	duality	duality	NOUN
ejpam-811	6	14	theorems	theorem	NOUN
ejpam-811	6	15	have	have	VERB
ejpam-811	6	16	no	no	DET
ejpam-811	6	17	duality	duality	NOUN
ejpam-811	6	18	gap	gap	NOUN
ejpam-811	6	19	to	to	ADP
ejpam-811	6	20	the	the	DET
ejpam-811	6	21	primal	primal	ADJ
ejpam-811	6	22	problem	problem	NOUN
ejpam-811	6	23	under	under	ADP
ejpam-811	6	24	some	some	DET
ejpam-811	6	25	assumptions	assumption	NOUN
ejpam-811	6	26	.	.	PUNCT
ejpam-811	7	1	the	the	DET
ejpam-811	7	2	processes	process	NOUN
ejpam-811	7	3	involves	involve	VERB
ejpam-811	7	4	to	to	PART
ejpam-811	7	5	show	show	VERB
ejpam-811	7	6	three	three	NUM
ejpam-811	7	7	theorems	theorem	NOUN
ejpam-811	7	8	:	:	PUNCT
ejpam-811	7	9	the	the	DET
ejpam-811	7	10	weak	weak	ADJ
ejpam-811	7	11	,	,	PUNCT
ejpam-811	7	12	strong	strong	ADJ
ejpam-811	7	13	and	and	CCONJ
ejpam-811	7	14	strictly	strictly	ADV
ejpam-811	7	15	converse	converse	NOUN
ejpam-811	7	16	duality	duality	NOUN
ejpam-811	7	17	theorem	theorem	VERB
ejpam-811	7	18	.	.	PROPN
ejpam-811	7	19	2000	2000	NUM
ejpam-811	7	20	mathematics	mathematic	NOUN
ejpam-811	7	21	subject	subject	NOUN
ejpam-811	7	22	classifications	classification	NOUN
ejpam-811	7	23	:	:	PUNCT
ejpam-811	7	24	26a51	26a51	NUM
ejpam-811	7	25	,	,	PUNCT
ejpam-811	7	26	32c15	32c15	NUM
ejpam-811	7	27	,	,	PUNCT
ejpam-811	7	28	90c32	90c32	NUM
ejpam-811	7	29	,	,	PUNCT
ejpam-811	7	30	90c46	90c46	NUM
ejpam-811	7	31	key	key	ADJ
ejpam-811	7	32	words	word	NOUN
ejpam-811	7	33	and	and	CCONJ
ejpam-811	7	34	phrases	phrase	NOUN
ejpam-811	7	35	:	:	PUNCT
ejpam-811	7	36	complex	complex	ADJ
ejpam-811	7	37	minimax	minimax	NOUN
ejpam-811	7	38	fractional	fractional	ADJ
ejpam-811	7	39	programming	programming	NOUN
ejpam-811	7	40	,	,	PUNCT
ejpam-811	7	41	generalized	generalized	ADJ
ejpam-811	7	42	convexity	convexity	NOUN
ejpam-811	7	43	,	,	PUNCT
ejpam-811	7	44	duality	duality	NOUN
ejpam-811	7	45	problems	problem	NOUN
ejpam-811	7	46	1	1	NUM
ejpam-811	7	47	.	.	PUNCT
ejpam-811	7	48	introduction	introduction	NOUN
ejpam-811	7	49	complex	complex	ADJ
ejpam-811	7	50	programming	programming	NOUN
ejpam-811	7	51	problem	problem	NOUN
ejpam-811	7	52	was	be	AUX
ejpam-811	7	53	studied	study	VERB
ejpam-811	7	54	first	first	ADV
ejpam-811	7	55	by	by	ADP
ejpam-811	7	56	levinson	levinson	PROPN
ejpam-811	8	1	[	[	X
ejpam-811	8	2	10	10	NUM
ejpam-811	8	3	]	]	X
ejpam-811	8	4	(	(	PUNCT
ejpam-811	8	5	in	in	ADP
ejpam-811	8	6	1966	1966	NUM
ejpam-811	8	7	)	)	PUNCT
ejpam-811	8	8	who	who	PRON
ejpam-811	8	9	considered	consider	VERB
ejpam-811	8	10	the	the	DET
ejpam-811	8	11	linear	linear	ADJ
ejpam-811	8	12	programming	programming	NOUN
ejpam-811	8	13	in	in	ADP
ejpam-811	8	14	complex	complex	ADJ
ejpam-811	8	15	space	space	NOUN
ejpam-811	8	16	.	.	PUNCT
ejpam-811	9	1	short	short	ADJ
ejpam-811	9	2	later	later	PROPN
ejpam-811	9	3	swarup	swarup	PROPN
ejpam-811	9	4	and	and	CCONJ
ejpam-811	9	5	sharma	sharma	PROPN
ejpam-811	10	1	[	[	X
ejpam-811	10	2	14	14	NUM
ejpam-811	10	3	]	]	PUNCT
ejpam-811	10	4	studied	study	VERB
ejpam-811	10	5	linear	linear	ADJ
ejpam-811	10	6	fractional	fractional	ADJ
ejpam-811	10	7	programming	programming	NOUN
ejpam-811	10	8	in	in	ADP
ejpam-811	10	9	complex	complex	ADJ
ejpam-811	10	10	space	space	NOUN
ejpam-811	10	11	.	.	PUNCT
ejpam-811	11	1	hence	hence	ADV
ejpam-811	11	2	after	after	SCONJ
ejpam-811	11	3	complex	complex	ADJ
ejpam-811	11	4	fractional	fractional	ADJ
ejpam-811	11	5	programming	programming	NOUN
ejpam-811	11	6	problems	problem	NOUN
ejpam-811	11	7	in	in	ADP
ejpam-811	11	8	the	the	DET
ejpam-811	11	9	linear	linear	NOUN
ejpam-811	11	10	and	and	CCONJ
ejpam-811	11	11	the	the	DET
ejpam-811	11	12	nonlinear	nonlinear	ADJ
ejpam-811	11	13	cases	case	NOUN
ejpam-811	11	14	were	be	AUX
ejpam-811	11	15	treated	treat	VERB
ejpam-811	11	16	by	by	ADP
ejpam-811	11	17	numerous	numerous	ADJ
ejpam-811	11	18	authors	author	NOUN
ejpam-811	11	19	(	(	PUNCT
ejpam-811	11	20	e.g.	e.g.	ADV
ejpam-811	11	21	lai	lai	PROPN
ejpam-811	11	22	et	et	PROPN
ejpam-811	11	23	al	al	PROPN
ejpam-811	11	24	.	.	PUNCT
ejpam-811	12	1	[	[	X
ejpam-811	12	2	3	3	NUM
ejpam-811	12	3	-	-	SYM
ejpam-811	12	4	9	9	NUM
ejpam-811	12	5	]	]	PUNCT
ejpam-811	12	6	,	,	PUNCT
ejpam-811	12	7	parkash	parkash	PROPN
ejpam-811	12	8	et	et	NOUN
ejpam-811	12	9	al	al	PROPN
ejpam-811	12	10	.	.	PUNCT
ejpam-811	13	1	[	[	X
ejpam-811	13	2	13	13	NUM
ejpam-811	13	3	]	]	PUNCT
ejpam-811	13	4	,	,	PUNCT
ejpam-811	13	5	ferrero	ferrero	X
ejpam-811	14	1	[	[	X
ejpam-811	14	2	1	1	NUM
ejpam-811	14	3	]	]	PUNCT
ejpam-811	14	4	and	and	CCONJ
ejpam-811	14	5	references	reference	NOUN
ejpam-811	14	6	therein	therein	ADV
ejpam-811	14	7	)	)	PUNCT
ejpam-811	14	8	.	.	PUNCT
ejpam-811	15	1	in	in	ADP
ejpam-811	15	2	applications	application	NOUN
ejpam-811	15	3	,	,	PUNCT
ejpam-811	15	4	many	many	ADJ
ejpam-811	15	5	practical	practical	ADJ
ejpam-811	15	6	problems	problem	NOUN
ejpam-811	15	7	related	relate	VERB
ejpam-811	15	8	to	to	ADP
ejpam-811	15	9	complex	complex	ADJ
ejpam-811	15	10	variables	variable	NOUN
ejpam-811	15	11	,	,	PUNCT
ejpam-811	15	12	for	for	ADP
ejpam-811	15	13	instance	instance	NOUN
ejpam-811	15	14	,	,	PUNCT
ejpam-811	15	15	in	in	ADP
ejpam-811	15	16	electrical	electrical	ADJ
ejpam-811	15	17	engineering	engineering	NOUN
ejpam-811	15	18	,	,	PUNCT
ejpam-811	15	19	filter	filter	NOUN
ejpam-811	15	20	∗corresponding	∗corresponde	VERB
ejpam-811	15	21	author	author	NOUN
ejpam-811	15	22	.	.	PUNCT
ejpam-811	16	1	email	email	NOUN
ejpam-811	16	2	addresses	address	NOUN
ejpam-811	16	3	:	:	PUNCT
ejpam-811	16	4	h	h	PROPN
ejpam-811	16	5	lai	lai	PROPN
ejpam-811	16	6	�	�	PROPN
ejpam-811	16	7	mx	mx	PROPN
ejpam-811	16	8	.	.	PUNCT
ejpam-811	17	1	y	y	PROPN
ejpam-811	17	2	u.edu.tw	u.edu.tw	PROPN
ejpam-811	17	3	(	(	PUNCT
ejpam-811	17	4	h.	h.	PROPN
ejpam-811	17	5	lai	lai	PROPN
ejpam-811	17	6	)	)	PUNCT
ejpam-811	17	7	,	,	PUNCT
ejpam-811	17	8	toneyau	toneyau	PROPN
ejpam-811	17	9	�	�	PROPN
ejpam-811	17	10	yahoo	yahoo	PROPN
ejpam-811	17	11	.	.	PUNCT
ejpam-811	17	12	om.tw	om.tw	PROPN
ejpam-811	17	13	&	&	CCONJ
ejpam-811	17	14	huangty	huangty	PROPN
ejpam-811	17	15	�	�	PROPN
ejpam-811	17	16	m.s	m.s	PROPN
ejpam-811	17	17	.niigata	.niigata	PROPN
ejpam-811	17	18	-	-	PUNCT
ejpam-811	17	19	u.a	u.a	PROPN
ejpam-811	17	20	.jp	.jp	PUNCT
ejpam-811	17	21	(	(	PUNCT
ejpam-811	17	22	t.	t.	PROPN
ejpam-811	17	23	huang	huang	PROPN
ejpam-811	17	24	)	)	PUNCT
ejpam-811	17	25	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-811	18	1	989	989	NUM
ejpam-811	19	1	c	c	X
ejpam-811	19	2	©	©	PROPN
ejpam-811	19	3	2010	2010	NUM
ejpam-811	19	4	ejpam	ejpam	NOUN
ejpam-811	19	5	all	all	DET
ejpam-811	19	6	rights	right	NOUN
ejpam-811	19	7	reserved	reserve	VERB
ejpam-811	19	8	.	.	PUNCT
ejpam-811	20	1	h.	h.	PROPN
ejpam-811	20	2	lai	lai	PROPN
ejpam-811	20	3	,	,	PUNCT
ejpam-811	20	4	t.	t.	PROPN
ejpam-811	20	5	huang	huang	PROPN
ejpam-811	20	6	/	/	SYM
ejpam-811	20	7	eur	eur	PROPN
ejpam-811	20	8	.	.	PUNCT
ejpam-811	21	1	j.	j.	PROPN
ejpam-811	21	2	pure	pure	PROPN
ejpam-811	21	3	appl	appl	PROPN
ejpam-811	21	4	.	.	PROPN
ejpam-811	21	5	math	math	PROPN
ejpam-811	21	6	,	,	PUNCT
ejpam-811	21	7	3	3	NUM
ejpam-811	21	8	(	(	PUNCT
ejpam-811	21	9	2010	2010	NUM
ejpam-811	21	10	)	)	PUNCT
ejpam-811	21	11	,	,	PUNCT
ejpam-811	21	12	989	989	NUM
ejpam-811	21	13	-	-	SYM
ejpam-811	21	14	1005	1005	NUM
ejpam-811	21	15	990	990	NUM
ejpam-811	21	16	theory	theory	NOUN
ejpam-811	21	17	,	,	PUNCT
ejpam-811	21	18	statistical	statistical	ADJ
ejpam-811	21	19	signal	signal	NOUN
ejpam-811	21	20	processing	processing	NOUN
ejpam-811	21	21	,	,	PUNCT
ejpam-811	21	22	etc	etc	X
ejpam-811	21	23	.	.	X
ejpam-811	21	24	for	for	ADP
ejpam-811	21	25	a	a	DET
ejpam-811	21	26	complex	complex	ADJ
ejpam-811	21	27	fractional	fractional	ADJ
ejpam-811	21	28	programming	programming	NOUN
ejpam-811	21	29	[	[	X
ejpam-811	21	30	cf	cf	NOUN
ejpam-811	21	31	.	.	PUNCT
ejpam-811	22	1	lai	lai	PROPN
ejpam-811	22	2	et	et	PROPN
ejpam-811	22	3	al	al	PROPN
ejpam-811	22	4	.	.	PROPN
ejpam-811	22	5	7	7	NUM
ejpam-811	22	6	]	]	PUNCT
ejpam-811	22	7	,	,	PUNCT
ejpam-811	22	8	one	one	PRON
ejpam-811	22	9	may	may	AUX
ejpam-811	22	10	maximize	maximize	VERB
ejpam-811	22	11	the	the	DET
ejpam-811	22	12	equalizer	equalizer	NOUN
ejpam-811	22	13	output	output	NOUN
ejpam-811	22	14	kurtosis	kurtosis	NOUN
ejpam-811	22	15	as	as	ADP
ejpam-811	22	16	k(z	k(z	PROPN
ejpam-811	22	17	)	)	PUNCT
ejpam-811	23	1	=	=	SYM
ejpam-811	23	2	�	�	PROPN
ejpam-811	23	3	�	�	PROPN
ejpam-811	23	4	�	�	PROPN
ejpam-811	23	5	e(|z|4)−	e(|z|4)−	CCONJ
ejpam-811	23	6	2	2	NUM
ejpam-811	23	7	�	�	PROPN
ejpam-811	23	8	e(|z|2	e(|z|2	PROPN
ejpam-811	23	9	)	)	PUNCT
ejpam-811	23	10	�	�	PROPN
ejpam-811	23	11	2	2	NUM
ejpam-811	23	12	−	−	PROPN
ejpam-811	23	13	|e(z2)|2	|e(z2)|2	PROPN
ejpam-811	23	14	�	�	PROPN
ejpam-811	23	15	�	�	PROPN
ejpam-811	23	16	�	�	PROPN
ejpam-811	23	17	e(|z|2)2	e(|z|2)2	PROPN
ejpam-811	23	18	where	where	SCONJ
ejpam-811	23	19	e	e	X
ejpam-811	23	20	(	(	PUNCT
ejpam-811	23	21	·	·	PUNCT
ejpam-811	23	22	)	)	PUNCT
ejpam-811	23	23	stands	stand	VERB
ejpam-811	23	24	for	for	ADP
ejpam-811	23	25	expectation	expectation	NOUN
ejpam-811	23	26	,	,	PUNCT
ejpam-811	23	27	and	and	CCONJ
ejpam-811	23	28	|z|2	|z|2	NOUN
ejpam-811	23	29	=	=	SYM
ejpam-811	23	30	z	z	X
ejpam-811	23	31	·	·	PUNCT
ejpam-811	23	32	z.	z.	PROPN
ejpam-811	24	1	while	while	SCONJ
ejpam-811	24	2	the	the	DET
ejpam-811	24	3	minimax	minimax	NOUN
ejpam-811	24	4	fractional	fractional	ADJ
ejpam-811	24	5	complex	complex	ADJ
ejpam-811	24	6	variable	variable	ADJ
ejpam-811	24	7	problem	problem	NOUN
ejpam-811	24	8	,	,	PUNCT
ejpam-811	24	9	one	one	PRON
ejpam-811	24	10	can	can	AUX
ejpam-811	24	11	find	find	VERB
ejpam-811	24	12	an	an	DET
ejpam-811	24	13	example	example	NOUN
ejpam-811	24	14	in	in	ADP
ejpam-811	24	15	the	the	DET
ejpam-811	24	16	book	book	NOUN
ejpam-811	24	17	haykin	haykin	NOUN
ejpam-811	24	18	[	[	X
ejpam-811	24	19	2	2	X
ejpam-811	24	20	]	]	PUNCT
ejpam-811	24	21	that	that	PRON
ejpam-811	24	22	is	be	AUX
ejpam-811	24	23	a	a	DET
ejpam-811	24	24	problem	problem	NOUN
ejpam-811	24	25	to	to	PART
ejpam-811	24	26	evaluate	evaluate	VERB
ejpam-811	24	27	the	the	DET
ejpam-811	24	28	eigenvalues	eigenvalue	NOUN
ejpam-811	24	29	λ1	λ1	ADJ
ejpam-811	24	30	,	,	PUNCT
ejpam-811	24	31	.	.	PUNCT
ejpam-811	24	32	.	.	PUNCT
ejpam-811	25	1	.	.	PUNCT
ejpam-811	26	1	,	,	PUNCT
ejpam-811	26	2	λm	λm	X
ejpam-811	26	3	of	of	ADP
ejpam-811	26	4	the	the	DET
ejpam-811	26	5	correlation	correlation	NOUN
ejpam-811	26	6	matrix	matrix	NOUN
ejpam-811	26	7	a	a	PRON
ejpam-811	26	8	as	as	SCONJ
ejpam-811	26	9	follows	follow	VERB
ejpam-811	26	10	λk	λk	ADP
ejpam-811	26	11	=	=	SYM
ejpam-811	26	12	min	min	PROPN
ejpam-811	26	13	dim(s)=k	dim(s)=k	PROPN
ejpam-811	26	14	max	max	PROPN
ejpam-811	26	15	z∈s	z∈s	PROPN
ejpam-811	26	16	zhaz	zhaz	PROPN
ejpam-811	26	17	zhz	zhz	NOUN
ejpam-811	26	18	,	,	PUNCT
ejpam-811	26	19	k	k	PROPN
ejpam-811	26	20	=	=	SYM
ejpam-811	26	21	1	1	NUM
ejpam-811	26	22	,	,	PUNCT
ejpam-811	26	23	.	.	PUNCT
ejpam-811	26	24	.	.	PUNCT
ejpam-811	26	25	.	.	PUNCT
ejpam-811	27	1	,	,	PUNCT
ejpam-811	27	2	m	m	VERB
ejpam-811	27	3	where	where	SCONJ
ejpam-811	27	4	s	s	VERB
ejpam-811	27	5	is	be	AUX
ejpam-811	27	6	a	a	DET
ejpam-811	27	7	subspace	subspace	NOUN
ejpam-811	27	8	of	of	ADP
ejpam-811	27	9	cm	cm	NOUN
ejpam-811	27	10	,	,	PUNCT
ejpam-811	27	11	dim(s	dim(s	PROPN
ejpam-811	27	12	)	)	PUNCT
ejpam-811	27	13	denotes	denote	VERB
ejpam-811	27	14	the	the	DET
ejpam-811	27	15	dimension	dimension	NOUN
ejpam-811	27	16	of	of	ADP
ejpam-811	27	17	subspace	subspace	NOUN
ejpam-811	27	18	s	s	PROPN
ejpam-811	27	19	⊂	⊂	PROPN
ejpam-811	27	20	cm	cm	PROPN
ejpam-811	27	21	,	,	PUNCT
ejpam-811	27	22	and	and	CCONJ
ejpam-811	27	23	the	the	DET
ejpam-811	27	24	maximum	maximum	NOUN
ejpam-811	27	25	is	be	AUX
ejpam-811	27	26	taken	take	VERB
ejpam-811	27	27	the	the	DET
ejpam-811	27	28	nonzero	nonzero	NOUN
ejpam-811	27	29	vector	vector	NOUN
ejpam-811	27	30	z	z	PROPN
ejpam-811	27	31	over	over	ADP
ejpam-811	27	32	the	the	DET
ejpam-811	27	33	subspace	subspace	NOUN
ejpam-811	27	34	s.	s.	PROPN
ejpam-811	27	35	note	note	VERB
ejpam-811	27	36	that	that	SCONJ
ejpam-811	27	37	a	a	PRON
ejpam-811	27	38	in	in	ADP
ejpam-811	27	39	the	the	DET
ejpam-811	27	40	above	above	ADJ
ejpam-811	27	41	expression	expression	NOUN
ejpam-811	27	42	is	be	AUX
ejpam-811	27	43	a	a	DET
ejpam-811	27	44	positive	positive	ADJ
ejpam-811	27	45	semidefinite	semidefinite	NOUN
ejpam-811	27	46	hermitian	hermitian	ADJ
ejpam-811	27	47	matrix	matrix	NOUN
ejpam-811	27	48	.	.	PUNCT
ejpam-811	28	1	in	in	ADP
ejpam-811	28	2	this	this	DET
ejpam-811	28	3	paper	paper	NOUN
ejpam-811	28	4	,	,	PUNCT
ejpam-811	28	5	we	we	PRON
ejpam-811	28	6	would	would	AUX
ejpam-811	28	7	study	study	VERB
ejpam-811	28	8	a	a	DET
ejpam-811	28	9	more	more	ADV
ejpam-811	28	10	general	general	ADJ
ejpam-811	28	11	minimax	minimax	NOUN
ejpam-811	28	12	fractional	fractional	ADJ
ejpam-811	28	13	programming	programming	NOUN
ejpam-811	28	14	problem	problem	NOUN
ejpam-811	28	15	with	with	ADP
ejpam-811	28	16	complex	complex	ADJ
ejpam-811	28	17	variables	variable	NOUN
ejpam-811	28	18	as	as	ADP
ejpam-811	28	19	in	in	ADP
ejpam-811	28	20	lai	lai	PROPN
ejpam-811	28	21	and	and	CCONJ
ejpam-811	28	22	huang	huang	PROPN
ejpam-811	29	1	[	[	X
ejpam-811	29	2	3	3	NUM
ejpam-811	29	3	]	]	PUNCT
ejpam-811	29	4	in	in	ADP
ejpam-811	29	5	which	which	PRON
ejpam-811	29	6	it	it	PRON
ejpam-811	29	7	has	have	AUX
ejpam-811	29	8	established	establish	VERB
ejpam-811	29	9	the	the	DET
ejpam-811	29	10	necessary	necessary	ADJ
ejpam-811	29	11	and	and	CCONJ
ejpam-811	29	12	the	the	DET
ejpam-811	29	13	sufficient	sufficient	ADJ
ejpam-811	29	14	optimality	optimality	NOUN
ejpam-811	29	15	conditions	condition	NOUN
ejpam-811	29	16	.	.	PUNCT
ejpam-811	30	1	it	it	PRON
ejpam-811	30	2	is	be	AUX
ejpam-811	30	3	remarkable	remarkable	ADJ
ejpam-811	30	4	that	that	SCONJ
ejpam-811	30	5	the	the	DET
ejpam-811	30	6	duality	duality	NOUN
ejpam-811	30	7	problem	problem	NOUN
ejpam-811	30	8	is	be	AUX
ejpam-811	30	9	also	also	ADV
ejpam-811	30	10	an	an	DET
ejpam-811	30	11	important	important	ADJ
ejpam-811	30	12	part	part	NOUN
ejpam-811	30	13	in	in	ADP
ejpam-811	30	14	optimization	optimization	NOUN
ejpam-811	30	15	theory	theory	NOUN
ejpam-811	30	16	,	,	PUNCT
ejpam-811	30	17	and	and	CCONJ
ejpam-811	30	18	the	the	DET
ejpam-811	30	19	duality	duality	NOUN
ejpam-811	30	20	models	model	NOUN
ejpam-811	30	21	are	be	AUX
ejpam-811	30	22	based	base	VERB
ejpam-811	30	23	on	on	ADP
ejpam-811	30	24	the	the	DET
ejpam-811	30	25	sufficient	sufficient	ADJ
ejpam-811	30	26	optimality	optimality	NOUN
ejpam-811	30	27	conditions	condition	NOUN
ejpam-811	30	28	established	establish	VERB
ejpam-811	30	29	in	in	ADP
ejpam-811	30	30	[	[	X
ejpam-811	30	31	3	3	NUM
ejpam-811	30	32	]	]	PUNCT
ejpam-811	30	33	,	,	PUNCT
ejpam-811	30	34	thus	thus	ADV
ejpam-811	30	35	if	if	SCONJ
ejpam-811	30	36	once	once	SCONJ
ejpam-811	30	37	we	we	PRON
ejpam-811	30	38	have	have	VERB
ejpam-811	30	39	the	the	DET
ejpam-811	30	40	optimality	optimality	NOUN
ejpam-811	30	41	conditions	condition	NOUN
ejpam-811	30	42	,	,	PUNCT
ejpam-811	30	43	it	it	PRON
ejpam-811	30	44	is	be	AUX
ejpam-811	30	45	naturally	naturally	ADV
ejpam-811	30	46	to	to	PART
ejpam-811	30	47	investigate	investigate	VERB
ejpam-811	30	48	the	the	DET
ejpam-811	30	49	duality	duality	NOUN
ejpam-811	30	50	models	model	NOUN
ejpam-811	30	51	,	,	PUNCT
ejpam-811	30	52	and	and	CCONJ
ejpam-811	30	53	proves	prove	VERB
ejpam-811	30	54	its	its	PRON
ejpam-811	30	55	duality	duality	NOUN
ejpam-811	30	56	theorems	theorem	NOUN
ejpam-811	30	57	with	with	ADP
ejpam-811	30	58	nonduality	nonduality	NOUN
ejpam-811	30	59	gap	gap	NOUN
ejpam-811	30	60	between	between	ADP
ejpam-811	30	61	the	the	DET
ejpam-811	30	62	dual	dual	ADJ
ejpam-811	30	63	problem	problem	NOUN
ejpam-811	30	64	and	and	CCONJ
ejpam-811	30	65	its	its	PRON
ejpam-811	30	66	primary	primary	ADJ
ejpam-811	30	67	problem	problem	NOUN
ejpam-811	30	68	.	.	PUNCT
ejpam-811	31	1	caused	cause	VERB
ejpam-811	31	2	by	by	ADP
ejpam-811	31	3	the	the	DET
ejpam-811	31	4	above	above	ADJ
ejpam-811	31	5	reasons	reason	NOUN
ejpam-811	31	6	,	,	PUNCT
ejpam-811	31	7	in	in	ADP
ejpam-811	31	8	this	this	DET
ejpam-811	31	9	paper	paper	NOUN
ejpam-811	31	10	we	we	PRON
ejpam-811	31	11	will	will	AUX
ejpam-811	31	12	constitute	constitute	VERB
ejpam-811	31	13	two	two	NUM
ejpam-811	31	14	duality	duality	NOUN
ejpam-811	31	15	models	model	NOUN
ejpam-811	31	16	:	:	PUNCT
ejpam-811	32	1	the	the	DET
ejpam-811	32	2	wolfe	wolfe	PROPN
ejpam-811	32	3	type	type	NOUN
ejpam-811	32	4	[	[	X
ejpam-811	32	5	cf	cf	NOUN
ejpam-811	32	6	.	.	NOUN
ejpam-811	32	7	15	15	NUM
ejpam-811	32	8	]	]	PUNCT
ejpam-811	32	9	and	and	CCONJ
ejpam-811	32	10	the	the	DET
ejpam-811	32	11	mond	mond	PROPN
ejpam-811	32	12	-	-	PUNCT
ejpam-811	32	13	weir	weir	PROPN
ejpam-811	32	14	type	type	NOUN
ejpam-811	32	15	dual	dual	ADJ
ejpam-811	32	16	[	[	X
ejpam-811	32	17	cf	cf	NOUN
ejpam-811	32	18	.	.	PUNCT
ejpam-811	33	1	mond	mond	PROPN
ejpam-811	33	2	-	-	PUNCT
ejpam-811	33	3	weir	weir	PROPN
ejpam-811	33	4	12	12	NUM
ejpam-811	33	5	]	]	PUNCT
ejpam-811	33	6	,	,	PUNCT
ejpam-811	34	1	and	and	CCONJ
ejpam-811	34	2	prove	prove	VERB
ejpam-811	34	3	three	three	NUM
ejpam-811	34	4	theorems	theorem	NOUN
ejpam-811	34	5	:	:	PUNCT
ejpam-811	34	6	weak	weak	ADJ
ejpam-811	34	7	,	,	PUNCT
ejpam-811	34	8	strong	strong	ADJ
ejpam-811	34	9	and	and	CCONJ
ejpam-811	34	10	strict	strict	ADJ
ejpam-811	34	11	converse	converse	NOUN
ejpam-811	34	12	duality	duality	NOUN
ejpam-811	34	13	theorem	theorem	VERB
ejpam-811	34	14	with	with	ADP
ejpam-811	34	15	respect	respect	NOUN
ejpam-811	34	16	to	to	ADP
ejpam-811	34	17	the	the	DET
ejpam-811	34	18	given	give	VERB
ejpam-811	34	19	primal	primal	ADJ
ejpam-811	34	20	problem	problem	NOUN
ejpam-811	34	21	with	with	ADP
ejpam-811	34	22	zero	zero	NUM
ejpam-811	34	23	duality	duality	NOUN
ejpam-811	34	24	gap	gap	NOUN
ejpam-811	34	25	in	in	ADP
ejpam-811	34	26	the	the	DET
ejpam-811	34	27	duality	duality	NOUN
ejpam-811	34	28	theorems	theorem	NOUN
ejpam-811	34	29	.	.	PUNCT
ejpam-811	35	1	2	2	X
ejpam-811	35	2	.	.	X
ejpam-811	35	3	minimax	minimax	NOUN
ejpam-811	35	4	fractional	fractional	ADJ
ejpam-811	35	5	programming	programming	NOUN
ejpam-811	35	6	problem	problem	NOUN
ejpam-811	35	7	with	with	ADP
ejpam-811	35	8	complex	complex	ADJ
ejpam-811	35	9	variables	variable	NOUN
ejpam-811	35	10	in	in	ADP
ejpam-811	35	11	this	this	DET
ejpam-811	35	12	paper	paper	NOUN
ejpam-811	35	13	,	,	PUNCT
ejpam-811	35	14	we	we	PRON
ejpam-811	35	15	consider	consider	VERB
ejpam-811	35	16	the	the	DET
ejpam-811	35	17	following	follow	VERB
ejpam-811	35	18	minimax	minimax	NOUN
ejpam-811	35	19	fractional	fractional	ADJ
ejpam-811	35	20	complex	complex	ADJ
ejpam-811	35	21	programming	programming	NOUN
ejpam-811	35	22	problem	problem	NOUN
ejpam-811	35	23	[	[	X
ejpam-811	35	24	see	see	VERB
ejpam-811	35	25	lai	lai	PROPN
ejpam-811	35	26	et	et	PROPN
ejpam-811	35	27	al	al	PROPN
ejpam-811	35	28	.	.	PROPN
ejpam-811	36	1	3	3	NUM
ejpam-811	36	2	]	]	PUNCT
ejpam-811	36	3	as	as	ADP
ejpam-811	36	4	the	the	DET
ejpam-811	36	5	following	following	NOUN
ejpam-811	36	6	:	:	PUNCT
ejpam-811	36	7	(	(	PUNCT
ejpam-811	36	8	p	p	X
ejpam-811	36	9	)	)	PUNCT
ejpam-811	36	10	minζ∈x	minζ∈x	PROPN
ejpam-811	36	11	maxη∈y	maxη∈y	NOUN
ejpam-811	36	12	re	re	ADP
ejpam-811	36	13	[	[	PUNCT
ejpam-811	36	14	f	f	X
ejpam-811	36	15	(	(	PUNCT
ejpam-811	36	16	ζ	ζ	NOUN
ejpam-811	36	17	,	,	PUNCT
ejpam-811	36	18	η)+(zh	η)+(zh	NOUN
ejpam-811	36	19	az)1/2	az)1/2	VERB
ejpam-811	36	20	]	]	PUNCT
ejpam-811	36	21	re	re	ADP
ejpam-811	36	22	[	[	X
ejpam-811	37	1	g(ζ	g(ζ	PROPN
ejpam-811	37	2	,	,	PUNCT
ejpam-811	37	3	η)−(zh	η)−(zh	X
ejpam-811	37	4	bz)1/2	bz)1/2	PROPN
ejpam-811	37	5	]	]	PUNCT
ejpam-811	37	6	s.t	s.t	PROPN
ejpam-811	37	7	.	.	PROPN
ejpam-811	37	8	x	x	X
ejpam-811	38	1	=	=	PUNCT
ejpam-811	38	2	�	�	PROPN
ejpam-811	38	3	ζ	ζ	NOUN
ejpam-811	38	4	=	=	SYM
ejpam-811	38	5	(	(	PUNCT
ejpam-811	38	6	z	z	NOUN
ejpam-811	38	7	,	,	PUNCT
ejpam-811	38	8	z	z	NOUN
ejpam-811	38	9	)	)	PUNCT
ejpam-811	38	10	∈	∈	PROPN
ejpam-811	38	11	c2n	c2n	NOUN
ejpam-811	38	12	|	|	ADV
ejpam-811	38	13	−	−	PROPN
ejpam-811	38	14	h(ζ	h(ζ	NOUN
ejpam-811	38	15	)	)	PUNCT
ejpam-811	38	16	∈	∈	PROPN
ejpam-811	38	17	s	s	PART
ejpam-811	38	18	⊂	⊂	NOUN
ejpam-811	38	19	c2n	c2n	NOUN
ejpam-811	38	20	where	where	SCONJ
ejpam-811	38	21	y	y	PROPN
ejpam-811	38	22	is	be	AUX
ejpam-811	38	23	a	a	DET
ejpam-811	38	24	compact	compact	ADJ
ejpam-811	38	25	subset	subset	NOUN
ejpam-811	38	26	of	of	ADP
ejpam-811	38	27	{	{	PUNCT
ejpam-811	38	28	η	η	PROPN
ejpam-811	38	29	=	=	PROPN
ejpam-811	38	30	(	(	PUNCT
ejpam-811	38	31	w	w	PROPN
ejpam-811	38	32	,	,	PUNCT
ejpam-811	38	33	w	w	NOUN
ejpam-811	38	34	)	)	PUNCT
ejpam-811	38	35	|	|	ADV
ejpam-811	38	36	w	w	PROPN
ejpam-811	38	37	∈	∈	PROPN
ejpam-811	38	38	cm	cm	NOUN
ejpam-811	38	39	}	}	PUNCT
ejpam-811	38	40	⊂	⊂	PROPN
ejpam-811	38	41	c2	c2	PROPN
ejpam-811	38	42	m	m	PROPN
ejpam-811	38	43	;	;	PUNCT
ejpam-811	38	44	a	a	DET
ejpam-811	38	45	and	and	CCONJ
ejpam-811	38	46	b	b	NOUN
ejpam-811	38	47	∈	∈	PROPN
ejpam-811	38	48	cn×n	cn×n	NOUN
ejpam-811	38	49	are	be	AUX
ejpam-811	38	50	positive	positive	ADJ
ejpam-811	38	51	semidefinite	semidefinite	NOUN
ejpam-811	38	52	hermitian	hermitian	ADJ
ejpam-811	38	53	matrices	matrix	NOUN
ejpam-811	38	54	;	;	PUNCT
ejpam-811	38	55	s	s	VERB
ejpam-811	38	56	is	be	AUX
ejpam-811	38	57	a	a	DET
ejpam-811	38	58	polyhedral	polyhedral	ADJ
ejpam-811	38	59	cone	cone	NOUN
ejpam-811	38	60	in	in	ADP
ejpam-811	38	61	cp	cp	PROPN
ejpam-811	38	62	;	;	PUNCT
ejpam-811	38	63	f	f	PROPN
ejpam-811	38	64	(	(	PUNCT
ejpam-811	38	65	·	·	PUNCT
ejpam-811	38	66	,	,	PUNCT
ejpam-811	38	67	·	·	PUNCT
ejpam-811	38	68	)	)	PUNCT
ejpam-811	38	69	and	and	CCONJ
ejpam-811	38	70	g	g	PROPN
ejpam-811	38	71	(	(	PUNCT
ejpam-811	38	72	·	·	PUNCT
ejpam-811	38	73	,	,	PUNCT
ejpam-811	38	74	·	·	PUNCT
ejpam-811	38	75	)	)	PUNCT
ejpam-811	38	76	are	be	AUX
ejpam-811	38	77	continuous	continuous	ADJ
ejpam-811	38	78	functions	function	NOUN
ejpam-811	38	79	,	,	PUNCT
ejpam-811	38	80	and	and	CCONJ
ejpam-811	38	81	for	for	ADP
ejpam-811	38	82	each	each	DET
ejpam-811	38	83	η	η	PROPN
ejpam-811	38	84	∈	∈	PROPN
ejpam-811	38	85	y	y	PROPN
ejpam-811	38	86	,	,	PUNCT
ejpam-811	38	87	f	f	PROPN
ejpam-811	38	88	(	(	PUNCT
ejpam-811	38	89	·	·	PUNCT
ejpam-811	38	90	,	,	PUNCT
ejpam-811	38	91	η	η	NOUN
ejpam-811	38	92	)	)	PUNCT
ejpam-811	38	93	and	and	CCONJ
ejpam-811	38	94	g(·,η	g(·,η	NOUN
ejpam-811	38	95	)	)	PUNCT
ejpam-811	38	96	:	:	PUNCT
ejpam-811	38	97	c2n	c2n	NOUN
ejpam-811	38	98	→	→	SYM
ejpam-811	38	99	c	c	NOUN
ejpam-811	38	100	are	be	AUX
ejpam-811	38	101	analytic	analytic	ADJ
ejpam-811	38	102	,	,	PUNCT
ejpam-811	38	103	we	we	PRON
ejpam-811	38	104	assume	assume	VERB
ejpam-811	38	105	further	far	ADV
ejpam-811	38	106	that	that	SCONJ
ejpam-811	38	107	h	h	NOUN
ejpam-811	38	108	(	(	PUNCT
ejpam-811	38	109	·	·	PUNCT
ejpam-811	38	110	)	)	PUNCT
ejpam-811	38	111	:	:	PUNCT
ejpam-811	39	1	c2n→	c2n→	NOUN
ejpam-811	39	2	cp	cp	PROPN
ejpam-811	39	3	is	be	AUX
ejpam-811	39	4	an	an	DET
ejpam-811	39	5	analytic	analytic	ADJ
ejpam-811	39	6	map	map	NOUN
ejpam-811	39	7	defined	define	VERB
ejpam-811	39	8	on	on	ADP
ejpam-811	39	9	ζ=	ζ=	NOUN
ejpam-811	39	10	(	(	PUNCT
ejpam-811	39	11	z	z	NOUN
ejpam-811	39	12	,	,	PUNCT
ejpam-811	39	13	z	z	NOUN
ejpam-811	39	14	)	)	PUNCT
ejpam-811	39	15	∈q	∈q	NOUN
ejpam-811	39	16	⊂	⊂	PROPN
ejpam-811	39	17	c2n	c2n	NOUN
ejpam-811	39	18	.	.	PUNCT
ejpam-811	40	1	this	this	PRON
ejpam-811	40	2	set	set	VERB
ejpam-811	40	3	q	q	NOUN
ejpam-811	40	4	=	=	PUNCT
ejpam-811	40	5	{	{	PUNCT
ejpam-811	40	6	(	(	PUNCT
ejpam-811	40	7	z	z	NOUN
ejpam-811	40	8	,	,	PUNCT
ejpam-811	40	9	z	z	NOUN
ejpam-811	40	10	)	)	PUNCT
ejpam-811	40	11	|	|	ADV
ejpam-811	40	12	z	z	NOUN
ejpam-811	40	13	∈	∈	PROPN
ejpam-811	40	14	cn	cn	PROPN
ejpam-811	40	15	}	}	PUNCT
ejpam-811	40	16	is	be	AUX
ejpam-811	40	17	a	a	DET
ejpam-811	40	18	linear	linear	NOUN
ejpam-811	40	19	manifold	manifold	NOUN
ejpam-811	40	20	over	over	ADP
ejpam-811	40	21	real	real	ADJ
ejpam-811	40	22	field	field	NOUN
ejpam-811	40	23	.	.	PUNCT
ejpam-811	41	1	without	without	ADP
ejpam-811	41	2	loss	loss	NOUN
ejpam-811	41	3	of	of	ADP
ejpam-811	41	4	generality	generality	NOUN
ejpam-811	41	5	,	,	PUNCT
ejpam-811	41	6	it	it	PRON
ejpam-811	41	7	is	be	AUX
ejpam-811	41	8	assumed	assume	VERB
ejpam-811	41	9	that	that	SCONJ
ejpam-811	41	10	re	re	ADP
ejpam-811	41	11	[	[	PUNCT
ejpam-811	41	12	f	f	X
ejpam-811	41	13	(	(	PUNCT
ejpam-811	41	14	ζ	ζ	PROPN
ejpam-811	41	15	,	,	PUNCT
ejpam-811	41	16	η	η	NOUN
ejpam-811	41	17	)	)	PUNCT
ejpam-811	41	18	+	+	CCONJ
ejpam-811	41	19	(	(	PUNCT
ejpam-811	41	20	zhaz)1/2	zhaz)1/2	NUM
ejpam-811	41	21	]	]	X
ejpam-811	41	22	≥	≥	X
ejpam-811	41	23	0	0	NUM
ejpam-811	41	24	and	and	CCONJ
ejpam-811	41	25	re	re	ADP
ejpam-811	41	26	[	[	X
ejpam-811	41	27	g(ζ	g(ζ	PROPN
ejpam-811	41	28	,	,	PUNCT
ejpam-811	41	29	η	η	NOUN
ejpam-811	41	30	)	)	PUNCT
ejpam-811	41	31	−	−	PROPN
ejpam-811	41	32	(	(	PUNCT
ejpam-811	41	33	zh	zh	X
ejpam-811	41	34	bz)1/2	bz)1/2	PROPN
ejpam-811	41	35	]	]	PUNCT
ejpam-811	41	36	>	>	X
ejpam-811	41	37	0	0	PUNCT
ejpam-811	41	38	for	for	ADP
ejpam-811	41	39	each	each	PRON
ejpam-811	41	40	(	(	PUNCT
ejpam-811	41	41	ζ	ζ	PROPN
ejpam-811	41	42	,	,	PUNCT
ejpam-811	41	43	η	η	NOUN
ejpam-811	41	44	)	)	PUNCT
ejpam-811	41	45	∈	∈	PROPN
ejpam-811	41	46	x	x	SYM
ejpam-811	41	47	×	×	PROPN
ejpam-811	41	48	y.	y.	NOUN
ejpam-811	41	49	this	this	DET
ejpam-811	41	50	problem	problem	NOUN
ejpam-811	41	51	will	will	AUX
ejpam-811	41	52	be	be	AUX
ejpam-811	41	53	nonsmooth	nonsmooth	ADJ
ejpam-811	41	54	if	if	SCONJ
ejpam-811	41	55	there	there	PRON
ejpam-811	41	56	is	be	VERB
ejpam-811	41	57	a	a	DET
ejpam-811	41	58	point	point	NOUN
ejpam-811	41	59	ζ0	ζ0	NOUN
ejpam-811	41	60	=	=	PUNCT
ejpam-811	41	61	(	(	PUNCT
ejpam-811	41	62	z0	z0	PROPN
ejpam-811	41	63	,	,	PUNCT
ejpam-811	41	64	z0	z0	PROPN
ejpam-811	41	65	)	)	PUNCT
ejpam-811	41	66	such	such	ADJ
ejpam-811	41	67	that	that	SCONJ
ejpam-811	41	68	zh	zh	PROPN
ejpam-811	41	69	0	0	NUM
ejpam-811	41	70	az0	az0	NOUN
ejpam-811	41	71	=	=	NOUN
ejpam-811	41	72	0	0	NUM
ejpam-811	41	73	or	or	CCONJ
ejpam-811	41	74	zh	zh	INTJ
ejpam-811	41	75	0	0	NUM
ejpam-811	41	76	bz0	bz0	ADV
ejpam-811	41	77	=	=	SYM
ejpam-811	41	78	0	0	X
ejpam-811	41	79	.	.	PUNCT
ejpam-811	42	1	h.	h.	PROPN
ejpam-811	42	2	lai	lai	PROPN
ejpam-811	42	3	,	,	PUNCT
ejpam-811	42	4	t.	t.	PROPN
ejpam-811	42	5	huang	huang	PROPN
ejpam-811	42	6	/	/	SYM
ejpam-811	42	7	eur	eur	PROPN
ejpam-811	42	8	.	.	PUNCT
ejpam-811	43	1	j.	j.	PROPN
ejpam-811	43	2	pure	pure	PROPN
ejpam-811	43	3	appl	appl	PROPN
ejpam-811	43	4	.	.	PROPN
ejpam-811	43	5	math	math	PROPN
ejpam-811	43	6	,	,	PUNCT
ejpam-811	43	7	3	3	NUM
ejpam-811	43	8	(	(	PUNCT
ejpam-811	43	9	2010	2010	NUM
ejpam-811	43	10	)	)	PUNCT
ejpam-811	43	11	,	,	PUNCT
ejpam-811	43	12	989	989	NUM
ejpam-811	43	13	-	-	SYM
ejpam-811	43	14	1005	1005	NUM
ejpam-811	43	15	991	991	NUM
ejpam-811	43	16	in	in	ADP
ejpam-811	43	17	complex	complex	ADJ
ejpam-811	43	18	programming	programming	NOUN
ejpam-811	43	19	problem	problem	NOUN
ejpam-811	43	20	,	,	PUNCT
ejpam-811	43	21	the	the	DET
ejpam-811	43	22	analytic	analytic	ADJ
ejpam-811	43	23	function	function	NOUN
ejpam-811	43	24	f	f	PROPN
ejpam-811	43	25	(	(	PUNCT
ejpam-811	43	26	z	z	PROPN
ejpam-811	43	27	,	,	PUNCT
ejpam-811	43	28	z	z	NOUN
ejpam-811	43	29	)	)	PUNCT
ejpam-811	43	30	is	be	AUX
ejpam-811	43	31	defined	define	VERB
ejpam-811	43	32	on	on	ADP
ejpam-811	43	33	the	the	DET
ejpam-811	43	34	set	set	NOUN
ejpam-811	43	35	q	q	NOUN
ejpam-811	43	36	since	since	SCONJ
ejpam-811	43	37	a	a	DET
ejpam-811	43	38	nonlinear	nonlinear	ADJ
ejpam-811	43	39	analytic	analytic	ADJ
ejpam-811	43	40	function	function	NOUN
ejpam-811	43	41	can	can	AUX
ejpam-811	43	42	not	not	PART
ejpam-811	43	43	have	have	VERB
ejpam-811	43	44	a	a	DET
ejpam-811	43	45	convex	convex	ADJ
ejpam-811	43	46	real	real	ADJ
ejpam-811	43	47	part	part	NOUN
ejpam-811	43	48	in	in	ADP
ejpam-811	43	49	our	our	PRON
ejpam-811	43	50	requirement	requirement	NOUN
ejpam-811	44	1	[	[	X
ejpam-811	44	2	cf	cf	NOUN
ejpam-811	44	3	.	.	PUNCT
ejpam-811	45	1	ferrero	ferrero	ADJ
ejpam-811	45	2	1	1	NUM
ejpam-811	45	3	]	]	PUNCT
ejpam-811	45	4	.	.	PUNCT
ejpam-811	46	1	by	by	ADP
ejpam-811	46	2	this	this	DET
ejpam-811	46	3	reason	reason	NOUN
ejpam-811	46	4	in	in	ADP
ejpam-811	46	5	our	our	PRON
ejpam-811	46	6	programming	programming	NOUN
ejpam-811	46	7	problem	problem	NOUN
ejpam-811	46	8	(	(	PUNCT
ejpam-811	46	9	p	p	NOUN
ejpam-811	46	10	)	)	PUNCT
ejpam-811	46	11	,	,	PUNCT
ejpam-811	46	12	the	the	DET
ejpam-811	46	13	complex	complex	ADJ
ejpam-811	46	14	variables	variable	NOUN
ejpam-811	46	15	are	be	AUX
ejpam-811	46	16	taken	take	VERB
ejpam-811	46	17	as	as	ADP
ejpam-811	46	18	the	the	DET
ejpam-811	46	19	form	form	NOUN
ejpam-811	46	20	ζ	ζ	NOUN
ejpam-811	46	21	=	=	SYM
ejpam-811	46	22	(	(	PUNCT
ejpam-811	46	23	z	z	NOUN
ejpam-811	46	24	,	,	PUNCT
ejpam-811	46	25	z	z	NOUN
ejpam-811	46	26	)	)	PUNCT
ejpam-811	46	27	∈	∈	PROPN
ejpam-811	46	28	c2n	c2n	NOUN
ejpam-811	46	29	.	.	PUNCT
ejpam-811	47	1	in	in	ADP
ejpam-811	47	2	order	order	NOUN
ejpam-811	47	3	to	to	PART
ejpam-811	47	4	understand	understand	VERB
ejpam-811	47	5	some	some	DET
ejpam-811	47	6	problems	problem	NOUN
ejpam-811	47	7	studied	study	VERB
ejpam-811	47	8	as	as	ADP
ejpam-811	47	9	before	before	ADV
ejpam-811	47	10	in	in	ADP
ejpam-811	47	11	different	different	ADJ
ejpam-811	47	12	view	view	NOUN
ejpam-811	47	13	points	point	NOUN
ejpam-811	47	14	that	that	PRON
ejpam-811	47	15	are	be	AUX
ejpam-811	47	16	the	the	DET
ejpam-811	47	17	special	special	ADJ
ejpam-811	47	18	cases	case	NOUN
ejpam-811	47	19	of	of	ADP
ejpam-811	47	20	problem	problem	NOUN
ejpam-811	47	21	(	(	PUNCT
ejpam-811	47	22	p	p	NOUN
ejpam-811	47	23	)	)	PUNCT
ejpam-811	47	24	,	,	PUNCT
ejpam-811	47	25	we	we	PRON
ejpam-811	47	26	recall	recall	VERB
ejpam-811	47	27	these	these	DET
ejpam-811	47	28	special	special	ADJ
ejpam-811	47	29	forms	form	NOUN
ejpam-811	47	30	as	as	ADP
ejpam-811	47	31	the	the	DET
ejpam-811	47	32	following	following	NOUN
ejpam-811	47	33	:	:	PUNCT
ejpam-811	47	34	(	(	PUNCT
ejpam-811	47	35	i	i	NOUN
ejpam-811	47	36	)	)	PUNCT
ejpam-811	47	37	in	in	ADP
ejpam-811	47	38	problem	problem	NOUN
ejpam-811	47	39	(	(	PUNCT
ejpam-811	47	40	p	p	NOUN
ejpam-811	47	41	)	)	PUNCT
ejpam-811	47	42	,	,	PUNCT
ejpam-811	47	43	if	if	SCONJ
ejpam-811	47	44	y	y	PROPN
ejpam-811	47	45	vanishes	vanish	VERB
ejpam-811	47	46	and	and	CCONJ
ejpam-811	47	47	rewrite	rewrite	VERB
ejpam-811	47	48	ζ	ζ	NOUN
ejpam-811	47	49	=	=	SYM
ejpam-811	47	50	(	(	PUNCT
ejpam-811	47	51	z	z	NOUN
ejpam-811	47	52	,	,	PUNCT
ejpam-811	47	53	z	z	NOUN
ejpam-811	47	54	)	)	PUNCT
ejpam-811	47	55	,	,	PUNCT
ejpam-811	47	56	then	then	ADV
ejpam-811	47	57	(	(	PUNCT
ejpam-811	47	58	p	p	X
ejpam-811	47	59	)	)	PUNCT
ejpam-811	47	60	is	be	AUX
ejpam-811	47	61	reduced	reduce	VERB
ejpam-811	47	62	to	to	ADP
ejpam-811	47	63	the	the	DET
ejpam-811	47	64	following	follow	VERB
ejpam-811	47	65	minimization	minimization	NOUN
ejpam-811	47	66	problem	problem	NOUN
ejpam-811	48	1	[	[	X
ejpam-811	48	2	cf	cf	X
ejpam-811	48	3	.	.	PUNCT
ejpam-811	49	1	lai	lai	PROPN
ejpam-811	49	2	el	el	PROPN
ejpam-811	49	3	al	al	PROPN
ejpam-811	49	4	.	.	PROPN
ejpam-811	50	1	7	7	NUM
ejpam-811	50	2	]	]	NUM
ejpam-811	50	3	:	:	PUNCT
ejpam-811	50	4	(	(	PUNCT
ejpam-811	50	5	p0	p0	NOUN
ejpam-811	50	6	)	)	PUNCT
ejpam-811	50	7	minζ=(z	minζ=(z	ADV
ejpam-811	50	8	,	,	PUNCT
ejpam-811	50	9	z)∈x	z)∈x	NUM
ejpam-811	50	10	re	re	X
ejpam-811	50	11	[	[	PUNCT
ejpam-811	50	12	f	f	X
ejpam-811	50	13	(	(	PUNCT
ejpam-811	50	14	z	z	NOUN
ejpam-811	50	15	,	,	PUNCT
ejpam-811	50	16	z)+(zh	z)+(zh	NOUN
ejpam-811	50	17	az)1/2	az)1/2	VERB
ejpam-811	50	18	]	]	PUNCT
ejpam-811	50	19	re	re	ADP
ejpam-811	50	20	[	[	X
ejpam-811	50	21	g(z	g(z	ADJ
ejpam-811	50	22	,	,	PUNCT
ejpam-811	50	23	z)−(zh	z)−(zh	NUM
ejpam-811	50	24	bz)1/2	bz)1/2	PROPN
ejpam-811	50	25	]	]	PUNCT
ejpam-811	50	26	.	.	PUNCT
ejpam-811	51	1	(	(	PUNCT
ejpam-811	51	2	ii	ii	NOUN
ejpam-811	51	3	)	)	PUNCT
ejpam-811	51	4	if	if	SCONJ
ejpam-811	51	5	a=	a=	PROPN
ejpam-811	51	6	0	0	NUM
ejpam-811	51	7	and	and	CCONJ
ejpam-811	51	8	b	b	X
ejpam-811	51	9	=	=	SYM
ejpam-811	51	10	0	0	NUM
ejpam-811	51	11	are	be	AUX
ejpam-811	51	12	zero	zero	NUM
ejpam-811	51	13	matrices	matrix	NOUN
ejpam-811	51	14	in	in	ADP
ejpam-811	51	15	problem	problem	NOUN
ejpam-811	51	16	(	(	PUNCT
ejpam-811	51	17	p	p	NOUN
ejpam-811	51	18	)	)	PUNCT
ejpam-811	51	19	,	,	PUNCT
ejpam-811	51	20	then	then	ADV
ejpam-811	51	21	(	(	PUNCT
ejpam-811	51	22	p	p	X
ejpam-811	51	23	)	)	PUNCT
ejpam-811	51	24	is	be	AUX
ejpam-811	51	25	reduced	reduce	VERB
ejpam-811	51	26	to	to	ADP
ejpam-811	51	27	(	(	PUNCT
ejpam-811	51	28	p1	p1	PROPN
ejpam-811	51	29	)	)	PUNCT
ejpam-811	51	30	which	which	PRON
ejpam-811	51	31	was	be	AUX
ejpam-811	51	32	studied	study	VERB
ejpam-811	51	33	by	by	ADP
ejpam-811	51	34	lai	lai	PROPN
ejpam-811	51	35	et	et	PROPN
ejpam-811	51	36	al	al	PROPN
ejpam-811	51	37	.	.	PUNCT
ejpam-811	52	1	[	[	X
ejpam-811	52	2	8	8	NUM
ejpam-811	52	3	]	]	PUNCT
ejpam-811	52	4	.	.	PUNCT
ejpam-811	53	1	(	(	PUNCT
ejpam-811	53	2	p1	p1	NOUN
ejpam-811	53	3	)	)	PUNCT
ejpam-811	53	4	minζ∈x	minζ∈x	PROPN
ejpam-811	53	5	maxη∈y	maxη∈y	NOUN
ejpam-811	53	6	re	re	ADP
ejpam-811	53	7	[	[	PUNCT
ejpam-811	53	8	f	f	X
ejpam-811	53	9	(	(	PUNCT
ejpam-811	53	10	ζ	ζ	PROPN
ejpam-811	53	11	,	,	PUNCT
ejpam-811	53	12	η	η	NOUN
ejpam-811	53	13	)	)	PUNCT
ejpam-811	53	14	]	]	PUNCT
ejpam-811	53	15	re	re	ADP
ejpam-811	53	16	[	[	X
ejpam-811	53	17	g(ζ	g(ζ	PROPN
ejpam-811	53	18	,	,	PUNCT
ejpam-811	53	19	η	η	NOUN
ejpam-811	53	20	)	)	PUNCT
ejpam-811	53	21	]	]	PUNCT
ejpam-811	53	22	subject	subject	NOUN
ejpam-811	53	23	to	to	ADP
ejpam-811	53	24	x	x	SYM
ejpam-811	53	25	=	=	SYM
ejpam-811	53	26	�	�	PROPN
ejpam-811	53	27	ζ=	ζ=	X
ejpam-811	53	28	(	(	PUNCT
ejpam-811	53	29	z	z	NOUN
ejpam-811	53	30	,	,	PUNCT
ejpam-811	53	31	z	z	NOUN
ejpam-811	53	32	)	)	PUNCT
ejpam-811	53	33	∈	∈	PROPN
ejpam-811	53	34	c2n	c2n	NOUN
ejpam-811	53	35	|	|	ADV
ejpam-811	53	36	−	−	PROPN
ejpam-811	53	37	h(ζ	h(ζ	NOUN
ejpam-811	53	38	)	)	PUNCT
ejpam-811	53	39	∈	∈	PROPN
ejpam-811	53	40	s	s	PART
ejpam-811	54	1	⊂	⊂	X
ejpam-811	54	2	cp	cp	INTJ
ejpam-811	54	3	.	.	PUNCT
ejpam-811	55	1	where	where	SCONJ
ejpam-811	55	2	y	y	PROPN
ejpam-811	55	3	is	be	AUX
ejpam-811	55	4	a	a	DET
ejpam-811	55	5	specified	specified	ADJ
ejpam-811	55	6	compact	compact	ADJ
ejpam-811	55	7	subset	subset	NOUN
ejpam-811	55	8	in	in	ADP
ejpam-811	55	9	c2	c2	PROPN
ejpam-811	55	10	m	m	PROPN
ejpam-811	55	11	,	,	PUNCT
ejpam-811	55	12	and	and	CCONJ
ejpam-811	55	13	for	for	ADP
ejpam-811	55	14	each	each	DET
ejpam-811	55	15	η	η	PROPN
ejpam-811	55	16	∈	∈	PROPN
ejpam-811	55	17	y	y	PROPN
ejpam-811	55	18	,	,	PUNCT
ejpam-811	55	19	f	f	PROPN
ejpam-811	55	20	(	(	PUNCT
ejpam-811	55	21	·	·	PUNCT
ejpam-811	55	22	,	,	PUNCT
ejpam-811	55	23	η	η	NOUN
ejpam-811	55	24	)	)	PUNCT
ejpam-811	55	25	and	and	CCONJ
ejpam-811	55	26	g(·,η	g(·,η	NOUN
ejpam-811	55	27	)	)	PUNCT
ejpam-811	55	28	are	be	AUX
ejpam-811	55	29	analytic	analytic	ADJ
ejpam-811	55	30	functions	function	NOUN
ejpam-811	55	31	.	.	PUNCT
ejpam-811	56	1	(	(	PUNCT
ejpam-811	56	2	iii	iii	X
ejpam-811	56	3	)	)	PUNCT
ejpam-811	56	4	if	if	SCONJ
ejpam-811	56	5	b	b	NOUN
ejpam-811	56	6	=	=	SYM
ejpam-811	56	7	0	0	PROPN
ejpam-811	56	8	,	,	PUNCT
ejpam-811	56	9	g	g	NOUN
ejpam-811	56	10	(	(	PUNCT
ejpam-811	56	11	·	·	PUNCT
ejpam-811	56	12	,	,	PUNCT
ejpam-811	56	13	·	·	PUNCT
ejpam-811	56	14	)	)	PUNCT
ejpam-811	56	15	≡	≡	PROPN
ejpam-811	56	16	1	1	NUM
ejpam-811	56	17	,	,	PUNCT
ejpam-811	56	18	then	then	ADV
ejpam-811	56	19	problem	problem	NOUN
ejpam-811	56	20	(	(	PUNCT
ejpam-811	56	21	p	p	X
ejpam-811	56	22	)	)	PUNCT
ejpam-811	56	23	is	be	AUX
ejpam-811	56	24	reduced	reduce	VERB
ejpam-811	56	25	to	to	ADP
ejpam-811	56	26	(	(	PUNCT
ejpam-811	56	27	p2	p2	PROPN
ejpam-811	56	28	)	)	PUNCT
ejpam-811	56	29	which	which	PRON
ejpam-811	56	30	was	be	AUX
ejpam-811	56	31	investigated	investigate	VERB
ejpam-811	56	32	by	by	ADP
ejpam-811	56	33	lai	lai	PROPN
ejpam-811	56	34	et	et	PROPN
ejpam-811	56	35	al	al	PROPN
ejpam-811	56	36	.	.	PUNCT
ejpam-811	57	1	[	[	X
ejpam-811	57	2	4	4	NUM
ejpam-811	57	3	,	,	PUNCT
ejpam-811	57	4	9	9	NUM
ejpam-811	57	5	]	]	PUNCT
ejpam-811	57	6	.	.	PUNCT
ejpam-811	58	1	(	(	PUNCT
ejpam-811	58	2	p2	p2	PROPN
ejpam-811	58	3	)	)	PUNCT
ejpam-811	58	4	minζ∈x	minζ∈x	PROPN
ejpam-811	58	5	maxη∈y	maxη∈y	PROPN
ejpam-811	58	6	re	re	X
ejpam-811	58	7	�	�	PROPN
ejpam-811	58	8	f	f	PROPN
ejpam-811	58	9	(	(	PUNCT
ejpam-811	58	10	ζ	ζ	PROPN
ejpam-811	58	11	,	,	PUNCT
ejpam-811	58	12	η	η	NOUN
ejpam-811	58	13	)	)	PUNCT
ejpam-811	59	1	+	+	CCONJ
ejpam-811	59	2	(	(	PUNCT
ejpam-811	59	3	zhaz)1/2	zhaz)1/2	VERB
ejpam-811	59	4	�	�	PROPN
ejpam-811	59	5	subject	subject	ADJ
ejpam-811	59	6	to	to	ADP
ejpam-811	59	7	ζ	ζ	SYM
ejpam-811	59	8	∈	∈	NOUN
ejpam-811	59	9	x	x	PUNCT
ejpam-811	59	10	=	=	SYM
ejpam-811	59	11	�	�	PROPN
ejpam-811	59	12	ζ	ζ	NOUN
ejpam-811	59	13	=	=	SYM
ejpam-811	59	14	(	(	PUNCT
ejpam-811	59	15	z	z	NOUN
ejpam-811	59	16	,	,	PUNCT
ejpam-811	59	17	z	z	NOUN
ejpam-811	59	18	)	)	PUNCT
ejpam-811	59	19	∈	∈	PROPN
ejpam-811	59	20	c2n	c2n	NOUN
ejpam-811	59	21	|	|	ADV
ejpam-811	59	22	−	−	PROPN
ejpam-811	59	23	h(ζ	h(ζ	NOUN
ejpam-811	59	24	)	)	PUNCT
ejpam-811	59	25	∈	∈	PROPN
ejpam-811	59	26	s	s	VERB
ejpam-811	59	27	where	where	SCONJ
ejpam-811	59	28	y	y	PROPN
ejpam-811	59	29	is	be	AUX
ejpam-811	59	30	a	a	DET
ejpam-811	59	31	specified	specified	ADJ
ejpam-811	59	32	compact	compact	ADJ
ejpam-811	59	33	subset	subset	NOUN
ejpam-811	59	34	in	in	ADP
ejpam-811	59	35	c2	c2	PROPN
ejpam-811	59	36	m.	m.	PROPN
ejpam-811	59	37	(	(	PUNCT
ejpam-811	59	38	iv	iv	X
ejpam-811	59	39	)	)	PUNCT
ejpam-811	59	40	if	if	SCONJ
ejpam-811	59	41	a=	a=	ADJ
ejpam-811	59	42	0	0	NUM
ejpam-811	59	43	,	,	PUNCT
ejpam-811	59	44	b	b	X
ejpam-811	59	45	=	=	SYM
ejpam-811	59	46	0	0	PROPN
ejpam-811	59	47	and	and	CCONJ
ejpam-811	59	48	g	g	PROPN
ejpam-811	59	49	(	(	PUNCT
ejpam-811	59	50	·	·	PUNCT
ejpam-811	59	51	,	,	PUNCT
ejpam-811	59	52	·	·	PUNCT
ejpam-811	59	53	)	)	PUNCT
ejpam-811	59	54	≡	≡	PROPN
ejpam-811	59	55	1	1	NUM
ejpam-811	59	56	,	,	PUNCT
ejpam-811	59	57	then	then	ADV
ejpam-811	59	58	problem	problem	NOUN
ejpam-811	59	59	(	(	PUNCT
ejpam-811	59	60	p	p	X
ejpam-811	59	61	)	)	PUNCT
ejpam-811	59	62	is	be	AUX
ejpam-811	59	63	reduced	reduce	VERB
ejpam-811	59	64	to	to	ADP
ejpam-811	59	65	(	(	PUNCT
ejpam-811	59	66	p3	p3	PROPN
ejpam-811	59	67	)	)	PUNCT
ejpam-811	59	68	which	which	PRON
ejpam-811	59	69	was	be	AUX
ejpam-811	59	70	considered	consider	VERB
ejpam-811	59	71	by	by	ADP
ejpam-811	59	72	lai	lai	PROPN
ejpam-811	59	73	et	et	PROPN
ejpam-811	59	74	al	al	PROPN
ejpam-811	59	75	.	.	PUNCT
ejpam-811	60	1	[	[	X
ejpam-811	60	2	6	6	NUM
ejpam-811	60	3	]	]	PUNCT
ejpam-811	60	4	.	.	PUNCT
ejpam-811	61	1	(	(	PUNCT
ejpam-811	61	2	p3	p3	PROPN
ejpam-811	61	3	)	)	PUNCT
ejpam-811	61	4	minζ∈x	minζ∈x	PROPN
ejpam-811	61	5	maxη∈y	maxη∈y	PROPN
ejpam-811	61	6	re	re	ADP
ejpam-811	61	7	f	f	PROPN
ejpam-811	61	8	(	(	PUNCT
ejpam-811	61	9	ζ	ζ	PROPN
ejpam-811	61	10	,	,	PUNCT
ejpam-811	61	11	η	η	NOUN
ejpam-811	61	12	)	)	PUNCT
ejpam-811	61	13	subject	subject	NOUN
ejpam-811	61	14	to	to	ADP
ejpam-811	61	15	ζ	ζ	SYM
ejpam-811	61	16	∈	∈	NOUN
ejpam-811	61	17	x	x	PUNCT
ejpam-811	61	18	=	=	SYM
ejpam-811	61	19	�	�	PROPN
ejpam-811	61	20	ζ	ζ	NOUN
ejpam-811	61	21	=	=	SYM
ejpam-811	61	22	(	(	PUNCT
ejpam-811	61	23	z	z	NOUN
ejpam-811	61	24	,	,	PUNCT
ejpam-811	61	25	z	z	NOUN
ejpam-811	61	26	)	)	PUNCT
ejpam-811	61	27	∈	∈	PROPN
ejpam-811	61	28	c2n	c2n	NOUN
ejpam-811	61	29	|	|	ADV
ejpam-811	61	30	−	−	PROPN
ejpam-811	61	31	h(ζ	h(ζ	NOUN
ejpam-811	61	32	)	)	PUNCT
ejpam-811	61	33	∈	∈	PROPN
ejpam-811	61	34	s	s	PART
ejpam-811	61	35	.	.	PUNCT
ejpam-811	62	1	(	(	PUNCT
ejpam-811	62	2	v	v	NOUN
ejpam-811	62	3	)	)	PUNCT
ejpam-811	62	4	if	if	SCONJ
ejpam-811	62	5	ζ	ζ	NOUN
ejpam-811	62	6	=	=	SYM
ejpam-811	62	7	x	x	SYM
ejpam-811	62	8	∈	∈	PROPN
ejpam-811	62	9	rn	rn	PROPN
ejpam-811	62	10	and	and	CCONJ
ejpam-811	62	11	η	η	PROPN
ejpam-811	62	12	=	=	PROPN
ejpam-811	62	13	y	y	PROPN
ejpam-811	62	14	∈	∈	PROPN
ejpam-811	62	15	y	y	PROPN
ejpam-811	62	16	⊂	⊂	PROPN
ejpam-811	62	17	rm	rm	PROPN
ejpam-811	62	18	,	,	PUNCT
ejpam-811	62	19	then	then	ADV
ejpam-811	62	20	problem	problem	NOUN
ejpam-811	62	21	(	(	PUNCT
ejpam-811	63	1	p	p	X
ejpam-811	63	2	)	)	PUNCT
ejpam-811	63	3	is	be	AUX
ejpam-811	63	4	reduced	reduce	VERB
ejpam-811	63	5	to	to	ADP
ejpam-811	63	6	the	the	DET
ejpam-811	63	7	real	real	ADJ
ejpam-811	63	8	variable	variable	ADJ
ejpam-811	63	9	problem	problem	NOUN
ejpam-811	63	10	which	which	PRON
ejpam-811	63	11	was	be	AUX
ejpam-811	63	12	studied	study	VERB
ejpam-811	63	13	by	by	ADP
ejpam-811	63	14	lai	lai	PROPN
ejpam-811	63	15	et	et	PROPN
ejpam-811	63	16	al	al	PROPN
ejpam-811	63	17	.	.	PUNCT
ejpam-811	64	1	[	[	X
ejpam-811	64	2	5	5	NUM
ejpam-811	64	3	]	]	PUNCT
ejpam-811	64	4	.	.	PUNCT
ejpam-811	65	1	3	3	X
ejpam-811	65	2	.	.	X
ejpam-811	65	3	notations	notation	NOUN
ejpam-811	65	4	at	at	ADP
ejpam-811	65	5	first	first	ADV
ejpam-811	65	6	we	we	PRON
ejpam-811	65	7	describe	describe	VERB
ejpam-811	65	8	briefly	briefly	ADV
ejpam-811	65	9	for	for	ADP
ejpam-811	65	10	some	some	DET
ejpam-811	65	11	notations	notation	NOUN
ejpam-811	65	12	and	and	CCONJ
ejpam-811	65	13	definitions	definition	NOUN
ejpam-811	65	14	that	that	PRON
ejpam-811	65	15	are	be	AUX
ejpam-811	65	16	used	use	VERB
ejpam-811	65	17	in	in	ADP
ejpam-811	65	18	lai	lai	PROPN
ejpam-811	65	19	et	et	PROPN
ejpam-811	65	20	al	al	PROPN
ejpam-811	65	21	.	.	PUNCT
ejpam-811	66	1	[	[	X
ejpam-811	66	2	3	3	X
ejpam-811	66	3	]	]	PUNCT
ejpam-811	66	4	as	as	SCONJ
ejpam-811	66	5	follows	follow	VERB
ejpam-811	66	6	.	.	PUNCT
ejpam-811	67	1	let	let	VERB
ejpam-811	67	2	s	s	PRON
ejpam-811	67	3	=	=	VERB
ejpam-811	67	4	�	�	PROPN
ejpam-811	67	5	ξ	ξ	X
ejpam-811	67	6	∈	∈	PROPN
ejpam-811	67	7	cp	cp	INTJ
ejpam-811	67	8	|	|	NOUN
ejpam-811	67	9	re(kξ	re(kξ	PROPN
ejpam-811	67	10	)	)	PUNCT
ejpam-811	67	11	≥	≥	NOUN
ejpam-811	67	12	0	0	NUM
ejpam-811	68	1	⊂	⊂	PRON
ejpam-811	68	2	cp	cp	INTJ
ejpam-811	68	3	be	be	AUX
ejpam-811	68	4	a	a	DET
ejpam-811	68	5	polyhedral	polyhedral	ADJ
ejpam-811	68	6	cone	cone	NOUN
ejpam-811	68	7	where	where	SCONJ
ejpam-811	68	8	k	k	PROPN
ejpam-811	68	9	∈	∈	PROPN
ejpam-811	68	10	ck×p	ck×p	PROPN
ejpam-811	68	11	is	be	AUX
ejpam-811	68	12	a	a	DET
ejpam-811	68	13	k	k	PROPN
ejpam-811	68	14	×	×	NOUN
ejpam-811	68	15	p	p	NOUN
ejpam-811	68	16	matrix	matrix	NOUN
ejpam-811	68	17	.	.	PUNCT
ejpam-811	69	1	the	the	DET
ejpam-811	69	2	dual	dual	ADJ
ejpam-811	69	3	cone	cone	NOUN
ejpam-811	69	4	s∗	s∗	NOUN
ejpam-811	69	5	of	of	ADP
ejpam-811	69	6	s	s	PROPN
ejpam-811	69	7	is	be	AUX
ejpam-811	69	8	defined	define	VERB
ejpam-811	69	9	by	by	ADP
ejpam-811	69	10	s∗	s∗	PROPN
ejpam-811	69	11	=	=	SYM
ejpam-811	69	12	�	�	PROPN
ejpam-811	69	13	µ	µ	X
ejpam-811	69	14	∈	∈	X
ejpam-811	69	15	cp	cp	INTJ
ejpam-811	69	16	|	|	ADV
ejpam-811	69	17	re〈ξ,µ	re〈ξ,µ	VERB
ejpam-811	69	18	〉	〉	NOUN
ejpam-811	69	19	≥	≥	NUM
ejpam-811	69	20	0	0	NUM
ejpam-811	69	21	,	,	PUNCT
ejpam-811	69	22	for	for	ADP
ejpam-811	69	23	ξ	ξ	PROPN
ejpam-811	69	24	∈	∈	PROPN
ejpam-811	69	25	s	s	PART
ejpam-811	69	26	.	.	PUNCT
ejpam-811	70	1	h.	h.	PROPN
ejpam-811	70	2	lai	lai	PROPN
ejpam-811	70	3	,	,	PUNCT
ejpam-811	70	4	t.	t.	PROPN
ejpam-811	70	5	huang	huang	PROPN
ejpam-811	70	6	/	/	SYM
ejpam-811	70	7	eur	eur	PROPN
ejpam-811	70	8	.	.	PUNCT
ejpam-811	71	1	j.	j.	PROPN
ejpam-811	71	2	pure	pure	PROPN
ejpam-811	71	3	appl	appl	PROPN
ejpam-811	71	4	.	.	PROPN
ejpam-811	71	5	math	math	PROPN
ejpam-811	71	6	,	,	PUNCT
ejpam-811	71	7	3	3	NUM
ejpam-811	71	8	(	(	PUNCT
ejpam-811	71	9	2010	2010	NUM
ejpam-811	71	10	)	)	PUNCT
ejpam-811	71	11	,	,	PUNCT
ejpam-811	71	12	989	989	NUM
ejpam-811	71	13	-	-	SYM
ejpam-811	71	14	1005	1005	NUM
ejpam-811	71	15	992	992	NUM
ejpam-811	71	16	for	for	ADP
ejpam-811	71	17	s0	s0	PROPN
ejpam-811	71	18	∈	∈	PROPN
ejpam-811	71	19	s	s	PROPN
ejpam-811	71	20	,	,	PUNCT
ejpam-811	71	21	the	the	DET
ejpam-811	71	22	set	set	NOUN
ejpam-811	71	23	s(s0	s(s0	NOUN
ejpam-811	71	24	)	)	PUNCT
ejpam-811	71	25	is	be	AUX
ejpam-811	71	26	the	the	DET
ejpam-811	71	27	intersection	intersection	NOUN
ejpam-811	71	28	of	of	ADP
ejpam-811	71	29	those	those	PRON
ejpam-811	71	30	closed	close	VERB
ejpam-811	71	31	half	half	ADJ
ejpam-811	71	32	spaces	space	NOUN
ejpam-811	71	33	that	that	PRON
ejpam-811	71	34	include	include	VERB
ejpam-811	71	35	s0	s0	NOUN
ejpam-811	71	36	in	in	ADP
ejpam-811	71	37	their	their	PRON
ejpam-811	71	38	boundaries	boundary	NOUN
ejpam-811	71	39	.	.	PUNCT
ejpam-811	72	1	thus	thus	ADV
ejpam-811	72	2	if	if	SCONJ
ejpam-811	72	3	s0	s0	PROPN
ejpam-811	72	4	∈	∈	PROPN
ejpam-811	72	5	int(s	int(s	PROPN
ejpam-811	72	6	)	)	PUNCT
ejpam-811	72	7	,	,	PUNCT
ejpam-811	72	8	then	then	ADV
ejpam-811	72	9	s(s0	s(s0	VERB
ejpam-811	72	10	)	)	PUNCT
ejpam-811	72	11	is	be	AUX
ejpam-811	72	12	the	the	DET
ejpam-811	72	13	whole	whole	ADJ
ejpam-811	72	14	space	space	NOUN
ejpam-811	73	1	cp	cp	INTJ
ejpam-811	73	2	.	.	PUNCT
ejpam-811	74	1	we	we	PRON
ejpam-811	74	2	say	say	VERB
ejpam-811	74	3	that	that	DET
ejpam-811	74	4	problem	problem	NOUN
ejpam-811	74	5	(	(	PUNCT
ejpam-811	74	6	p	p	NOUN
ejpam-811	74	7	)	)	PUNCT
ejpam-811	74	8	has	have	VERB
ejpam-811	74	9	the	the	DET
ejpam-811	74	10	constraint	constraint	NOUN
ejpam-811	74	11	qualification	qualification	NOUN
ejpam-811	74	12	at	at	ADP
ejpam-811	74	13	a	a	DET
ejpam-811	74	14	point	point	NOUN
ejpam-811	74	15	ζ0	ζ0	NOUN
ejpam-811	74	16	=	=	SYM
ejpam-811	74	17	(	(	PUNCT
ejpam-811	74	18	z0	z0	PROPN
ejpam-811	74	19	,	,	PUNCT
ejpam-811	74	20	z0	z0	PROPN
ejpam-811	74	21	)	)	PUNCT
ejpam-811	74	22	if	if	SCONJ
ejpam-811	74	23	for	for	ADP
ejpam-811	74	24	any	any	DET
ejpam-811	74	25	nonzero	nonzero	NOUN
ejpam-811	74	26	µ	µ	PRON
ejpam-811	74	27	∈	∈	NOUN
ejpam-811	74	28	s∗	s∗	PROPN
ejpam-811	74	29	⊂	⊂	PROPN
ejpam-811	74	30	cp	cp	PROPN
ejpam-811	74	31	,	,	PUNCT
ejpam-811	74	32	we	we	PRON
ejpam-811	74	33	have	have	AUX
ejpam-811	74	34	re	re	VERB
ejpam-811	74	35	h′(ζ0)(ζ−	h′(ζ0)(ζ−	NOUN
ejpam-811	74	36	ζ0),µ	ζ0),µ	ADJ
ejpam-811	74	37	�	�	PROPN
ejpam-811	74	38	6=	6=	ADP
ejpam-811	74	39	0	0	NUM
ejpam-811	74	40	for	for	SCONJ
ejpam-811	74	41	ζ	ζ	NOUN
ejpam-811	74	42	6=	6=	ADV
ejpam-811	74	43	ζ0	ζ0	ADJ
ejpam-811	74	44	.	.	PUNCT
ejpam-811	75	1	generalized	generalized	ADJ
ejpam-811	75	2	convexity	convexity	NOUN
ejpam-811	75	3	is	be	AUX
ejpam-811	75	4	an	an	DET
ejpam-811	75	5	important	important	ADJ
ejpam-811	75	6	role	role	NOUN
ejpam-811	75	7	in	in	ADP
ejpam-811	75	8	optimization	optimization	NOUN
ejpam-811	75	9	theory	theory	NOUN
ejpam-811	75	10	.	.	PUNCT
ejpam-811	76	1	thus	thus	ADV
ejpam-811	76	2	,	,	PUNCT
ejpam-811	76	3	for	for	ADP
ejpam-811	76	4	convenience	convenience	NOUN
ejpam-811	76	5	,	,	PUNCT
ejpam-811	76	6	we	we	PRON
ejpam-811	76	7	recall	recall	VERB
ejpam-811	76	8	the	the	DET
ejpam-811	76	9	generalized	generalized	ADJ
ejpam-811	76	10	convexities	convexity	NOUN
ejpam-811	76	11	of	of	ADP
ejpam-811	76	12	complex	complex	ADJ
ejpam-811	76	13	functions	function	NOUN
ejpam-811	76	14	as	as	SCONJ
ejpam-811	76	15	follows	follow	VERB
ejpam-811	76	16	[	[	X
ejpam-811	76	17	cf	cf	NOUN
ejpam-811	76	18	.	.	PUNCT
ejpam-811	77	1	lai	lai	PROPN
ejpam-811	77	2	et	et	PROPN
ejpam-811	77	3	al	al	PROPN
ejpam-811	77	4	.	.	PROPN
ejpam-811	77	5	7	7	NUM
ejpam-811	77	6	,	,	PUNCT
ejpam-811	77	7	8	8	NUM
ejpam-811	77	8	]	]	PUNCT
ejpam-811	77	9	.	.	PUNCT
ejpam-811	78	1	definition	definition	NOUN
ejpam-811	78	2	1	1	NUM
ejpam-811	78	3	.	.	PUNCT
ejpam-811	79	1	the	the	DET
ejpam-811	79	2	real	real	ADJ
ejpam-811	79	3	part	part	NOUN
ejpam-811	79	4	of	of	ADP
ejpam-811	79	5	an	an	DET
ejpam-811	79	6	analytic	analytic	ADJ
ejpam-811	79	7	function	function	NOUN
ejpam-811	79	8	f	f	PROPN
ejpam-811	79	9	(	(	PUNCT
ejpam-811	79	10	·	·	PUNCT
ejpam-811	79	11	)	)	PUNCT
ejpam-811	79	12	from	from	ADP
ejpam-811	79	13	c2n	c2n	NOUN
ejpam-811	79	14	to	to	ADP
ejpam-811	79	15	r	r	NOUN
ejpam-811	79	16	is	be	AUX
ejpam-811	79	17	called	call	VERB
ejpam-811	79	18	,	,	PUNCT
ejpam-811	79	19	respectively	respectively	ADV
ejpam-811	79	20	,	,	PUNCT
ejpam-811	79	21	(	(	PUNCT
ejpam-811	79	22	i	i	NOUN
ejpam-811	79	23	)	)	PUNCT
ejpam-811	79	24	convex	convex	NOUN
ejpam-811	79	25	(	(	PUNCT
ejpam-811	79	26	strictly	strictly	ADV
ejpam-811	79	27	)	)	PUNCT
ejpam-811	79	28	at	at	ADP
ejpam-811	79	29	ζ	ζ	NOUN
ejpam-811	79	30	=	=	SYM
ejpam-811	79	31	ζ0	ζ0	PROPN
ejpam-811	79	32	∈q	∈q	NOUN
ejpam-811	79	33	⊂	⊂	PROPN
ejpam-811	79	34	c2n	c2n	NOUN
ejpam-811	79	35	if	if	SCONJ
ejpam-811	79	36	re	re	VERB
ejpam-811	80	1	�	�	PROPN
ejpam-811	80	2	f	f	PROPN
ejpam-811	80	3	(	(	PUNCT
ejpam-811	80	4	ζ)−	ζ)−	PROPN
ejpam-811	80	5	f	f	PROPN
ejpam-811	80	6	(	(	PUNCT
ejpam-811	80	7	ζ0	ζ0	PROPN
ejpam-811	80	8	)	)	PUNCT
ejpam-811	80	9	�	�	PROPN
ejpam-811	80	10	≥	≥	NUM
ejpam-811	80	11	re	re	NOUN
ejpam-811	80	12	�	�	PROPN
ejpam-811	80	13	f	f	PROPN
ejpam-811	80	14	′	′	NUM
ejpam-811	80	15	ζ	ζ	NOUN
ejpam-811	80	16	(	(	PUNCT
ejpam-811	80	17	ζ0)(ζ−	ζ0)(ζ−	NOUN
ejpam-811	80	18	ζ0	ζ0	ADJ
ejpam-811	80	19	)	)	PUNCT
ejpam-811	80	20	�	�	PROPN
ejpam-811	80	21	,	,	PUNCT
ejpam-811	80	22	(	(	PUNCT
ejpam-811	80	23	>	>	PUNCT
ejpam-811	80	24	)	)	PUNCT
ejpam-811	80	25	(	(	PUNCT
ejpam-811	80	26	ii	ii	NOUN
ejpam-811	80	27	)	)	PUNCT
ejpam-811	80	28	pseudoconvex	pseudoconvex	NOUN
ejpam-811	80	29	(	(	PUNCT
ejpam-811	80	30	strictly	strictly	ADV
ejpam-811	80	31	)	)	PUNCT
ejpam-811	80	32	at	at	ADP
ejpam-811	80	33	ζ=	ζ=	ADJ
ejpam-811	80	34	ζ0	ζ0	NOUN
ejpam-811	80	35	∈q	∈q	NOUN
ejpam-811	80	36	if	if	SCONJ
ejpam-811	80	37	re	re	VERB
ejpam-811	80	38	�	�	PROPN
ejpam-811	80	39	f	f	PROPN
ejpam-811	80	40	′	′	NUM
ejpam-811	80	41	ζ	ζ	NOUN
ejpam-811	80	42	(	(	PUNCT
ejpam-811	80	43	ζ0)(ζ−	ζ0)(ζ−	NOUN
ejpam-811	80	44	ζ0	ζ0	ADJ
ejpam-811	80	45	)	)	PUNCT
ejpam-811	80	46	�	�	PROPN
ejpam-811	80	47	≥	≥	NUM
ejpam-811	80	48	0⇒	0⇒	PROPN
ejpam-811	80	49	re	re	NOUN
ejpam-811	80	50	�	�	PROPN
ejpam-811	80	51	f	f	PROPN
ejpam-811	80	52	(	(	PUNCT
ejpam-811	80	53	ζ)−	ζ)−	PROPN
ejpam-811	80	54	f	f	PROPN
ejpam-811	80	55	(	(	PUNCT
ejpam-811	80	56	ζ0	ζ0	PROPN
ejpam-811	80	57	)	)	PUNCT
ejpam-811	80	58	�	�	PROPN
ejpam-811	80	59	≥	≥	NUM
ejpam-811	80	60	0	0	NUM
ejpam-811	80	61	,	,	PUNCT
ejpam-811	80	62	(	(	PUNCT
ejpam-811	80	63	>	>	X
ejpam-811	80	64	0	0	NUM
ejpam-811	80	65	)	)	PUNCT
ejpam-811	80	66	(	(	PUNCT
ejpam-811	80	67	iii	iii	X
ejpam-811	80	68	)	)	PUNCT
ejpam-811	80	69	quasiconvex	quasiconvex	NOUN
ejpam-811	80	70	at	at	ADP
ejpam-811	80	71	ζ	ζ	NOUN
ejpam-811	80	72	=	=	SYM
ejpam-811	80	73	ζ0	ζ0	NOUN
ejpam-811	80	74	∈q	∈q	NOUN
ejpam-811	80	75	if	if	SCONJ
ejpam-811	80	76	re	re	VERB
ejpam-811	80	77	�	�	PROPN
ejpam-811	80	78	f	f	PROPN
ejpam-811	80	79	(	(	PUNCT
ejpam-811	80	80	ζ)−	ζ)−	PROPN
ejpam-811	80	81	f	f	PROPN
ejpam-811	80	82	(	(	PUNCT
ejpam-811	80	83	ζ0	ζ0	PROPN
ejpam-811	80	84	)	)	PUNCT
ejpam-811	80	85	�	�	PROPN
ejpam-811	80	86	≤	≤	NUM
ejpam-811	80	87	0⇒	0⇒	PROPN
ejpam-811	80	88	re	re	NOUN
ejpam-811	80	89	�	�	PROPN
ejpam-811	80	90	f	f	PROPN
ejpam-811	80	91	′ζ(ζ0)(ζ−	′ζ(ζ0)(ζ−	NOUN
ejpam-811	80	92	ζ0	ζ0	ADJ
ejpam-811	80	93	)	)	PUNCT
ejpam-811	80	94	�	�	PROPN
ejpam-811	80	95	≤	≤	ADJ
ejpam-811	80	96	0	0	X
ejpam-811	80	97	.	.	PUNCT
ejpam-811	81	1	definition	definition	NOUN
ejpam-811	81	2	2	2	NUM
ejpam-811	81	3	.	.	PUNCT
ejpam-811	82	1	an	an	DET
ejpam-811	82	2	analytic	analytic	ADJ
ejpam-811	82	3	mapping	mapping	NOUN
ejpam-811	82	4	h	h	NOUN
ejpam-811	82	5	(	(	PUNCT
ejpam-811	82	6	·	·	PUNCT
ejpam-811	82	7	)	)	PUNCT
ejpam-811	82	8	:	:	PUNCT
ejpam-811	82	9	c2n→	c2n→	NOUN
ejpam-811	82	10	cp	cp	PROPN
ejpam-811	82	11	is	be	AUX
ejpam-811	82	12	called	call	VERB
ejpam-811	82	13	,	,	PUNCT
ejpam-811	82	14	respectively	respectively	ADV
ejpam-811	82	15	,	,	PUNCT
ejpam-811	82	16	(	(	PUNCT
ejpam-811	82	17	i	i	NOUN
ejpam-811	82	18	)	)	PUNCT
ejpam-811	82	19	convex	convex	VERB
ejpam-811	82	20	at	at	ADP
ejpam-811	82	21	ζ	ζ	NOUN
ejpam-811	82	22	=	=	SYM
ejpam-811	82	23	ζ0	ζ0	NOUN
ejpam-811	82	24	∈	∈	PROPN
ejpam-811	82	25	q	q	PUNCT
ejpam-811	82	26	with	with	ADP
ejpam-811	82	27	respect	respect	NOUN
ejpam-811	82	28	to	to	ADP
ejpam-811	82	29	(	(	PUNCT
ejpam-811	82	30	w.r.t	w.r.t	NOUN
ejpam-811	82	31	.	.	PUNCT
ejpam-811	82	32	)	)	PUNCT
ejpam-811	83	1	a	a	DET
ejpam-811	83	2	polyhedral	polyhedral	ADJ
ejpam-811	83	3	cone	cone	NOUN
ejpam-811	83	4	s	s	X
ejpam-811	83	5	in	in	ADP
ejpam-811	83	6	cp	cp	INTJ
ejpam-811	83	7	if	if	SCONJ
ejpam-811	83	8	there	there	PRON
ejpam-811	83	9	is	be	VERB
ejpam-811	83	10	a	a	DET
ejpam-811	83	11	nonzero	nonzero	NOUN
ejpam-811	83	12	µ	µ	PRON
ejpam-811	83	13	∈	∈	NOUN
ejpam-811	83	14	s∗	s∗	PROPN
ejpam-811	83	15	�	�	PROPN
ejpam-811	83	16	⊂	⊂	PROPN
ejpam-811	83	17	cp	cp	PROPN
ejpam-811	83	18	�	�	PROPN
ejpam-811	83	19	,	,	PUNCT
ejpam-811	83	20	the	the	DET
ejpam-811	83	21	dual	dual	ADJ
ejpam-811	83	22	cone	cone	NOUN
ejpam-811	83	23	of	of	ADP
ejpam-811	83	24	s	s	PROPN
ejpam-811	83	25	,	,	PUNCT
ejpam-811	83	26	such	such	ADJ
ejpam-811	83	27	that	that	SCONJ
ejpam-811	83	28	re〈h(ζ)−	re〈h(ζ)−	PROPN
ejpam-811	83	29	h(ζ0),µ	h(ζ0),µ	PROPN
ejpam-811	83	30	〉	〉	PROPN
ejpam-811	83	31	≥	≥	NUM
ejpam-811	83	32	re〈h′(ζ0)(ζ−	re〈h′(ζ0)(ζ−	NOUN
ejpam-811	83	33	ζ0),µ	ζ0),µ	ADJ
ejpam-811	83	34	〉	〉	NOUN
ejpam-811	83	35	.	.	PUNCT
ejpam-811	84	1	here	here	ADV
ejpam-811	84	2	〈	〈	PROPN
ejpam-811	84	3	·	·	SYM
ejpam-811	84	4	,	,	PUNCT
ejpam-811	84	5	·	·	PUNCT
ejpam-811	84	6	〉	〉	NOUN
ejpam-811	84	7	stands	stand	VERB
ejpam-811	84	8	for	for	ADP
ejpam-811	84	9	the	the	DET
ejpam-811	84	10	inner	inner	ADJ
ejpam-811	84	11	product	product	NOUN
ejpam-811	84	12	in	in	ADP
ejpam-811	84	13	complex	complex	ADJ
ejpam-811	84	14	spaces	space	NOUN
ejpam-811	84	15	.	.	PUNCT
ejpam-811	85	1	(	(	PUNCT
ejpam-811	85	2	ii	ii	NOUN
ejpam-811	85	3	)	)	PUNCT
ejpam-811	85	4	pseudoconvex	pseudoconvex	NOUN
ejpam-811	85	5	(	(	PUNCT
ejpam-811	85	6	strictly	strictly	ADV
ejpam-811	85	7	)	)	PUNCT
ejpam-811	85	8	at	at	ADP
ejpam-811	85	9	ζ	ζ	NOUN
ejpam-811	85	10	=	=	SYM
ejpam-811	85	11	ζ0	ζ0	NOUN
ejpam-811	85	12	∈	∈	PROPN
ejpam-811	85	13	q	q	NOUN
ejpam-811	85	14	w.r.t	w.r.t	NOUN
ejpam-811	85	15	.	.	PUNCT
ejpam-811	85	16	s	s	VERB
ejpam-811	85	17	if	if	SCONJ
ejpam-811	85	18	there	there	PRON
ejpam-811	85	19	is	be	VERB
ejpam-811	85	20	a	a	DET
ejpam-811	85	21	nonzero	nonzero	NOUN
ejpam-811	85	22	µ	µ	PRON
ejpam-811	85	23	∈	∈	NOUN
ejpam-811	86	1	s∗	s∗	PROPN
ejpam-811	86	2	�	�	PROPN
ejpam-811	86	3	⊂	⊂	PROPN
ejpam-811	86	4	cp	cp	PROPN
ejpam-811	86	5	�	�	PROPN
ejpam-811	86	6	the	the	DET
ejpam-811	86	7	dual	dual	ADJ
ejpam-811	86	8	cone	cone	NOUN
ejpam-811	86	9	of	of	ADP
ejpam-811	86	10	s	s	PROPN
ejpam-811	86	11	,	,	PUNCT
ejpam-811	86	12	such	such	ADJ
ejpam-811	86	13	that	that	SCONJ
ejpam-811	86	14	re〈h′(ζ0)(ζ−	re〈h′(ζ0)(ζ−	NOUN
ejpam-811	86	15	ζ0),µ	ζ0),µ	ADJ
ejpam-811	86	16	〉	〉	X
ejpam-811	86	17	≥	≥	NOUN
ejpam-811	86	18	0⇒	0⇒	NUM
ejpam-811	86	19	re〈h(ζ)−	re〈h(ζ)−	PROPN
ejpam-811	86	20	h(ζ0),µ	h(ζ0),µ	PROPN
ejpam-811	86	21	〉	〉	PROPN
ejpam-811	86	22	≥	≥	NUM
ejpam-811	86	23	0	0	NUM
ejpam-811	86	24	,	,	PUNCT
ejpam-811	86	25	(	(	PUNCT
ejpam-811	86	26	>	>	X
ejpam-811	86	27	0	0	NUM
ejpam-811	86	28	)	)	PUNCT
ejpam-811	86	29	(	(	PUNCT
ejpam-811	86	30	iii	iii	X
ejpam-811	86	31	)	)	PUNCT
ejpam-811	86	32	quasiconvex	quasiconvex	NOUN
ejpam-811	86	33	at	at	ADP
ejpam-811	86	34	ζ	ζ	NOUN
ejpam-811	86	35	=	=	SYM
ejpam-811	86	36	ζ0	ζ0	NOUN
ejpam-811	86	37	∈q	∈q	NOUN
ejpam-811	86	38	w.r.t	w.r.t	VERB
ejpam-811	86	39	.	.	PUNCT
ejpam-811	87	1	s	s	VERB
ejpam-811	87	2	if	if	SCONJ
ejpam-811	87	3	there	there	PRON
ejpam-811	87	4	is	be	VERB
ejpam-811	87	5	a	a	DET
ejpam-811	87	6	nonzero	nonzero	NOUN
ejpam-811	87	7	µ	µ	PRON
ejpam-811	87	8	∈	∈	NOUN
ejpam-811	88	1	s∗	s∗	PROPN
ejpam-811	88	2	�	�	PROPN
ejpam-811	88	3	⊂	⊂	PROPN
ejpam-811	88	4	cp	cp	PROPN
ejpam-811	88	5	�	�	PROPN
ejpam-811	88	6	such	such	ADJ
ejpam-811	88	7	that	that	SCONJ
ejpam-811	88	8	re〈h(ζ)−	re〈h(ζ)−	PROPN
ejpam-811	88	9	h(ζ0),µ	h(ζ0),µ	PROPN
ejpam-811	88	10	〉	〉	NOUN
ejpam-811	88	11	≤	≤	NUM
ejpam-811	88	12	0⇒	0⇒	NOUN
ejpam-811	88	13	re〈h′(ζ0)(ζ−	re〈h′(ζ0)(ζ−	NOUN
ejpam-811	88	14	ζ0),µ	ζ0),µ	ADJ
ejpam-811	88	15	〉	〉	NOUN
ejpam-811	88	16	≤	≤	NUM
ejpam-811	88	17	0	0	NUM
ejpam-811	88	18	.	.	PUNCT
ejpam-811	89	1	h.	h.	PROPN
ejpam-811	89	2	lai	lai	PROPN
ejpam-811	89	3	,	,	PUNCT
ejpam-811	89	4	t.	t.	PROPN
ejpam-811	89	5	huang	huang	PROPN
ejpam-811	89	6	/	/	SYM
ejpam-811	89	7	eur	eur	PROPN
ejpam-811	89	8	.	.	PUNCT
ejpam-811	90	1	j.	j.	PROPN
ejpam-811	90	2	pure	pure	PROPN
ejpam-811	90	3	appl	appl	PROPN
ejpam-811	90	4	.	.	PROPN
ejpam-811	90	5	math	math	PROPN
ejpam-811	90	6	,	,	PUNCT
ejpam-811	90	7	3	3	NUM
ejpam-811	90	8	(	(	PUNCT
ejpam-811	90	9	2010	2010	NUM
ejpam-811	90	10	)	)	PUNCT
ejpam-811	90	11	,	,	PUNCT
ejpam-811	90	12	989	989	NUM
ejpam-811	90	13	-	-	SYM
ejpam-811	90	14	1005	1005	NUM
ejpam-811	90	15	993	993	NUM
ejpam-811	90	16	throughout	throughout	ADP
ejpam-811	90	17	this	this	DET
ejpam-811	90	18	paper	paper	NOUN
ejpam-811	90	19	,	,	PUNCT
ejpam-811	90	20	x	x	X
ejpam-811	90	21	is	be	AUX
ejpam-811	90	22	a	a	DET
ejpam-811	90	23	subset	subset	NOUN
ejpam-811	90	24	of	of	ADP
ejpam-811	90	25	c2n	c2n	NOUN
ejpam-811	90	26	,	,	PUNCT
ejpam-811	90	27	and	and	CCONJ
ejpam-811	90	28	for	for	ADP
ejpam-811	90	29	ζ	ζ	NOUN
ejpam-811	90	30	=	=	SYM
ejpam-811	90	31	(	(	PUNCT
ejpam-811	90	32	z	z	NOUN
ejpam-811	90	33	,	,	PUNCT
ejpam-811	90	34	z	z	NOUN
ejpam-811	90	35	)	)	PUNCT
ejpam-811	90	36	∈	∈	PROPN
ejpam-811	90	37	x	x	X
ejpam-811	90	38	,	,	PUNCT
ejpam-811	90	39	f	f	PROPN
ejpam-811	90	40	(	(	PUNCT
ejpam-811	90	41	ζ	ζ	NOUN
ejpam-811	90	42	,	,	PUNCT
ejpam-811	90	43	·	·	PUNCT
ejpam-811	90	44	)	)	PUNCT
ejpam-811	90	45	and	and	CCONJ
ejpam-811	90	46	g(ζ	g(ζ	PROPN
ejpam-811	90	47	,	,	PUNCT
ejpam-811	90	48	·	·	PUNCT
ejpam-811	90	49	)	)	PUNCT
ejpam-811	90	50	are	be	AUX
ejpam-811	90	51	continuous	continuous	ADJ
ejpam-811	90	52	on	on	ADP
ejpam-811	90	53	the	the	DET
ejpam-811	90	54	compact	compact	ADJ
ejpam-811	90	55	set	set	NOUN
ejpam-811	90	56	y	y	PROPN
ejpam-811	90	57	.	.	PUNCT
ejpam-811	91	1	thus	thus	ADV
ejpam-811	91	2	we	we	PRON
ejpam-811	91	3	can	can	AUX
ejpam-811	91	4	denote	denote	VERB
ejpam-811	91	5	y	y	PROPN
ejpam-811	91	6	(	(	PUNCT
ejpam-811	91	7	ζ	ζ	NOUN
ejpam-811	91	8	)	)	PUNCT
ejpam-811	91	9	=	=	SYM
ejpam-811	91	10	�	�	PROPN
ejpam-811	91	11	η	η	PROPN
ejpam-811	91	12	∈	∈	PROPN
ejpam-811	91	13	y	y	PROPN
ejpam-811	91	14	�	�	PROPN
ejpam-811	91	15	�	�	PROPN
ejpam-811	91	16	�	�	PROPN
ejpam-811	91	17	re	re	PROPN
ejpam-811	91	18	[	[	PUNCT
ejpam-811	91	19	f	f	X
ejpam-811	91	20	(	(	PUNCT
ejpam-811	91	21	ζ	ζ	PROPN
ejpam-811	91	22	,	,	PUNCT
ejpam-811	91	23	η	η	NOUN
ejpam-811	91	24	)	)	PUNCT
ejpam-811	91	25	+	+	CCONJ
ejpam-811	91	26	(	(	PUNCT
ejpam-811	91	27	zhaz)1/2	zhaz)1/2	NUM
ejpam-811	91	28	]	]	X
ejpam-811	91	29	re[g(ζ	re[g(ζ	PROPN
ejpam-811	91	30	,	,	PUNCT
ejpam-811	91	31	η)−	η)−	PROPN
ejpam-811	91	32	(	(	PUNCT
ejpam-811	91	33	zh	zh	X
ejpam-811	91	34	bz)1/2	bz)1/2	PROPN
ejpam-811	91	35	]	]	PUNCT
ejpam-811	92	1	=	=	PUNCT
ejpam-811	92	2	max	max	X
ejpam-811	92	3	ν∈y	ν∈y	X
ejpam-811	92	4	re	re	PROPN
ejpam-811	92	5	[	[	PUNCT
ejpam-811	92	6	f	f	X
ejpam-811	92	7	(	(	PUNCT
ejpam-811	92	8	ζ	ζ	NOUN
ejpam-811	92	9	,	,	PUNCT
ejpam-811	92	10	ν	ν	NOUN
ejpam-811	92	11	)	)	PUNCT
ejpam-811	92	12	+	+	CCONJ
ejpam-811	92	13	(	(	PUNCT
ejpam-811	92	14	zhaz)1/2	zhaz)1/2	NUM
ejpam-811	92	15	]	]	X
ejpam-811	92	16	re[g(ζ	re[g(ζ	PROPN
ejpam-811	92	17	,	,	PUNCT
ejpam-811	92	18	ν)−	ν)−	PROPN
ejpam-811	92	19	(	(	PUNCT
ejpam-811	92	20	zh	zh	X
ejpam-811	92	21	bz)1/2	bz)1/2	PROPN
ejpam-811	92	22	]	]	X
ejpam-811	92	23	�	�	PROPN
ejpam-811	92	24	since	since	SCONJ
ejpam-811	92	25	y	y	PROPN
ejpam-811	92	26	is	be	AUX
ejpam-811	92	27	compact	compact	ADJ
ejpam-811	92	28	,	,	PUNCT
ejpam-811	92	29	the	the	DET
ejpam-811	92	30	supremum	supremum	NOUN
ejpam-811	92	31	in	in	ADP
ejpam-811	92	32	the	the	DET
ejpam-811	92	33	above	above	NOUN
ejpam-811	92	34	v	v	NOUN
ejpam-811	92	35	∈	∈	NOUN
ejpam-811	92	36	y	y	NOUN
ejpam-811	92	37	is	be	AUX
ejpam-811	92	38	attained	attain	VERB
ejpam-811	92	39	.	.	PUNCT
ejpam-811	93	1	this	this	DET
ejpam-811	93	2	set	set	VERB
ejpam-811	93	3	y	y	PROPN
ejpam-811	93	4	(	(	PUNCT
ejpam-811	93	5	ζ	ζ	NOUN
ejpam-811	93	6	)	)	PUNCT
ejpam-811	93	7	is	be	AUX
ejpam-811	93	8	also	also	ADV
ejpam-811	93	9	a	a	DET
ejpam-811	93	10	compact	compact	ADJ
ejpam-811	93	11	subset	subset	NOUN
ejpam-811	93	12	of	of	ADP
ejpam-811	93	13	y	y	PROPN
ejpam-811	93	14	.	.	PUNCT
ejpam-811	94	1	we	we	PRON
ejpam-811	94	2	need	need	VERB
ejpam-811	94	3	use	use	VERB
ejpam-811	94	4	the	the	DET
ejpam-811	94	5	differential	differential	NOUN
ejpam-811	94	6	of	of	ADP
ejpam-811	94	7	a	a	DET
ejpam-811	94	8	complex	complex	ADJ
ejpam-811	94	9	function	function	NOUN
ejpam-811	94	10	by	by	ADP
ejpam-811	94	11	the	the	DET
ejpam-811	94	12	gradient	gradient	ADJ
ejpam-811	94	13	symbols	symbol	NOUN
ejpam-811	94	14	∇z	∇z	PROPN
ejpam-811	94	15	and	and	CCONJ
ejpam-811	94	16	∇z	∇z	PROPN
ejpam-811	94	17	as	as	ADP
ejpam-811	94	18	the	the	DET
ejpam-811	94	19	following	following	NOUN
ejpam-811	94	20	[	[	X
ejpam-811	94	21	cf	cf	NOUN
ejpam-811	94	22	.	.	NOUN
ejpam-811	94	23	4	4	NUM
ejpam-811	94	24	]	]	PUNCT
ejpam-811	94	25	:	:	PUNCT
ejpam-811	94	26	for	for	ADP
ejpam-811	94	27	each	each	DET
ejpam-811	94	28	η	η	PROPN
ejpam-811	94	29	∈	∈	PROPN
ejpam-811	94	30	y	y	PROPN
ejpam-811	94	31	⊂	⊂	PROPN
ejpam-811	94	32	c2	c2	PROPN
ejpam-811	94	33	m	m	PROPN
ejpam-811	94	34	,	,	PUNCT
ejpam-811	94	35	w	w	PROPN
ejpam-811	94	36	∈	∈	PROPN
ejpam-811	94	37	cn	cn	NOUN
ejpam-811	94	38	and	and	CCONJ
ejpam-811	94	39	ζ	ζ	NOUN
ejpam-811	94	40	=	=	SYM
ejpam-811	94	41	(	(	PUNCT
ejpam-811	94	42	z	z	NOUN
ejpam-811	94	43	,	,	PUNCT
ejpam-811	94	44	z	z	NOUN
ejpam-811	94	45	)	)	PUNCT
ejpam-811	94	46	∈	∈	PROPN
ejpam-811	94	47	q	q	X
ejpam-811	95	1	⊂	⊂	PROPN
ejpam-811	95	2	c2n	c2n	PROPN
ejpam-811	95	3	,	,	PUNCT
ejpam-811	95	4	suppose	suppose	VERB
ejpam-811	95	5	that	that	SCONJ
ejpam-811	95	6	the	the	DET
ejpam-811	95	7	function	function	NOUN
ejpam-811	95	8	φ(ζ	φ(ζ	ADV
ejpam-811	95	9	)	)	PUNCT
ejpam-811	95	10	=	=	SYM
ejpam-811	95	11	f	f	X
ejpam-811	95	12	(	(	PUNCT
ejpam-811	95	13	ζ	ζ	PROPN
ejpam-811	95	14	,	,	PUNCT
ejpam-811	95	15	η	η	NOUN
ejpam-811	95	16	)	)	PUNCT
ejpam-811	95	17	+	+	NUM
ejpam-811	95	18	zhaw	zhaw	NOUN
ejpam-811	95	19	+	+	CCONJ
ejpam-811	95	20	〈	〈	NOUN
ejpam-811	95	21	h(ζ),µ	h(ζ),µ	NOUN
ejpam-811	95	22	〉	〉	NOUN
ejpam-811	95	23	is	be	AUX
ejpam-811	95	24	differentiable	differentiable	ADJ
ejpam-811	95	25	at	at	ADP
ejpam-811	95	26	ζ0	ζ0	PROPN
ejpam-811	95	27	=	=	SYM
ejpam-811	95	28	(	(	PUNCT
ejpam-811	95	29	z0	z0	PROPN
ejpam-811	95	30	,	,	PUNCT
ejpam-811	95	31	z0	z0	PROPN
ejpam-811	95	32	)	)	PUNCT
ejpam-811	95	33	.	.	PUNCT
ejpam-811	96	1	then	then	ADV
ejpam-811	96	2	re[φ′(ζ0)(ζ−	re[φ′(ζ0)(ζ−	NOUN
ejpam-811	96	3	ζ0	ζ0	ADJ
ejpam-811	96	4	)	)	PUNCT
ejpam-811	96	5	]	]	PUNCT
ejpam-811	97	1	=	=	SYM
ejpam-811	97	2	re	re	X
ejpam-811	97	3	�	�	PROPN
ejpam-811	97	4	d	d	PROPN
ejpam-811	97	5	z	z	NOUN
ejpam-811	97	6	−	−	PROPN
ejpam-811	97	7	z0	z0	PROPN
ejpam-811	97	8	,	,	PUNCT
ejpam-811	97	9	∇z	∇z	PROPN
ejpam-811	97	10	f	f	NOUN
ejpam-811	97	11	(	(	PUNCT
ejpam-811	97	12	ζ0,η	ζ0,η	PROPN
ejpam-811	97	13	)	)	PUNCT
ejpam-811	97	14	+	+	PROPN
ejpam-811	97	15	∇z	∇z	ADJ
ejpam-811	97	16	f	f	X
ejpam-811	97	17	(	(	PUNCT
ejpam-811	97	18	ζ0,η	ζ0,η	PROPN
ejpam-811	97	19	)	)	PUNCT
ejpam-811	97	20	+	+	SYM
ejpam-811	97	21	aw+µt∇zh(ζ0	aw+µt∇zh(ζ0	NOUN
ejpam-811	97	22	)	)	PUNCT
ejpam-811	98	1	+	+	NOUN
ejpam-811	98	2	µ	µ	X
ejpam-811	98	3	h∇zh(ζ0	h∇zh(ζ0	PROPN
ejpam-811	98	4	)	)	PUNCT
ejpam-811	98	5	e	e	VERB
ejpam-811	98	6	�	�	PROPN
ejpam-811	98	7	.	.	PUNCT
ejpam-811	99	1	the	the	DET
ejpam-811	99	2	generalized	generalize	VERB
ejpam-811	99	3	schwarz	schwarz	NOUN
ejpam-811	99	4	inequality	inequality	NOUN
ejpam-811	99	5	in	in	ADP
ejpam-811	99	6	complex	complex	ADJ
ejpam-811	99	7	space	space	NOUN
ejpam-811	99	8	can	can	AUX
ejpam-811	99	9	be	be	AUX
ejpam-811	99	10	as	as	ADP
ejpam-811	99	11	the	the	DET
ejpam-811	99	12	inequality	inequality	NOUN
ejpam-811	99	13	:	:	PUNCT
ejpam-811	99	14	re(zhau)≤	re(zhau)≤	NUM
ejpam-811	99	15	(	(	PUNCT
ejpam-811	99	16	zhaz)1/2(uhau)1/2	zhaz)1/2(uhau)1/2	X
ejpam-811	99	17	.	.	PUNCT
ejpam-811	100	1	(	(	PUNCT
ejpam-811	100	2	1	1	X
ejpam-811	100	3	)	)	PUNCT
ejpam-811	100	4	4	4	NUM
ejpam-811	100	5	.	.	NOUN
ejpam-811	100	6	necessary	necessary	ADJ
ejpam-811	100	7	and	and	CCONJ
ejpam-811	100	8	sufficient	sufficient	ADJ
ejpam-811	100	9	optimality	optimality	NOUN
ejpam-811	100	10	conditions	condition	NOUN
ejpam-811	100	11	in	in	ADP
ejpam-811	100	12	lai	lai	PROPN
ejpam-811	100	13	et	et	PROPN
ejpam-811	100	14	al	al	PROPN
ejpam-811	100	15	.	.	PUNCT
ejpam-811	101	1	[	[	X
ejpam-811	101	2	3	3	NUM
ejpam-811	101	3	]	]	PUNCT
ejpam-811	101	4	,	,	PUNCT
ejpam-811	101	5	the	the	DET
ejpam-811	101	6	authors	author	NOUN
ejpam-811	101	7	have	have	AUX
ejpam-811	101	8	established	establish	VERB
ejpam-811	101	9	the	the	DET
ejpam-811	101	10	optimality	optimality	NOUN
ejpam-811	101	11	conditions	condition	NOUN
ejpam-811	101	12	.	.	PUNCT
ejpam-811	102	1	for	for	ADP
ejpam-811	102	2	convenient	convenient	ADJ
ejpam-811	102	3	,	,	PUNCT
ejpam-811	102	4	we	we	PRON
ejpam-811	102	5	restate	restate	VERB
ejpam-811	102	6	the	the	DET
ejpam-811	102	7	necessary	necessary	ADJ
ejpam-811	102	8	optimality	optimality	NOUN
ejpam-811	102	9	conditions	condition	NOUN
ejpam-811	102	10	as	as	SCONJ
ejpam-811	102	11	follows	follow	VERB
ejpam-811	102	12	.	.	PUNCT
ejpam-811	103	1	theorem	theorem	NOUN
ejpam-811	103	2	1	1	NUM
ejpam-811	103	3	.	.	PUNCT
ejpam-811	104	1	(	(	PUNCT
ejpam-811	104	2	necessary	necessary	ADJ
ejpam-811	104	3	optimality	optimality	NOUN
ejpam-811	104	4	conditions	condition	NOUN
ejpam-811	104	5	,	,	PUNCT
ejpam-811	104	6	[	[	X
ejpam-811	104	7	cf	cf	NOUN
ejpam-811	104	8	.	.	NOUN
ejpam-811	104	9	3	3	NUM
ejpam-811	104	10	,	,	PUNCT
ejpam-811	104	11	theorem	theorem	VERB
ejpam-811	104	12	2	2	NUM
ejpam-811	104	13	]	]	PUNCT
ejpam-811	104	14	)	)	PUNCT
ejpam-811	104	15	let	let	VERB
ejpam-811	104	16	ζ0	ζ0	NOUN
ejpam-811	104	17	=	=	SYM
ejpam-811	104	18	(	(	PUNCT
ejpam-811	104	19	z0	z0	PROPN
ejpam-811	104	20	,	,	PUNCT
ejpam-811	104	21	z0	z0	PROPN
ejpam-811	104	22	)	)	PUNCT
ejpam-811	104	23	∈	∈	PROPN
ejpam-811	104	24	q	q	AUX
ejpam-811	104	25	be	be	AUX
ejpam-811	104	26	a	a	DET
ejpam-811	104	27	(	(	PUNCT
ejpam-811	104	28	p)optimal	p)optimal	PROPN
ejpam-811	104	29	with	with	ADP
ejpam-811	104	30	optimal	optimal	ADJ
ejpam-811	104	31	value	value	NOUN
ejpam-811	104	32	v∗.	v∗.	PRON
ejpam-811	104	33	suppose	suppose	VERB
ejpam-811	104	34	that	that	SCONJ
ejpam-811	104	35	the	the	DET
ejpam-811	104	36	problem	problem	NOUN
ejpam-811	104	37	(	(	PUNCT
ejpam-811	104	38	p	p	NOUN
ejpam-811	104	39	)	)	PUNCT
ejpam-811	104	40	satisfies	satisfy	VERB
ejpam-811	104	41	the	the	DET
ejpam-811	104	42	constraint	constraint	NOUN
ejpam-811	104	43	qualification	qualification	NOUN
ejpam-811	104	44	at	at	ADP
ejpam-811	104	45	ζ0	ζ0	ADJ
ejpam-811	104	46	with	with	ADP
ejpam-811	104	47	assumptions	assumption	NOUN
ejpam-811	104	48	zh	zh	PROPN
ejpam-811	104	49	0	0	NUM
ejpam-811	104	50	az0	az0	NOUN
ejpam-811	104	51	=	=	PUNCT
ejpam-811	105	1	〈	〈	NOUN
ejpam-811	105	2	az0	az0	NOUN
ejpam-811	105	3	,	,	PUNCT
ejpam-811	105	4	z0	z0	NOUN
ejpam-811	105	5	〉	〉	NOUN
ejpam-811	105	6	>	>	X
ejpam-811	105	7	0	0	PUNCT
ejpam-811	105	8	and	and	CCONJ
ejpam-811	105	9	zh	zh	PROPN
ejpam-811	105	10	0	0	PROPN
ejpam-811	105	11	bz0	bz0	ADV
ejpam-811	105	12	=	=	SYM
ejpam-811	105	13	〈	〈	NOUN
ejpam-811	105	14	bz0	bz0	NUM
ejpam-811	105	15	,	,	PUNCT
ejpam-811	105	16	z0	z0	NOUN
ejpam-811	105	17	〉	〉	NOUN
ejpam-811	105	18	>	>	X
ejpam-811	105	19	0	0	X
ejpam-811	105	20	.	.	PUNCT
ejpam-811	106	1	then	then	ADV
ejpam-811	106	2	there	there	PRON
ejpam-811	106	3	exist	exist	VERB
ejpam-811	106	4	0	0	NUM
ejpam-811	106	5	6=	6=	NUM
ejpam-811	106	6	µ	µ	X
ejpam-811	106	7	∈	∈	NOUN
ejpam-811	106	8	s∗	s∗	PROPN
ejpam-811	106	9	⊂	⊂	PROPN
ejpam-811	106	10	cp	cp	PROPN
ejpam-811	106	11	,	,	PUNCT
ejpam-811	106	12	u1,u2	u1,u2	PROPN
ejpam-811	106	13	∈	∈	PROPN
ejpam-811	106	14	c	c	NOUN
ejpam-811	106	15	n	n	NOUN
ejpam-811	106	16	and	and	CCONJ
ejpam-811	106	17	positive	positive	ADJ
ejpam-811	106	18	integer	integer	NOUN
ejpam-811	106	19	k	k	PROPN
ejpam-811	106	20	with	with	ADP
ejpam-811	106	21	the	the	DET
ejpam-811	106	22	following	follow	VERB
ejpam-811	106	23	properties	property	NOUN
ejpam-811	106	24	(	(	PUNCT
ejpam-811	106	25	as	as	ADP
ejpam-811	106	26	y	y	PROPN
ejpam-811	106	27	(	(	PUNCT
ejpam-811	106	28	ζ0)⊂	ζ0)⊂	NOUN
ejpam-811	106	29	y	y	PROPN
ejpam-811	106	30	is	be	AUX
ejpam-811	106	31	provided	provide	VERB
ejpam-811	106	32	a	a	DET
ejpam-811	106	33	compact	compact	ADJ
ejpam-811	106	34	subset	subset	NOUN
ejpam-811	106	35	in	in	ADP
ejpam-811	106	36	c2	c2	PROPN
ejpam-811	106	37	m	m	PROPN
ejpam-811	106	38	):	):	PUNCT
ejpam-811	106	39	(	(	PUNCT
ejpam-811	106	40	i	i	NOUN
ejpam-811	106	41	)	)	PUNCT
ejpam-811	106	42	finite	finite	PROPN
ejpam-811	106	43	points	point	NOUN
ejpam-811	106	44	ηi	ηi	PROPN
ejpam-811	106	45	∈	∈	PROPN
ejpam-811	106	46	y	y	PROPN
ejpam-811	106	47	(	(	PUNCT
ejpam-811	106	48	ζ0	ζ0	PROPN
ejpam-811	106	49	)	)	PUNCT
ejpam-811	106	50	for	for	ADP
ejpam-811	106	51	i	i	PROPN
ejpam-811	106	52	=	=	SYM
ejpam-811	106	53	1	1	NUM
ejpam-811	106	54	,	,	PUNCT
ejpam-811	106	55	·	·	PUNCT
ejpam-811	106	56	·	·	PUNCT
ejpam-811	106	57	·	·	PUNCT
ejpam-811	106	58	,	,	PUNCT
ejpam-811	106	59	k	k	X
ejpam-811	106	60	;	;	PUNCT
ejpam-811	106	61	(	(	PUNCT
ejpam-811	106	62	ii	ii	NOUN
ejpam-811	106	63	)	)	PUNCT
ejpam-811	106	64	for	for	ADP
ejpam-811	106	65	i	i	PROPN
ejpam-811	106	66	=	=	NOUN
ejpam-811	106	67	1	1	NUM
ejpam-811	106	68	,	,	PUNCT
ejpam-811	106	69	·	·	PUNCT
ejpam-811	106	70	·	·	PUNCT
ejpam-811	106	71	·	·	PUNCT
ejpam-811	106	72	,	,	PUNCT
ejpam-811	106	73	k	k	X
ejpam-811	106	74	,	,	PUNCT
ejpam-811	106	75	multipliers	multiplier	NOUN
ejpam-811	106	76	λi	λi	INTJ
ejpam-811	106	77	>	>	X
ejpam-811	106	78	0	0	PUNCT
ejpam-811	107	1	and	and	CCONJ
ejpam-811	107	2	∑k	∑k	PROPN
ejpam-811	107	3	i=1λi	i=1λi	X
ejpam-811	108	1	=	=	SYM
ejpam-811	108	2	1	1	NUM
ejpam-811	108	3	such	such	ADJ
ejpam-811	108	4	that	that	SCONJ
ejpam-811	108	5	∑k	∑k	PROPN
ejpam-811	108	6	i=1λi	i=1λi	PROPN
ejpam-811	108	7	[	[	X
ejpam-811	108	8	f	f	X
ejpam-811	108	9	(	(	PUNCT
ejpam-811	108	10	ζ	ζ	NOUN
ejpam-811	108	11	,	,	PUNCT
ejpam-811	108	12	ηi)−	ηi)−	PUNCT
ejpam-811	108	13	v∗g(ζ	v∗g(ζ	PROPN
ejpam-811	108	14	,	,	PUNCT
ejpam-811	108	15	ηi	ηi	PROPN
ejpam-811	108	16	)	)	PUNCT
ejpam-811	108	17	]	]	PUNCT
ejpam-811	109	1	+	+	CCONJ
ejpam-811	109	2	〈	〈	PROPN
ejpam-811	109	3	h(ζ),µ〉+	h(ζ),µ〉+	PROPN
ejpam-811	109	4	〈	〈	PROPN
ejpam-811	109	5	az	az	PROPN
ejpam-811	109	6	,	,	PUNCT
ejpam-811	109	7	z〉1/2	z〉1/2	PROPN
ejpam-811	109	8	+	+	CCONJ
ejpam-811	109	9	v∗〈bz	v∗〈bz	ADJ
ejpam-811	109	10	,	,	PUNCT
ejpam-811	109	11	z〉1/2	z〉1/2	NOUN
ejpam-811	109	12	satisfies	satisfy	VERB
ejpam-811	109	13	the	the	DET
ejpam-811	109	14	following	follow	VERB
ejpam-811	109	15	conditions	condition	NOUN
ejpam-811	109	16	k∑	k∑	VERB
ejpam-811	109	17	i=1	i=1	PROPN
ejpam-811	110	1	λi	λi	PROPN
ejpam-811	110	2	�	�	PROPN
ejpam-811	110	3	h	h	PROPN
ejpam-811	110	4	∇z	∇z	PROPN
ejpam-811	110	5	f	f	PROPN
ejpam-811	110	6	(	(	PUNCT
ejpam-811	110	7	ζ0,ηi	ζ0,ηi	PROPN
ejpam-811	110	8	)	)	PUNCT
ejpam-811	111	1	+	+	PROPN
ejpam-811	111	2	∇z	∇z	ADJ
ejpam-811	111	3	f	f	X
ejpam-811	111	4	(	(	PUNCT
ejpam-811	111	5	ζ0,ηi	ζ0,ηi	PROPN
ejpam-811	111	6	)	)	PUNCT
ejpam-811	112	1	i	i	PRON
ejpam-811	112	2	−	−	VERB
ejpam-811	112	3	v∗	v∗	PROPN
ejpam-811	112	4	h	h	NOUN
ejpam-811	112	5	∇z	∇z	PROPN
ejpam-811	112	6	g(ζ0,ηi	g(ζ0,ηi	NUM
ejpam-811	112	7	)	)	PUNCT
ejpam-811	113	1	+	+	X
ejpam-811	113	2	∇z	∇z	NOUN
ejpam-811	113	3	g(ζ0,ηi	g(ζ0,ηi	NUM
ejpam-811	113	4	)	)	PUNCT
ejpam-811	114	1	i	i	PRON
ejpam-811	114	2	�	�	PROPN
ejpam-811	114	3	+	+	CCONJ
ejpam-811	114	4	�	�	PROPN
ejpam-811	114	5	µt∇zh(ζ0	µt∇zh(ζ0	PROPN
ejpam-811	114	6	)	)	PUNCT
ejpam-811	115	1	+	+	ADP
ejpam-811	115	2	µ	µ	X
ejpam-811	115	3	h∇zh(ζ0	h∇zh(ζ0	PROPN
ejpam-811	115	4	)	)	PUNCT
ejpam-811	115	5	�	�	PROPN
ejpam-811	115	6	+	+	CCONJ
ejpam-811	115	7	�	�	PROPN
ejpam-811	115	8	au1	au1	PROPN
ejpam-811	115	9	+	+	PROPN
ejpam-811	115	10	v∗bu2	v∗bu2	NUM
ejpam-811	115	11	�	�	PROPN
ejpam-811	115	12	=	=	SYM
ejpam-811	115	13	0	0	NUM
ejpam-811	115	14	;	;	PUNCT
ejpam-811	115	15	(	(	PUNCT
ejpam-811	115	16	2	2	X
ejpam-811	115	17	)	)	PUNCT
ejpam-811	115	18	re	re	VERB
ejpam-811	115	19	〈	〈	PROPN
ejpam-811	115	20	h(ζ0),µ	h(ζ0),µ	PROPN
ejpam-811	115	21	〉	〉	NOUN
ejpam-811	115	22	=	=	SYM
ejpam-811	115	23	0	0	NUM
ejpam-811	116	1	;	;	PUNCT
ejpam-811	116	2	(	(	PUNCT
ejpam-811	116	3	3	3	X
ejpam-811	116	4	)	)	PUNCT
ejpam-811	116	5	h.	h.	PROPN
ejpam-811	116	6	lai	lai	PROPN
ejpam-811	116	7	,	,	PUNCT
ejpam-811	116	8	t.	t.	PROPN
ejpam-811	116	9	huang	huang	PROPN
ejpam-811	116	10	/	/	SYM
ejpam-811	116	11	eur	eur	PROPN
ejpam-811	116	12	.	.	PUNCT
ejpam-811	117	1	j.	j.	PROPN
ejpam-811	117	2	pure	pure	PROPN
ejpam-811	117	3	appl	appl	PROPN
ejpam-811	117	4	.	.	PROPN
ejpam-811	117	5	math	math	PROPN
ejpam-811	117	6	,	,	PUNCT
ejpam-811	117	7	3	3	NUM
ejpam-811	117	8	(	(	PUNCT
ejpam-811	117	9	2010	2010	NUM
ejpam-811	117	10	)	)	PUNCT
ejpam-811	117	11	,	,	PUNCT
ejpam-811	117	12	989	989	NUM
ejpam-811	117	13	-	-	SYM
ejpam-811	117	14	1005	1005	NUM
ejpam-811	117	15	994	994	NUM
ejpam-811	117	16	uh	uh	INTJ
ejpam-811	117	17	1	1	NUM
ejpam-811	117	18	au1	au1	PRON
ejpam-811	117	19	≤	≤	NUM
ejpam-811	117	20	1	1	NUM
ejpam-811	117	21	,	,	PUNCT
ejpam-811	117	22	(	(	PUNCT
ejpam-811	117	23	zh	zh	PART
ejpam-811	117	24	0	0	NUM
ejpam-811	117	25	az0	az0	NOUN
ejpam-811	117	26	)	)	PUNCT
ejpam-811	117	27	1/2	1/2	NUM
ejpam-811	117	28	=	=	SYM
ejpam-811	117	29	re(zh	re(zh	NOUN
ejpam-811	117	30	0	0	NUM
ejpam-811	117	31	au1	au1	NOUN
ejpam-811	117	32	)	)	PUNCT
ejpam-811	117	33	;	;	PUNCT
ejpam-811	117	34	(	(	PUNCT
ejpam-811	117	35	4	4	X
ejpam-811	117	36	)	)	PUNCT
ejpam-811	117	37	uh	uh	INTJ
ejpam-811	117	38	2	2	NUM
ejpam-811	117	39	bu2	bu2	X
ejpam-811	117	40	≤	≤	NOUN
ejpam-811	117	41	1	1	NUM
ejpam-811	117	42	,	,	PUNCT
ejpam-811	117	43	(	(	PUNCT
ejpam-811	117	44	zh	zh	INTJ
ejpam-811	117	45	0	0	NUM
ejpam-811	117	46	bz0	bz0	NUM
ejpam-811	117	47	)	)	PUNCT
ejpam-811	118	1	1/2	1/2	NUM
ejpam-811	118	2	=	=	SYM
ejpam-811	118	3	re(zh	re(zh	NOUN
ejpam-811	118	4	0	0	NUM
ejpam-811	118	5	bu2	bu2	NOUN
ejpam-811	118	6	)	)	PUNCT
ejpam-811	118	7	.	.	PUNCT
ejpam-811	119	1	(	(	PUNCT
ejpam-811	119	2	5	5	X
ejpam-811	119	3	)	)	PUNCT
ejpam-811	119	4	in	in	ADP
ejpam-811	119	5	order	order	NOUN
ejpam-811	119	6	to	to	PART
ejpam-811	119	7	get	get	VERB
ejpam-811	119	8	the	the	DET
ejpam-811	119	9	necessary	necessary	ADJ
ejpam-811	119	10	optimality	optimality	NOUN
ejpam-811	119	11	conditions	condition	NOUN
ejpam-811	119	12	of	of	ADP
ejpam-811	119	13	(	(	PUNCT
ejpam-811	119	14	p	p	NOUN
ejpam-811	119	15	)	)	PUNCT
ejpam-811	119	16	for	for	ADP
ejpam-811	119	17	nonsmooth	nonsmooth	ADJ
ejpam-811	119	18	situation	situation	NOUN
ejpam-811	119	19	at	at	ADP
ejpam-811	119	20	ζ0	ζ0	PROPN
ejpam-811	119	21	=	=	SYM
ejpam-811	119	22	(	(	PUNCT
ejpam-811	119	23	z0	z0	PROPN
ejpam-811	119	24	,	,	PUNCT
ejpam-811	119	25	z0	z0	PROPN
ejpam-811	119	26	)	)	PUNCT
ejpam-811	119	27	∈	∈	PROPN
ejpam-811	120	1	q	q	NOUN
ejpam-811	120	2	,	,	PUNCT
ejpam-811	120	3	that	that	ADV
ejpam-811	120	4	is	is	ADV
ejpam-811	120	5	,	,	PUNCT
ejpam-811	120	6	if	if	SCONJ
ejpam-811	120	7	zh	zh	PROPN
ejpam-811	120	8	0	0	NUM
ejpam-811	120	9	az0	az0	NOUN
ejpam-811	121	1	=	=	NOUN
ejpam-811	121	2	0	0	NUM
ejpam-811	121	3	or	or	CCONJ
ejpam-811	121	4	zh	zh	INTJ
ejpam-811	121	5	0	0	NUM
ejpam-811	121	6	bz0	bz0	ADV
ejpam-811	121	7	=	=	SYM
ejpam-811	121	8	0	0	NUM
ejpam-811	121	9	,	,	PUNCT
ejpam-811	121	10	the	the	DET
ejpam-811	121	11	problem	problem	NOUN
ejpam-811	121	12	(	(	PUNCT
ejpam-811	121	13	p	p	NOUN
ejpam-811	121	14	)	)	PUNCT
ejpam-811	121	15	is	be	AUX
ejpam-811	121	16	a	a	DET
ejpam-811	121	17	complex	complex	ADJ
ejpam-811	121	18	nondifferentiable	nondifferentiable	ADJ
ejpam-811	121	19	minimax	minimax	NOUN
ejpam-811	121	20	programming	programming	NOUN
ejpam-811	121	21	.	.	PUNCT
ejpam-811	122	1	in	in	ADP
ejpam-811	122	2	this	this	DET
ejpam-811	122	3	case	case	NOUN
ejpam-811	122	4	,	,	PUNCT
ejpam-811	122	5	we	we	PRON
ejpam-811	122	6	define	define	VERB
ejpam-811	122	7	a	a	DET
ejpam-811	122	8	set	set	NOUN
ejpam-811	122	9	:	:	PUNCT
ejpam-811	122	10	zeη(ζ0	zeη(ζ0	X
ejpam-811	122	11	)	)	PUNCT
ejpam-811	122	12	=	=	SYM
ejpam-811	122	13	n	n	CCONJ
ejpam-811	122	14	ζ	ζ	PROPN
ejpam-811	122	15	∈	∈	PROPN
ejpam-811	122	16	c2n	c2n	NOUN
ejpam-811	122	17	�	�	PROPN
ejpam-811	122	18	�	�	PROPN
ejpam-811	122	19	�	�	PROPN
ejpam-811	122	20	−	−	PROPN
ejpam-811	122	21	h′ζ(ζ0)ζ	h′ζ(ζ0)ζ	PROPN
ejpam-811	122	22	∈	∈	PROPN
ejpam-811	122	23	s(−h(ζ0	s(−h(ζ0	NOUN
ejpam-811	122	24	)	)	PUNCT
ejpam-811	122	25	)	)	PUNCT
ejpam-811	122	26	,	,	PUNCT
ejpam-811	122	27	ζ	ζ	NOUN
ejpam-811	122	28	=	=	SYM
ejpam-811	122	29	(	(	PUNCT
ejpam-811	122	30	z	z	NOUN
ejpam-811	122	31	,	,	PUNCT
ejpam-811	122	32	z	z	NOUN
ejpam-811	122	33	)	)	PUNCT
ejpam-811	122	34	∈	∈	PROPN
ejpam-811	122	35	q	q	NOUN
ejpam-811	122	36	with	with	ADP
ejpam-811	122	37	any	any	DET
ejpam-811	122	38	one	one	NUM
ejpam-811	122	39	of	of	ADP
ejpam-811	122	40	the	the	DET
ejpam-811	122	41	next	next	ADJ
ejpam-811	122	42	conditions	condition	NOUN
ejpam-811	122	43	(	(	PUNCT
ejpam-811	122	44	i	i	NOUN
ejpam-811	122	45	)	)	PUNCT
ejpam-811	122	46	,	,	PUNCT
ejpam-811	122	47	(	(	PUNCT
ejpam-811	122	48	ii)and	ii)and	X
ejpam-811	122	49	(	(	PUNCT
ejpam-811	122	50	iii	iii	NOUN
ejpam-811	122	51	)	)	PUNCT
ejpam-811	122	52	holds	hold	VERB
ejpam-811	122	53	o	o	NOUN
ejpam-811	122	54	.	.	PUNCT
ejpam-811	123	1	(	(	PUNCT
ejpam-811	123	2	i	i	NOUN
ejpam-811	123	3	)	)	PUNCT
ejpam-811	123	4	re	re	ADP
ejpam-811	123	5	n	n	PROPN
ejpam-811	123	6	∑k	∑k	PROPN
ejpam-811	123	7	i=1λi	i=1λi	INTJ
ejpam-811	124	1	h	h	NOUN
ejpam-811	124	2	f	f	PROPN
ejpam-811	125	1	′	′	NUM
ejpam-811	125	2	ζ	ζ	NOUN
ejpam-811	125	3	(	(	PUNCT
ejpam-811	125	4	ζ0,ηi)−	ζ0,ηi)−	NOUN
ejpam-811	125	5	v∗g′	v∗g′	NOUN
ejpam-811	125	6	ζ	ζ	X
ejpam-811	125	7	(	(	PUNCT
ejpam-811	125	8	ζ0,ηi	ζ0,ηi	PROPN
ejpam-811	125	9	)	)	PUNCT
ejpam-811	126	1	i	i	PRON
ejpam-811	126	2	ζ+	ζ+	VERB
ejpam-811	126	3	〈	〈	ADJ
ejpam-811	126	4	az0,z	az0,z	ADJ
ejpam-811	126	5	〉	〉	NOUN
ejpam-811	126	6	〈	〈	NOUN
ejpam-811	126	7	az0,z0〉1/2	az0,z0〉1/2	PROPN
ejpam-811	126	8	+	+	CCONJ
ejpam-811	126	9	〈	〈	PROPN
ejpam-811	126	10	(	(	PUNCT
ejpam-811	126	11	v∗)2bz	v∗)2bz	ADJ
ejpam-811	126	12	,	,	PUNCT
ejpam-811	126	13	z〉1/2	z〉1/2	NOUN
ejpam-811	126	14	o	o	X
ejpam-811	126	15	<	<	X
ejpam-811	126	16	0	0	NUM
ejpam-811	126	17	,	,	PUNCT
ejpam-811	126	18	if	if	SCONJ
ejpam-811	126	19	zh	zh	PROPN
ejpam-811	126	20	0	0	NUM
ejpam-811	126	21	az0	az0	NOUN
ejpam-811	126	22	>	>	X
ejpam-811	126	23	0	0	PUNCT
ejpam-811	126	24	and	and	CCONJ
ejpam-811	126	25	zh	zh	PROPN
ejpam-811	126	26	0	0	PROPN
ejpam-811	126	27	bz0	bz0	ADV
ejpam-811	126	28	=	=	SYM
ejpam-811	126	29	0	0	NUM
ejpam-811	126	30	;	;	PUNCT
ejpam-811	126	31	(	(	PUNCT
ejpam-811	126	32	ii	ii	NOUN
ejpam-811	126	33	)	)	PUNCT
ejpam-811	126	34	re	re	ADP
ejpam-811	126	35	n	n	PROPN
ejpam-811	126	36	∑k	∑k	PROPN
ejpam-811	126	37	i=1λi	i=1λi	INTJ
ejpam-811	127	1	h	h	NOUN
ejpam-811	127	2	f	f	PROPN
ejpam-811	128	1	′	′	NUM
ejpam-811	128	2	ζ	ζ	NOUN
ejpam-811	128	3	(	(	PUNCT
ejpam-811	128	4	ζ0,ηi)−	ζ0,ηi)−	NOUN
ejpam-811	128	5	v∗g′	v∗g′	NOUN
ejpam-811	128	6	ζ	ζ	X
ejpam-811	128	7	(	(	PUNCT
ejpam-811	128	8	ζ0,ηi	ζ0,ηi	PROPN
ejpam-811	128	9	)	)	PUNCT
ejpam-811	129	1	i	i	PRON
ejpam-811	129	2	ζ+	ζ+	X
ejpam-811	129	3	〈	〈	PROPN
ejpam-811	129	4	az	az	PROPN
ejpam-811	129	5	,	,	PUNCT
ejpam-811	129	6	z〉1/2	z〉1/2	PROPN
ejpam-811	129	7	+	+	CCONJ
ejpam-811	129	8	〈	〈	PROPN
ejpam-811	129	9	v	v	ADJ
ejpam-811	129	10	∗bz0,z	∗bz0,z	NUM
ejpam-811	129	11	〉	〉	NOUN
ejpam-811	129	12	〈	〈	NOUN
ejpam-811	129	13	bz0,z0〉1/2	bz0,z0〉1/2	NOUN
ejpam-811	129	14	o	o	NOUN
ejpam-811	129	15	<	<	X
ejpam-811	129	16	0	0	PROPN
ejpam-811	129	17	,	,	PUNCT
ejpam-811	129	18	if	if	SCONJ
ejpam-811	129	19	zh	zh	PROPN
ejpam-811	129	20	0	0	NUM
ejpam-811	129	21	az0	az0	NOUN
ejpam-811	130	1	=	=	NOUN
ejpam-811	130	2	0	0	NUM
ejpam-811	130	3	and	and	CCONJ
ejpam-811	130	4	zh	zh	PROPN
ejpam-811	130	5	0	0	NUM
ejpam-811	130	6	bz0	bz0	ADV
ejpam-811	130	7	>	>	X
ejpam-811	130	8	0	0	NUM
ejpam-811	130	9	;	;	PUNCT
ejpam-811	130	10	(	(	PUNCT
ejpam-811	130	11	iii	iii	NOUN
ejpam-811	130	12	)	)	PUNCT
ejpam-811	130	13	re	re	X
ejpam-811	130	14	n	n	PROPN
ejpam-811	131	1	∑k	∑k	PROPN
ejpam-811	131	2	i=1λi	i=1λi	INTJ
ejpam-811	132	1	h	h	NOUN
ejpam-811	132	2	f	f	PROPN
ejpam-811	133	1	′	′	NUM
ejpam-811	133	2	ζ	ζ	NOUN
ejpam-811	133	3	(	(	PUNCT
ejpam-811	133	4	ζ0,ηi)−	ζ0,ηi)−	NOUN
ejpam-811	133	5	v∗g′	v∗g′	NOUN
ejpam-811	133	6	ζ	ζ	X
ejpam-811	133	7	(	(	PUNCT
ejpam-811	133	8	ζ0,ηi	ζ0,ηi	PROPN
ejpam-811	133	9	)	)	PUNCT
ejpam-811	134	1	i	i	PRON
ejpam-811	134	2	ζ+	ζ+	VERB
ejpam-811	134	3	〈	〈	PROPN
ejpam-811	134	4	[	[	X
ejpam-811	134	5	a+	a+	PUNCT
ejpam-811	134	6	(	(	PUNCT
ejpam-811	134	7	v∗)2b]z	v∗)2b]z	NOUN
ejpam-811	134	8	,	,	PUNCT
ejpam-811	134	9	z〉1/2	z〉1/2	NOUN
ejpam-811	134	10	o	o	X
ejpam-811	134	11	<	<	X
ejpam-811	134	12	0	0	NUM
ejpam-811	134	13	,	,	PUNCT
ejpam-811	134	14	if	if	SCONJ
ejpam-811	134	15	zh	zh	PROPN
ejpam-811	134	16	0	0	NUM
ejpam-811	134	17	az0	az0	NOUN
ejpam-811	135	1	=	=	NOUN
ejpam-811	135	2	0	0	NUM
ejpam-811	135	3	and	and	CCONJ
ejpam-811	135	4	zh	zh	PROPN
ejpam-811	135	5	0	0	PROPN
ejpam-811	135	6	bz0	bz0	ADV
ejpam-811	135	7	=	=	SYM
ejpam-811	135	8	0	0	X
ejpam-811	135	9	.	.	PUNCT
ejpam-811	136	1	this	this	DET
ejpam-811	136	2	set	set	ADJ
ejpam-811	136	3	zeη(ζ0	zeη(ζ0	NOUN
ejpam-811	136	4	)	)	PUNCT
ejpam-811	136	5	plays	play	VERB
ejpam-811	136	6	an	an	DET
ejpam-811	136	7	important	important	ADJ
ejpam-811	136	8	role	role	NOUN
ejpam-811	136	9	for	for	ADP
ejpam-811	136	10	the	the	DET
ejpam-811	136	11	cases	case	NOUN
ejpam-811	136	12	either	either	CCONJ
ejpam-811	136	13	〈	〈	PROPN
ejpam-811	136	14	az0	az0	NOUN
ejpam-811	136	15	,	,	PUNCT
ejpam-811	136	16	z0	z0	NOUN
ejpam-811	136	17	〉	〉	NOUN
ejpam-811	136	18	=	=	SYM
ejpam-811	136	19	0	0	NUM
ejpam-811	136	20	or	or	CCONJ
ejpam-811	136	21	〈	〈	PROPN
ejpam-811	136	22	bz0	bz0	NUM
ejpam-811	136	23	,	,	PUNCT
ejpam-811	136	24	z0	z0	NOUN
ejpam-811	136	25	〉	〉	NOUN
ejpam-811	136	26	=	=	SYM
ejpam-811	137	1	0	0	X
ejpam-811	137	2	.	.	PUNCT
ejpam-811	138	1	if	if	SCONJ
ejpam-811	138	2	the	the	DET
ejpam-811	138	3	set	set	NOUN
ejpam-811	138	4	zeη(ζ0	zeη(ζ0	NOUN
ejpam-811	138	5	)	)	PUNCT
ejpam-811	138	6	=	=	PUNCT
ejpam-811	138	7	;	;	PUNCT
ejpam-811	138	8	,	,	PUNCT
ejpam-811	138	9	then	then	ADV
ejpam-811	138	10	we	we	PRON
ejpam-811	138	11	can	can	AUX
ejpam-811	138	12	obtain	obtain	VERB
ejpam-811	138	13	the	the	DET
ejpam-811	138	14	necessary	necessary	ADJ
ejpam-811	138	15	optimality	optimality	NOUN
ejpam-811	138	16	conditions	condition	NOUN
ejpam-811	138	17	of	of	ADP
ejpam-811	138	18	problem	problem	NOUN
ejpam-811	138	19	(	(	PUNCT
ejpam-811	138	20	p	p	NOUN
ejpam-811	138	21	)	)	PUNCT
ejpam-811	138	22	as	as	ADP
ejpam-811	138	23	the	the	DET
ejpam-811	138	24	following	following	NOUN
ejpam-811	138	25	.	.	PUNCT
ejpam-811	139	1	theorem	theorem	NOUN
ejpam-811	139	2	2	2	NUM
ejpam-811	139	3	.	.	PUNCT
ejpam-811	140	1	(	(	PUNCT
ejpam-811	140	2	necessary	necessary	ADJ
ejpam-811	140	3	optimality	optimality	NOUN
ejpam-811	140	4	conditions	condition	NOUN
ejpam-811	140	5	,	,	PUNCT
ejpam-811	140	6	[	[	X
ejpam-811	140	7	cf	cf	NOUN
ejpam-811	140	8	.	.	NOUN
ejpam-811	140	9	3	3	NUM
ejpam-811	140	10	,	,	PUNCT
ejpam-811	140	11	theorem	theorem	VERB
ejpam-811	140	12	3	3	NUM
ejpam-811	140	13	]	]	PUNCT
ejpam-811	140	14	)	)	PUNCT
ejpam-811	140	15	let	let	VERB
ejpam-811	140	16	ζ0	ζ0	NOUN
ejpam-811	140	17	=	=	SYM
ejpam-811	140	18	(	(	PUNCT
ejpam-811	140	19	z0	z0	PROPN
ejpam-811	140	20	,	,	PUNCT
ejpam-811	140	21	z0	z0	PROPN
ejpam-811	140	22	)	)	PUNCT
ejpam-811	140	23	∈	∈	PROPN
ejpam-811	140	24	q	q	AUX
ejpam-811	140	25	be	be	AUX
ejpam-811	140	26	(	(	PUNCT
ejpam-811	140	27	p)-optimal	p)-optimal	ADJ
ejpam-811	140	28	with	with	ADP
ejpam-811	140	29	optimal	optimal	ADJ
ejpam-811	140	30	value	value	NOUN
ejpam-811	140	31	v∗.	v∗.	PRON
ejpam-811	140	32	suppose	suppose	VERB
ejpam-811	140	33	that	that	SCONJ
ejpam-811	140	34	problem	problem	NOUN
ejpam-811	140	35	(	(	PUNCT
ejpam-811	140	36	p	p	NOUN
ejpam-811	140	37	)	)	PUNCT
ejpam-811	140	38	possesses	possess	VERB
ejpam-811	140	39	constraint	constraint	NOUN
ejpam-811	140	40	qualification	qualification	NOUN
ejpam-811	140	41	at	at	ADP
ejpam-811	140	42	ζ0	ζ0	ADJ
ejpam-811	140	43	and	and	CCONJ
ejpam-811	140	44	zeη(ζ0	zeη(ζ0	NOUN
ejpam-811	140	45	)	)	PUNCT
ejpam-811	140	46	=	=	PUNCT
ejpam-811	140	47	;	;	PUNCT
ejpam-811	140	48	.	.	PUNCT
ejpam-811	141	1	then	then	ADV
ejpam-811	141	2	there	there	PRON
ejpam-811	141	3	exist	exist	VERB
ejpam-811	141	4	a	a	DET
ejpam-811	141	5	nonzero	nonzero	NOUN
ejpam-811	141	6	µ	µ	PRON
ejpam-811	141	7	∈	∈	NOUN
ejpam-811	141	8	s∗	s∗	PROPN
ejpam-811	141	9	⊂	⊂	PROPN
ejpam-811	141	10	cp	cp	INTJ
ejpam-811	141	11	and	and	CCONJ
ejpam-811	141	12	vectors	vector	NOUN
ejpam-811	141	13	u1,u2	u1,u2	PROPN
ejpam-811	141	14	∈	∈	PROPN
ejpam-811	141	15	c	c	NOUN
ejpam-811	141	16	n	n	PRON
ejpam-811	141	17	such	such	ADJ
ejpam-811	141	18	that	that	SCONJ
ejpam-811	141	19	the	the	DET
ejpam-811	141	20	conditions	condition	NOUN
ejpam-811	141	21	(	(	PUNCT
ejpam-811	141	22	2)s(5	2)s(5	NUM
ejpam-811	141	23	)	)	PUNCT
ejpam-811	141	24	hold	hold	VERB
ejpam-811	141	25	.	.	PUNCT
ejpam-811	142	1	we	we	PRON
ejpam-811	142	2	know	know	VERB
ejpam-811	142	3	that	that	SCONJ
ejpam-811	142	4	the	the	DET
ejpam-811	142	5	sufficient	sufficient	ADJ
ejpam-811	142	6	optimality	optimality	NOUN
ejpam-811	142	7	conditions	condition	NOUN
ejpam-811	142	8	for	for	ADP
ejpam-811	142	9	problem	problem	NOUN
ejpam-811	142	10	(	(	PUNCT
ejpam-811	142	11	p	p	NOUN
ejpam-811	142	12	)	)	PUNCT
ejpam-811	142	13	follows	follow	VERB
ejpam-811	142	14	from	from	ADP
ejpam-811	142	15	the	the	DET
ejpam-811	142	16	converse	converse	NOUN
ejpam-811	142	17	of	of	ADP
ejpam-811	142	18	necessary	necessary	ADJ
ejpam-811	142	19	optimality	optimality	NOUN
ejpam-811	142	20	conditions	condition	NOUN
ejpam-811	142	21	with	with	ADP
ejpam-811	142	22	extra	extra	ADJ
ejpam-811	142	23	assumptions	assumption	NOUN
ejpam-811	142	24	,	,	PUNCT
ejpam-811	142	25	thus	thus	ADV
ejpam-811	142	26	the	the	DET
ejpam-811	142	27	sufficient	sufficient	ADJ
ejpam-811	142	28	optimality	optimality	NOUN
ejpam-811	142	29	conditions	condition	NOUN
ejpam-811	142	30	are	be	AUX
ejpam-811	142	31	various	various	ADJ
ejpam-811	142	32	.	.	PUNCT
ejpam-811	143	1	the	the	DET
ejpam-811	143	2	additional	additional	ADJ
ejpam-811	143	3	assumptions	assumption	NOUN
ejpam-811	143	4	are	be	AUX
ejpam-811	143	5	convex	convex	ADJ
ejpam-811	143	6	as	as	ADV
ejpam-811	143	7	well	well	ADV
ejpam-811	143	8	as	as	ADP
ejpam-811	143	9	the	the	DET
ejpam-811	143	10	generalized	generalized	ADJ
ejpam-811	143	11	convexities	convexity	NOUN
ejpam-811	143	12	,	,	PUNCT
ejpam-811	143	13	for	for	ADP
ejpam-811	143	14	instance	instance	NOUN
ejpam-811	143	15	,	,	PUNCT
ejpam-811	143	16	we	we	PRON
ejpam-811	143	17	can	can	AUX
ejpam-811	143	18	state	state	VERB
ejpam-811	143	19	the	the	DET
ejpam-811	143	20	sufficient	sufficient	ADJ
ejpam-811	143	21	optimality	optimality	NOUN
ejpam-811	143	22	conditions	condition	NOUN
ejpam-811	143	23	of	of	ADP
ejpam-811	143	24	(	(	PUNCT
ejpam-811	143	25	p	p	NOUN
ejpam-811	143	26	)	)	PUNCT
ejpam-811	143	27	as	as	SCONJ
ejpam-811	143	28	follows	follow	VERB
ejpam-811	143	29	[	[	X
ejpam-811	143	30	cf	cf	NOUN
ejpam-811	143	31	.	.	NOUN
ejpam-811	143	32	3	3	NUM
ejpam-811	143	33	,	,	PUNCT
ejpam-811	143	34	theorem	theorem	VERB
ejpam-811	143	35	4	4	NUM
ejpam-811	143	36	]	]	PUNCT
ejpam-811	143	37	.	.	PUNCT
ejpam-811	144	1	theorem	theorem	ADJ
ejpam-811	144	2	3	3	NUM
ejpam-811	144	3	(	(	PUNCT
ejpam-811	144	4	sufficient	sufficient	ADJ
ejpam-811	144	5	optimality	optimality	NOUN
ejpam-811	144	6	conditions	condition	NOUN
ejpam-811	144	7	)	)	PUNCT
ejpam-811	144	8	.	.	PUNCT
ejpam-811	145	1	let	let	VERB
ejpam-811	145	2	ζ0	ζ0	NOUN
ejpam-811	145	3	=	=	SYM
ejpam-811	145	4	(	(	PUNCT
ejpam-811	145	5	z0	z0	PROPN
ejpam-811	145	6	,	,	PUNCT
ejpam-811	145	7	z0	z0	PROPN
ejpam-811	145	8	)	)	PUNCT
ejpam-811	145	9	∈	∈	PROPN
ejpam-811	145	10	q	q	AUX
ejpam-811	145	11	be	be	AUX
ejpam-811	145	12	a	a	DET
ejpam-811	145	13	feasible	feasible	ADJ
ejpam-811	145	14	solution	solution	NOUN
ejpam-811	145	15	of	of	ADP
ejpam-811	145	16	(	(	PUNCT
ejpam-811	145	17	p	p	NOUN
ejpam-811	145	18	)	)	PUNCT
ejpam-811	145	19	.	.	PUNCT
ejpam-811	146	1	suppose	suppose	VERB
ejpam-811	146	2	that	that	SCONJ
ejpam-811	146	3	there	there	PRON
ejpam-811	146	4	exist	exist	VERB
ejpam-811	146	5	a	a	DET
ejpam-811	146	6	positive	positive	ADJ
ejpam-811	146	7	integer	integer	NOUN
ejpam-811	147	1	k	k	PROPN
ejpam-811	147	2	>	>	PUNCT
ejpam-811	147	3	0	0	PROPN
ejpam-811	147	4	,	,	PUNCT
ejpam-811	147	5	v∗	v∗	PROPN
ejpam-811	147	6	∈	∈	PROPN
ejpam-811	147	7	r+	r+	NOUN
ejpam-811	147	8	,	,	PUNCT
ejpam-811	147	9	for	for	ADP
ejpam-811	147	10	i	i	PROPN
ejpam-811	147	11	=	=	SYM
ejpam-811	147	12	1	1	NUM
ejpam-811	147	13	,	,	PUNCT
ejpam-811	147	14	·	·	PUNCT
ejpam-811	147	15	·	·	PUNCT
ejpam-811	147	16	·	·	PUNCT
ejpam-811	147	17	,	,	PUNCT
ejpam-811	147	18	k	k	X
ejpam-811	147	19	,	,	PUNCT
ejpam-811	147	20	λi	λi	SYM
ejpam-811	147	21	>	>	X
ejpam-811	147	22	0	0	NUM
ejpam-811	147	23	,	,	PUNCT
ejpam-811	147	24	ηi	ηi	PROPN
ejpam-811	147	25	∈	∈	PROPN
ejpam-811	147	26	y	y	PROPN
ejpam-811	147	27	(	(	PUNCT
ejpam-811	147	28	ζ0	ζ0	PROPN
ejpam-811	147	29	)	)	PUNCT
ejpam-811	147	30	with	with	ADP
ejpam-811	147	31	∑k	∑k	PROPN
ejpam-811	147	32	i=1λi	i=1λi	X
ejpam-811	147	33	=	=	SYM
ejpam-811	147	34	1	1	NUM
ejpam-811	147	35	,	,	PUNCT
ejpam-811	147	36	and	and	CCONJ
ejpam-811	147	37	that	that	SCONJ
ejpam-811	147	38	0	0	X
ejpam-811	147	39	6=	6=	NUM
ejpam-811	147	40	µ	µ	PROPN
ejpam-811	147	41	∈	∈	NOUN
ejpam-811	147	42	s∗	s∗	PROPN
ejpam-811	147	43	⊂	⊂	PROPN
ejpam-811	147	44	cp	cp	PROPN
ejpam-811	147	45	,	,	PUNCT
ejpam-811	147	46	u1	u1	NOUN
ejpam-811	147	47	,	,	PUNCT
ejpam-811	147	48	u2	u2	PROPN
ejpam-811	147	49	∈	∈	PROPN
ejpam-811	147	50	c	c	NOUN
ejpam-811	147	51	n	n	CCONJ
ejpam-811	147	52	satisfying	satisfy	VERB
ejpam-811	147	53	conditions	condition	NOUN
ejpam-811	147	54	(	(	PUNCT
ejpam-811	147	55	2)s(5	2)s(5	NUM
ejpam-811	147	56	)	)	PUNCT
ejpam-811	147	57	of	of	ADP
ejpam-811	147	58	theorem	theorem	NOUN
ejpam-811	147	59	1	1	NUM
ejpam-811	147	60	for	for	ADP
ejpam-811	147	61	zeη(ζ0	zeη(ζ0	NOUN
ejpam-811	147	62	)	)	PUNCT
ejpam-811	147	63	=	=	PUNCT
ejpam-811	147	64	;	;	PUNCT
ejpam-811	147	65	.	.	PUNCT
ejpam-811	147	66	assume	assume	VERB
ejpam-811	147	67	that	that	SCONJ
ejpam-811	147	68	any	any	DET
ejpam-811	147	69	one	one	NUM
ejpam-811	147	70	of	of	ADP
ejpam-811	147	71	the	the	DET
ejpam-811	147	72	following	follow	VERB
ejpam-811	147	73	conditions	condition	NOUN
ejpam-811	147	74	(	(	PUNCT
ejpam-811	147	75	i	i	NOUN
ejpam-811	147	76	)	)	PUNCT
ejpam-811	147	77	,	,	PUNCT
ejpam-811	147	78	(	(	PUNCT
ejpam-811	147	79	ii	ii	NOUN
ejpam-811	147	80	)	)	PUNCT
ejpam-811	147	81	and	and	CCONJ
ejpam-811	147	82	(	(	PUNCT
ejpam-811	147	83	iii	iii	NOUN
ejpam-811	147	84	)	)	PUNCT
ejpam-811	147	85	holds	hold	VERB
ejpam-811	147	86	:	:	PUNCT
ejpam-811	147	87	(	(	PUNCT
ejpam-811	147	88	i	i	NOUN
ejpam-811	147	89	)	)	PUNCT
ejpam-811	147	90	re	re	VERB
ejpam-811	147	91	n∑k	n∑k	PROPN
ejpam-811	147	92	i=1λi	i=1λi	PROPN
ejpam-811	147	93	h	h	PROPN
ejpam-811	147	94	�	�	PROPN
ejpam-811	147	95	f	f	PROPN
ejpam-811	147	96	(	(	PUNCT
ejpam-811	147	97	ζ	ζ	PROPN
ejpam-811	147	98	,	,	PUNCT
ejpam-811	147	99	ηi	ηi	NOUN
ejpam-811	147	100	)	)	PUNCT
ejpam-811	147	101	+	+	CCONJ
ejpam-811	147	102	zhau1	zhau1	PROPN
ejpam-811	147	103	�	�	PROPN
ejpam-811	147	104	−	−	PROPN
ejpam-811	147	105	v∗	v∗	PROPN
ejpam-811	147	106	�	�	PROPN
ejpam-811	147	107	g(ζ	g(ζ	PROPN
ejpam-811	147	108	,	,	PUNCT
ejpam-811	147	109	ηi)−	ηi)−	PUNCT
ejpam-811	147	110	zh	zh	X
ejpam-811	147	111	bu2	bu2	X
ejpam-811	147	112	�	�	PROPN
ejpam-811	147	113	io	io	PROPN
ejpam-811	147	114	is	be	AUX
ejpam-811	147	115	pseudoconvex	pseudoconvex	NOUN
ejpam-811	147	116	on	on	ADP
ejpam-811	147	117	ζ	ζ	NOUN
ejpam-811	147	118	=	=	SYM
ejpam-811	147	119	(	(	PUNCT
ejpam-811	147	120	z	z	NOUN
ejpam-811	147	121	,	,	PUNCT
ejpam-811	147	122	z	z	NOUN
ejpam-811	147	123	)	)	PUNCT
ejpam-811	147	124	∈q	∈q	NOUN
ejpam-811	147	125	,	,	PUNCT
ejpam-811	147	126	and	and	CCONJ
ejpam-811	147	127	h(ζ	h(ζ	NOUN
ejpam-811	147	128	)	)	PUNCT
ejpam-811	147	129	is	be	AUX
ejpam-811	147	130	quasiconvex	quasiconvex	NOUN
ejpam-811	147	131	on	on	ADP
ejpam-811	147	132	q	q	PROPN
ejpam-811	147	133	w.r.t	w.r.t	NOUN
ejpam-811	147	134	.	.	PUNCT
ejpam-811	148	1	the	the	DET
ejpam-811	148	2	polyhedral	polyhedral	ADJ
ejpam-811	148	3	cone	cone	NOUN
ejpam-811	148	4	s	s	PROPN
ejpam-811	148	5	⊂	⊂	PROPN
ejpam-811	148	6	cp	cp	PROPN
ejpam-811	148	7	;	;	PUNCT
ejpam-811	148	8	h.	h.	PROPN
ejpam-811	148	9	lai	lai	PROPN
ejpam-811	148	10	,	,	PUNCT
ejpam-811	148	11	t.	t.	PROPN
ejpam-811	148	12	huang	huang	PROPN
ejpam-811	148	13	/	/	SYM
ejpam-811	148	14	eur	eur	PROPN
ejpam-811	148	15	.	.	PUNCT
ejpam-811	149	1	j.	j.	PROPN
ejpam-811	149	2	pure	pure	PROPN
ejpam-811	149	3	appl	appl	PROPN
ejpam-811	149	4	.	.	PROPN
ejpam-811	149	5	math	math	PROPN
ejpam-811	149	6	,	,	PUNCT
ejpam-811	149	7	3	3	NUM
ejpam-811	149	8	(	(	PUNCT
ejpam-811	149	9	2010	2010	NUM
ejpam-811	149	10	)	)	PUNCT
ejpam-811	149	11	,	,	PUNCT
ejpam-811	149	12	989	989	NUM
ejpam-811	149	13	-	-	SYM
ejpam-811	149	14	1005	1005	NUM
ejpam-811	149	15	995	995	NUM
ejpam-811	149	16	(	(	PUNCT
ejpam-811	149	17	ii	ii	NOUN
ejpam-811	149	18	)	)	PUNCT
ejpam-811	149	19	re	re	VERB
ejpam-811	149	20	n∑k	n∑k	PROPN
ejpam-811	149	21	i=1λi	i=1λi	PROPN
ejpam-811	149	22	h	h	PROPN
ejpam-811	149	23	�	�	PROPN
ejpam-811	149	24	f	f	PROPN
ejpam-811	149	25	(	(	PUNCT
ejpam-811	149	26	ζ	ζ	PROPN
ejpam-811	149	27	,	,	PUNCT
ejpam-811	149	28	ηi	ηi	NOUN
ejpam-811	149	29	)	)	PUNCT
ejpam-811	149	30	+	+	CCONJ
ejpam-811	149	31	zhau1	zhau1	PROPN
ejpam-811	149	32	�	�	PROPN
ejpam-811	149	33	−	−	PROPN
ejpam-811	149	34	v∗	v∗	PROPN
ejpam-811	149	35	�	�	PROPN
ejpam-811	149	36	g(ζ	g(ζ	PROPN
ejpam-811	149	37	,	,	PUNCT
ejpam-811	149	38	ηi)−	ηi)−	PUNCT
ejpam-811	149	39	zh	zh	X
ejpam-811	149	40	bu2	bu2	X
ejpam-811	149	41	�	�	PROPN
ejpam-811	149	42	io	io	PROPN
ejpam-811	149	43	is	be	AUX
ejpam-811	149	44	quasiconvex	quasiconvex	NOUN
ejpam-811	149	45	on	on	ADP
ejpam-811	149	46	ζ	ζ	NOUN
ejpam-811	149	47	=	=	SYM
ejpam-811	149	48	(	(	PUNCT
ejpam-811	149	49	z	z	NOUN
ejpam-811	149	50	,	,	PUNCT
ejpam-811	149	51	z	z	NOUN
ejpam-811	149	52	)	)	PUNCT
ejpam-811	149	53	∈q	∈q	NOUN
ejpam-811	149	54	,	,	PUNCT
ejpam-811	149	55	and	and	CCONJ
ejpam-811	149	56	h(ζ	h(ζ	NOUN
ejpam-811	149	57	)	)	PUNCT
ejpam-811	149	58	is	be	AUX
ejpam-811	149	59	strictly	strictly	ADV
ejpam-811	149	60	pseudoconvex	pseudoconvex	NOUN
ejpam-811	149	61	on	on	ADP
ejpam-811	149	62	q	q	NOUN
ejpam-811	149	63	w.r.t	w.r.t	NOUN
ejpam-811	149	64	.	.	PUNCT
ejpam-811	150	1	s	s	PART
ejpam-811	151	1	⊂	⊂	PROPN
ejpam-811	151	2	cp	cp	PROPN
ejpam-811	151	3	;	;	PUNCT
ejpam-811	151	4	(	(	PUNCT
ejpam-811	151	5	iii	iii	NOUN
ejpam-811	151	6	)	)	PUNCT
ejpam-811	151	7	re	re	X
ejpam-811	151	8	n∑k	n∑k	PROPN
ejpam-811	151	9	i=1λi	i=1λi	PROPN
ejpam-811	151	10	h	h	PROPN
ejpam-811	151	11	�	�	PROPN
ejpam-811	151	12	f	f	PROPN
ejpam-811	151	13	(	(	PUNCT
ejpam-811	151	14	ζ	ζ	PROPN
ejpam-811	151	15	,	,	PUNCT
ejpam-811	151	16	ηi	ηi	NOUN
ejpam-811	151	17	)	)	PUNCT
ejpam-811	151	18	+	+	CCONJ
ejpam-811	151	19	zhau1	zhau1	PROPN
ejpam-811	151	20	�	�	PROPN
ejpam-811	151	21	−	−	PROPN
ejpam-811	151	22	v∗	v∗	PROPN
ejpam-811	151	23	�	�	PROPN
ejpam-811	151	24	g(ζ	g(ζ	PROPN
ejpam-811	151	25	,	,	PUNCT
ejpam-811	151	26	ηi)−	ηi)−	PUNCT
ejpam-811	151	27	zh	zh	X
ejpam-811	151	28	bu2	bu2	PROPN
ejpam-811	151	29	�	�	PROPN
ejpam-811	151	30	i	i	PROPN
ejpam-811	151	31	+	+	CCONJ
ejpam-811	151	32	〈	〈	PROPN
ejpam-811	151	33	h(ζ),µ	h(ζ),µ	NOUN
ejpam-811	151	34	〉	〉	NOUN
ejpam-811	151	35	o	o	NOUN
ejpam-811	151	36	is	be	AUX
ejpam-811	151	37	pseudoconvex	pseudoconvex	NOUN
ejpam-811	151	38	on	on	ADP
ejpam-811	151	39	ζ	ζ	NOUN
ejpam-811	151	40	=	=	SYM
ejpam-811	151	41	(	(	PUNCT
ejpam-811	151	42	z	z	NOUN
ejpam-811	151	43	,	,	PUNCT
ejpam-811	151	44	z	z	NOUN
ejpam-811	151	45	)	)	PUNCT
ejpam-811	151	46	∈	∈	PROPN
ejpam-811	151	47	q.	q.	NOUN
ejpam-811	151	48	then	then	ADV
ejpam-811	151	49	ζ0	ζ0	PROPN
ejpam-811	151	50	=	=	SYM
ejpam-811	151	51	(	(	PUNCT
ejpam-811	151	52	z0	z0	PROPN
ejpam-811	151	53	,	,	PUNCT
ejpam-811	151	54	z0	z0	PROPN
ejpam-811	151	55	)	)	PUNCT
ejpam-811	151	56	is	be	AUX
ejpam-811	151	57	an	an	DET
ejpam-811	151	58	optimal	optimal	ADJ
ejpam-811	151	59	solution	solution	NOUN
ejpam-811	151	60	of	of	ADP
ejpam-811	151	61	(	(	PUNCT
ejpam-811	151	62	p	p	NOUN
ejpam-811	151	63	)	)	PUNCT
ejpam-811	151	64	.	.	PUNCT
ejpam-811	152	1	5	5	X
ejpam-811	152	2	.	.	X
ejpam-811	152	3	wolfe	wolfe	PROPN
ejpam-811	152	4	type	type	PROPN
ejpam-811	152	5	dual	dual	ADJ
ejpam-811	152	6	model	model	NOUN
ejpam-811	152	7	in	in	ADP
ejpam-811	152	8	order	order	NOUN
ejpam-811	152	9	to	to	PART
ejpam-811	152	10	construct	construct	VERB
ejpam-811	152	11	a	a	DET
ejpam-811	152	12	duality	duality	NOUN
ejpam-811	152	13	problems	problem	NOUN
ejpam-811	152	14	respect	respect	VERB
ejpam-811	152	15	to	to	ADP
ejpam-811	152	16	the	the	DET
ejpam-811	152	17	primal	primal	ADJ
ejpam-811	152	18	problem	problem	NOUN
ejpam-811	152	19	(	(	PUNCT
ejpam-811	152	20	p	p	NOUN
ejpam-811	152	21	)	)	PUNCT
ejpam-811	152	22	,	,	PUNCT
ejpam-811	152	23	we	we	PRON
ejpam-811	152	24	take	take	VERB
ejpam-811	152	25	some	some	DET
ejpam-811	152	26	preparation	preparation	NOUN
ejpam-811	152	27	.	.	PUNCT
ejpam-811	153	1	let	let	VERB
ejpam-811	153	2	ζ	ζ	NOUN
ejpam-811	153	3	=	=	SYM
ejpam-811	153	4	(	(	PUNCT
ejpam-811	153	5	z	z	NOUN
ejpam-811	153	6	,	,	PUNCT
ejpam-811	153	7	z	z	NOUN
ejpam-811	153	8	)	)	PUNCT
ejpam-811	153	9	∈	∈	PROPN
ejpam-811	153	10	q	q	PROPN
ejpam-811	154	1	⊂	⊂	PUNCT
ejpam-811	154	2	c2n	c2n	NOUN
ejpam-811	154	3	be	be	AUX
ejpam-811	154	4	any	any	DET
ejpam-811	154	5	feasible	feasible	ADJ
ejpam-811	154	6	solution	solution	NOUN
ejpam-811	154	7	of	of	ADP
ejpam-811	154	8	problem	problem	NOUN
ejpam-811	154	9	(	(	PUNCT
ejpam-811	154	10	p	p	NOUN
ejpam-811	154	11	)	)	PUNCT
ejpam-811	154	12	.	.	PUNCT
ejpam-811	155	1	by	by	ADP
ejpam-811	155	2	the	the	DET
ejpam-811	155	3	compactness	compactness	NOUN
ejpam-811	155	4	of	of	ADP
ejpam-811	155	5	y	y	PROPN
ejpam-811	155	6	in	in	ADP
ejpam-811	155	7	(	(	PUNCT
ejpam-811	155	8	p	p	NOUN
ejpam-811	155	9	)	)	PUNCT
ejpam-811	155	10	,	,	PUNCT
ejpam-811	155	11	the	the	DET
ejpam-811	155	12	closed	closed	ADJ
ejpam-811	155	13	subset	subset	ADJ
ejpam-811	155	14	y	y	PROPN
ejpam-811	155	15	(	(	PUNCT
ejpam-811	155	16	ζ	ζ	NOUN
ejpam-811	155	17	)	)	PUNCT
ejpam-811	155	18	is	be	AUX
ejpam-811	155	19	also	also	ADV
ejpam-811	155	20	compact	compact	ADJ
ejpam-811	155	21	which	which	PRON
ejpam-811	155	22	is	be	AUX
ejpam-811	155	23	the	the	DET
ejpam-811	155	24	set	set	NOUN
ejpam-811	155	25	of	of	ADP
ejpam-811	155	26	points	point	NOUN
ejpam-811	155	27	in	in	ADP
ejpam-811	155	28	y	y	NOUN
ejpam-811	155	29	maximizing	maximize	VERB
ejpam-811	155	30	the	the	DET
ejpam-811	155	31	fractional	fractional	ADJ
ejpam-811	155	32	function	function	NOUN
ejpam-811	155	33	max	max	PROPN
ejpam-811	155	34	η∈y	η∈y	PROPN
ejpam-811	155	35	re	re	X
ejpam-811	155	36	�	�	PROPN
ejpam-811	155	37	f	f	PROPN
ejpam-811	155	38	(	(	PUNCT
ejpam-811	155	39	ζ	ζ	PROPN
ejpam-811	155	40	,	,	PUNCT
ejpam-811	155	41	η	η	NOUN
ejpam-811	155	42	)	)	PUNCT
ejpam-811	155	43	+	+	CCONJ
ejpam-811	155	44	(	(	PUNCT
ejpam-811	155	45	zhaz)1/2	zhaz)1/2	VERB
ejpam-811	155	46	�	�	PROPN
ejpam-811	155	47	re	re	NOUN
ejpam-811	155	48	�	�	PROPN
ejpam-811	155	49	g(ζ	g(ζ	PROPN
ejpam-811	155	50	,	,	PUNCT
ejpam-811	155	51	η)−	η)−	PROPN
ejpam-811	155	52	(	(	PUNCT
ejpam-811	155	53	zh	zh	PROPN
ejpam-811	155	54	bz)1/2	bz)1/2	PROPN
ejpam-811	155	55	�	�	PROPN
ejpam-811	155	56	at	at	ADP
ejpam-811	155	57	η1	η1	NOUN
ejpam-811	155	58	,	,	PUNCT
ejpam-811	155	59	η2	η2	NOUN
ejpam-811	155	60	,	,	PUNCT
ejpam-811	155	61	.	.	PUNCT
ejpam-811	155	62	.	.	PUNCT
ejpam-811	156	1	.	.	PUNCT
ejpam-811	157	1	,	,	PUNCT
ejpam-811	157	2	ηk	ηk	VERB
ejpam-811	157	3	for	for	ADP
ejpam-811	157	4	some	some	DET
ejpam-811	157	5	k	k	PROPN
ejpam-811	157	6	∈	∈	PROPN
ejpam-811	157	7	n.	n.	NOUN
ejpam-811	157	8	since	since	SCONJ
ejpam-811	157	9	for	for	ADP
ejpam-811	157	10	each	each	DET
ejpam-811	157	11	ζ	ζ	NOUN
ejpam-811	157	12	=	=	SYM
ejpam-811	157	13	(	(	PUNCT
ejpam-811	157	14	z	z	NOUN
ejpam-811	157	15	,	,	PUNCT
ejpam-811	157	16	z	z	NOUN
ejpam-811	157	17	)	)	PUNCT
ejpam-811	157	18	∈	∈	PROPN
ejpam-811	158	1	q	q	NOUN
ejpam-811	158	2	,	,	PUNCT
ejpam-811	158	3	the	the	DET
ejpam-811	158	4	functions	function	NOUN
ejpam-811	158	5	f	f	X
ejpam-811	158	6	(	(	PUNCT
ejpam-811	158	7	ζ	ζ	NOUN
ejpam-811	158	8	,	,	PUNCT
ejpam-811	158	9	·	·	PUNCT
ejpam-811	158	10	)	)	PUNCT
ejpam-811	158	11	and	and	CCONJ
ejpam-811	158	12	g(ζ	g(ζ	PROPN
ejpam-811	158	13	,	,	PUNCT
ejpam-811	158	14	·	·	PUNCT
ejpam-811	158	15	)	)	PUNCT
ejpam-811	158	16	are	be	AUX
ejpam-811	158	17	continuous	continuous	ADJ
ejpam-811	158	18	on	on	ADP
ejpam-811	158	19	y	y	PROPN
ejpam-811	158	20	.	.	PUNCT
ejpam-811	159	1	thus	thus	ADV
ejpam-811	159	2	one	one	NUM
ejpam-811	159	3	can	can	AUX
ejpam-811	159	4	show	show	VERB
ejpam-811	159	5	easily	easily	ADV
ejpam-811	159	6	that	that	SCONJ
ejpam-811	159	7	the	the	DET
ejpam-811	159	8	fractional	fractional	ADJ
ejpam-811	159	9	function	function	NOUN
ejpam-811	159	10	:	:	PUNCT
ejpam-811	159	11	ϕ(ζ)≡max	ϕ(ζ)≡max	PROPN
ejpam-811	159	12	η∈y	η∈y	PROPN
ejpam-811	159	13	re	re	X
ejpam-811	159	14	�	�	PROPN
ejpam-811	159	15	f	f	PROPN
ejpam-811	159	16	(	(	PUNCT
ejpam-811	159	17	ζ	ζ	PROPN
ejpam-811	159	18	,	,	PUNCT
ejpam-811	159	19	η	η	NOUN
ejpam-811	159	20	)	)	PUNCT
ejpam-811	159	21	+	+	CCONJ
ejpam-811	159	22	(	(	PUNCT
ejpam-811	159	23	zhaz)1/2	zhaz)1/2	VERB
ejpam-811	159	24	�	�	PROPN
ejpam-811	159	25	re	re	NOUN
ejpam-811	159	26	�	�	PROPN
ejpam-811	159	27	g(ζ	g(ζ	PROPN
ejpam-811	159	28	,	,	PUNCT
ejpam-811	159	29	η)−	η)−	PROPN
ejpam-811	159	30	(	(	PUNCT
ejpam-811	159	31	zh	zh	PROPN
ejpam-811	159	32	bz)1/2	bz)1/2	PROPN
ejpam-811	159	33	�	�	PROPN
ejpam-811	159	34	=	=	SYM
ejpam-811	159	35	k∑	k∑	PROPN
ejpam-811	159	36	i=1	i=1	PROPN
ejpam-811	159	37	λire	λire	PROPN
ejpam-811	160	1	�	�	PROPN
ejpam-811	160	2	f	f	PROPN
ejpam-811	160	3	(	(	PUNCT
ejpam-811	160	4	ζ	ζ	PROPN
ejpam-811	160	5	,	,	PUNCT
ejpam-811	160	6	ηi	ηi	PROPN
ejpam-811	160	7	)	)	PUNCT
ejpam-811	160	8	+	+	CCONJ
ejpam-811	160	9	(	(	PUNCT
ejpam-811	160	10	z	z	NOUN
ejpam-811	160	11	haz)1/2	haz)1/2	PROPN
ejpam-811	160	12	�	�	PROPN
ejpam-811	160	13	k∑	k∑	VERB
ejpam-811	160	14	i=1	i=1	PROPN
ejpam-811	160	15	λire	λire	PROPN
ejpam-811	160	16	�	�	PROPN
ejpam-811	160	17	g(ζ	g(ζ	PROPN
ejpam-811	160	18	,	,	PUNCT
ejpam-811	160	19	ηi)−	ηi)−	PUNCT
ejpam-811	160	20	(	(	PUNCT
ejpam-811	160	21	z	z	NOUN
ejpam-811	160	22	h	h	PROPN
ejpam-811	160	23	bz)1/2	bz)1/2	PROPN
ejpam-811	160	24	�	�	PROPN
ejpam-811	160	25	(	(	PUNCT
ejpam-811	160	26	6	6	NUM
ejpam-811	160	27	)	)	PUNCT
ejpam-811	160	28	and	and	CCONJ
ejpam-811	160	29	so	so	ADV
ejpam-811	160	30	the	the	DET
ejpam-811	160	31	problem	problem	NOUN
ejpam-811	160	32	(	(	PUNCT
ejpam-811	160	33	p	p	X
ejpam-811	160	34	)	)	PUNCT
ejpam-811	160	35	become	become	VERB
ejpam-811	160	36	(	(	PUNCT
ejpam-811	160	37	p	p	NOUN
ejpam-811	160	38	)	)	PUNCT
ejpam-811	160	39	min	min	NOUN
ejpam-811	160	40	ζ∈x	ζ∈x	NOUN
ejpam-811	160	41	ϕ(ζ	ϕ(ζ	PROPN
ejpam-811	160	42	)	)	PUNCT
ejpam-811	160	43	.	.	PUNCT
ejpam-811	161	1	based	base	VERB
ejpam-811	161	2	on	on	ADP
ejpam-811	161	3	the	the	DET
ejpam-811	161	4	optimality	optimality	NOUN
ejpam-811	161	5	conditions	condition	NOUN
ejpam-811	161	6	(	(	PUNCT
ejpam-811	161	7	2)∼(5	2)∼(5	NUM
ejpam-811	161	8	)	)	PUNCT
ejpam-811	161	9	in	in	ADP
ejpam-811	161	10	theorem	theorem	NOUN
ejpam-811	161	11	1	1	NUM
ejpam-811	161	12	as	as	ADV
ejpam-811	161	13	well	well	ADV
ejpam-811	161	14	as	as	ADP
ejpam-811	161	15	in	in	ADP
ejpam-811	161	16	theorem	theorem	NOUN
ejpam-811	161	17	2	2	NUM
ejpam-811	161	18	,	,	PUNCT
ejpam-811	161	19	the	the	DET
ejpam-811	161	20	existence	existence	NOUN
ejpam-811	161	21	of	of	ADP
ejpam-811	161	22	optimal	optimal	ADJ
ejpam-811	161	23	solution	solution	NOUN
ejpam-811	161	24	for	for	ADP
ejpam-811	161	25	problem	problem	NOUN
ejpam-811	161	26	(	(	PUNCT
ejpam-811	161	27	p	p	X
ejpam-811	161	28	)	)	PUNCT
ejpam-811	161	29	even	even	ADV
ejpam-811	161	30	(	(	PUNCT
ejpam-811	161	31	p	p	X
ejpam-811	161	32	)	)	PUNCT
ejpam-811	161	33	is	be	AUX
ejpam-811	161	34	a	a	DET
ejpam-811	161	35	nondifferentiable	nondifferentiable	ADJ
ejpam-811	161	36	minimax	minimax	NOUN
ejpam-811	161	37	programming	programming	NOUN
ejpam-811	161	38	problem	problem	NOUN
ejpam-811	161	39	with	with	ADP
ejpam-811	161	40	complex	complex	ADJ
ejpam-811	161	41	variables	variable	NOUN
ejpam-811	161	42	under	under	ADP
ejpam-811	161	43	some	some	DET
ejpam-811	161	44	generalized	generalized	ADJ
ejpam-811	161	45	convexities	convexity	NOUN
ejpam-811	161	46	has	have	AUX
ejpam-811	161	47	established	establish	VERB
ejpam-811	161	48	by	by	ADP
ejpam-811	161	49	theorem	theorem	NOUN
ejpam-811	161	50	3	3	NUM
ejpam-811	161	51	.	.	PUNCT
ejpam-811	161	52	by	by	ADP
ejpam-811	161	53	using	use	VERB
ejpam-811	161	54	the	the	DET
ejpam-811	161	55	optimality	optimality	NOUN
ejpam-811	161	56	conditions	condition	NOUN
ejpam-811	161	57	(	(	PUNCT
ejpam-811	161	58	2)∼(5	2)∼(5	NUM
ejpam-811	161	59	)	)	PUNCT
ejpam-811	161	60	and	and	CCONJ
ejpam-811	161	61	the	the	DET
ejpam-811	161	62	existence	existence	NOUN
ejpam-811	161	63	for	for	ADP
ejpam-811	161	64	optimal	optimal	ADJ
ejpam-811	161	65	solutions	solution	NOUN
ejpam-811	161	66	of	of	ADP
ejpam-811	161	67	problem	problem	NOUN
ejpam-811	161	68	(	(	PUNCT
ejpam-811	161	69	p	p	NOUN
ejpam-811	161	70	)	)	PUNCT
ejpam-811	161	71	,	,	PUNCT
ejpam-811	161	72	one	one	PRON
ejpam-811	161	73	may	may	AUX
ejpam-811	161	74	consider	consider	VERB
ejpam-811	161	75	the	the	DET
ejpam-811	161	76	duality	duality	NOUN
ejpam-811	161	77	model	model	NOUN
ejpam-811	161	78	with	with	ADP
ejpam-811	161	79	respect	respect	NOUN
ejpam-811	161	80	to	to	ADP
ejpam-811	161	81	the	the	DET
ejpam-811	161	82	primal	primal	ADJ
ejpam-811	161	83	problem	problem	NOUN
ejpam-811	161	84	(	(	PUNCT
ejpam-811	161	85	p	p	NOUN
ejpam-811	161	86	)	)	PUNCT
ejpam-811	161	87	.	.	PUNCT
ejpam-811	162	1	in	in	ADP
ejpam-811	162	2	this	this	DET
ejpam-811	162	3	section	section	NOUN
ejpam-811	162	4	,	,	PUNCT
ejpam-811	162	5	we	we	PRON
ejpam-811	162	6	would	would	AUX
ejpam-811	162	7	construct	construct	VERB
ejpam-811	162	8	the	the	DET
ejpam-811	162	9	wolfe	wolfe	PROPN
ejpam-811	162	10	type	type	NOUN
ejpam-811	162	11	dual	dual	ADJ
ejpam-811	162	12	in	in	ADP
ejpam-811	162	13	fractional	fractional	ADJ
ejpam-811	162	14	programming	programming	NOUN
ejpam-811	162	15	problem	problem	NOUN
ejpam-811	162	16	(	(	PUNCT
ejpam-811	162	17	wd	wd	PROPN
ejpam-811	162	18	)	)	PUNCT
ejpam-811	162	19	by	by	ADP
ejpam-811	162	20	considering	consider	VERB
ejpam-811	162	21	the	the	DET
ejpam-811	162	22	objective	objective	NOUN
ejpam-811	162	23	from	from	ADP
ejpam-811	162	24	the	the	DET
ejpam-811	162	25	original	original	ADJ
ejpam-811	162	26	fractional	fractional	ADJ
ejpam-811	162	27	functional	functional	NOUN
ejpam-811	162	28	added	add	VERB
ejpam-811	162	29	the	the	DET
ejpam-811	162	30	constraints	constraint	NOUN
ejpam-811	162	31	of	of	ADP
ejpam-811	162	32	(	(	PUNCT
ejpam-811	162	33	p	p	NOUN
ejpam-811	162	34	)	)	PUNCT
ejpam-811	162	35	with	with	ADP
ejpam-811	162	36	a	a	DET
ejpam-811	162	37	multiplier	multipli	ADJ
ejpam-811	162	38	µ	µ	PRON
ejpam-811	162	39	∈	∈	NOUN
ejpam-811	162	40	s∗	s∗	NOUN
ejpam-811	162	41	into	into	ADP
ejpam-811	162	42	the	the	DET
ejpam-811	162	43	numerator	numerator	NOUN
ejpam-811	162	44	of	of	ADP
ejpam-811	162	45	the	the	DET
ejpam-811	162	46	fractional	fractional	ADJ
ejpam-811	162	47	functional	functional	ADJ
ejpam-811	162	48	in	in	ADP
ejpam-811	162	49	(	(	PUNCT
ejpam-811	162	50	p	p	NOUN
ejpam-811	162	51	)	)	PUNCT
ejpam-811	162	52	.	.	PUNCT
ejpam-811	163	1	precisely	precisely	ADV
ejpam-811	163	2	it	it	PRON
ejpam-811	163	3	likes	like	VERB
ejpam-811	163	4	φ(ζ	φ(ζ	NOUN
ejpam-811	163	5	)	)	PUNCT
ejpam-811	164	1	=	=	PRON
ejpam-811	164	2	k∑	k∑	VERB
ejpam-811	164	3	i=1	i=1	PROPN
ejpam-811	164	4	λire	λire	PROPN
ejpam-811	165	1	�	�	PROPN
ejpam-811	165	2	f	f	PROPN
ejpam-811	165	3	(	(	PUNCT
ejpam-811	165	4	ζ	ζ	PROPN
ejpam-811	165	5	,	,	PUNCT
ejpam-811	165	6	ηi	ηi	PROPN
ejpam-811	165	7	)	)	PUNCT
ejpam-811	165	8	+	+	CCONJ
ejpam-811	165	9	(	(	PUNCT
ejpam-811	165	10	z	z	NOUN
ejpam-811	165	11	haz)1/2	haz)1/2	PROPN
ejpam-811	165	12	+	+	CCONJ
ejpam-811	165	13	〈	〈	PROPN
ejpam-811	165	14	h(ζ),µ	h(ζ),µ	NOUN
ejpam-811	165	15	〉	〉	ADJ
ejpam-811	165	16	�	�	PROPN
ejpam-811	165	17	k∑	k∑	PROPN
ejpam-811	165	18	i=1	i=1	PROPN
ejpam-811	165	19	λire	λire	PROPN
ejpam-811	165	20	�	�	PROPN
ejpam-811	165	21	g(ζ	g(ζ	PROPN
ejpam-811	165	22	,	,	PUNCT
ejpam-811	165	23	ηi)−	ηi)−	PUNCT
ejpam-811	165	24	(	(	PUNCT
ejpam-811	165	25	z	z	NOUN
ejpam-811	165	26	h	h	PROPN
ejpam-811	165	27	bz)1/2	bz)1/2	PROPN
ejpam-811	165	28	�	�	PROPN
ejpam-811	165	29	,	,	PUNCT
ejpam-811	165	30	(	(	PUNCT
ejpam-811	165	31	7	7	X
ejpam-811	165	32	)	)	PUNCT
ejpam-811	165	33	h.	h.	PROPN
ejpam-811	165	34	lai	lai	PROPN
ejpam-811	165	35	,	,	PUNCT
ejpam-811	165	36	t.	t.	PROPN
ejpam-811	165	37	huang	huang	PROPN
ejpam-811	165	38	/	/	SYM
ejpam-811	165	39	eur	eur	PROPN
ejpam-811	165	40	.	.	PUNCT
ejpam-811	166	1	j.	j.	PROPN
ejpam-811	166	2	pure	pure	PROPN
ejpam-811	166	3	appl	appl	PROPN
ejpam-811	166	4	.	.	PROPN
ejpam-811	166	5	math	math	PROPN
ejpam-811	166	6	,	,	PUNCT
ejpam-811	166	7	3	3	NUM
ejpam-811	166	8	(	(	PUNCT
ejpam-811	166	9	2010	2010	NUM
ejpam-811	166	10	)	)	PUNCT
ejpam-811	166	11	,	,	PUNCT
ejpam-811	166	12	989	989	NUM
ejpam-811	166	13	-	-	SYM
ejpam-811	166	14	1005	1005	NUM
ejpam-811	166	15	996	996	NUM
ejpam-811	166	16	and	and	CCONJ
ejpam-811	166	17	then	then	ADV
ejpam-811	166	18	maximize	maximize	VERB
ejpam-811	166	19	φ(ζ	φ(ζ	NOUN
ejpam-811	166	20	)	)	PUNCT
ejpam-811	166	21	under	under	ADP
ejpam-811	166	22	suitable	suitable	ADJ
ejpam-811	166	23	constraints	constraint	NOUN
ejpam-811	166	24	.	.	PUNCT
ejpam-811	167	1	in	in	ADP
ejpam-811	167	2	order	order	NOUN
ejpam-811	167	3	to	to	PART
ejpam-811	167	4	distinguish	distinguish	VERB
ejpam-811	167	5	the	the	DET
ejpam-811	167	6	feasible	feasible	ADJ
ejpam-811	167	7	variable	variable	ADJ
ejpam-811	167	8	ζ	ζ	NOUN
ejpam-811	167	9	=	=	SYM
ejpam-811	167	10	(	(	PUNCT
ejpam-811	167	11	z	z	NOUN
ejpam-811	167	12	,	,	PUNCT
ejpam-811	167	13	z	z	NOUN
ejpam-811	167	14	)	)	PUNCT
ejpam-811	167	15	∈	∈	PROPN
ejpam-811	167	16	q	q	X
ejpam-811	167	17	in	in	ADP
ejpam-811	167	18	(	(	PUNCT
ejpam-811	167	19	p	p	NOUN
ejpam-811	167	20	)	)	PUNCT
ejpam-811	167	21	from	from	ADP
ejpam-811	167	22	the	the	DET
ejpam-811	167	23	dual	dual	ADJ
ejpam-811	167	24	problem	problem	NOUN
ejpam-811	167	25	,	,	PUNCT
ejpam-811	167	26	we	we	PRON
ejpam-811	167	27	replace	replace	VERB
ejpam-811	167	28	the	the	DET
ejpam-811	167	29	variable	variable	NOUN
ejpam-811	167	30	in	in	ADP
ejpam-811	167	31	the	the	DET
ejpam-811	167	32	dual	dual	ADJ
ejpam-811	167	33	problem	problem	NOUN
ejpam-811	167	34	(	(	PUNCT
ejpam-811	167	35	wd	wd	PROPN
ejpam-811	167	36	)	)	PUNCT
ejpam-811	167	37	by	by	ADP
ejpam-811	167	38	ξ	ξ	PROPN
ejpam-811	167	39	.	.	PUNCT
ejpam-811	167	40	of	of	ADV
ejpam-811	167	41	course	course	ADV
ejpam-811	167	42	this	this	PRON
ejpam-811	167	43	ξ	ξ	X
ejpam-811	167	44	=	=	SYM
ejpam-811	167	45	(	(	PUNCT
ejpam-811	167	46	α	α	X
ejpam-811	167	47	,	,	PUNCT
ejpam-811	167	48	α	α	NOUN
ejpam-811	167	49	)	)	PUNCT
ejpam-811	167	50	∈	∈	PROPN
ejpam-811	167	51	q	q	X
ejpam-811	168	1	⊂	⊂	ADJ
ejpam-811	168	2	c2n	c2n	PRON
ejpam-811	168	3	still	still	ADV
ejpam-811	168	4	plays	play	VERB
ejpam-811	168	5	as	as	ADP
ejpam-811	168	6	a	a	DET
ejpam-811	168	7	feasible	feasible	ADJ
ejpam-811	168	8	solution	solution	NOUN
ejpam-811	168	9	of	of	ADP
ejpam-811	168	10	(	(	PUNCT
ejpam-811	168	11	p	p	NOUN
ejpam-811	168	12	)	)	PUNCT
ejpam-811	168	13	and	and	CCONJ
ejpam-811	168	14	also	also	ADV
ejpam-811	168	15	assumes	assume	VERB
ejpam-811	168	16	to	to	PART
ejpam-811	168	17	satisfy	satisfy	VERB
ejpam-811	168	18	the	the	DET
ejpam-811	168	19	necessary	necessary	ADJ
ejpam-811	168	20	conditions	condition	NOUN
ejpam-811	168	21	(	(	PUNCT
ejpam-811	168	22	2)∼(5	2)∼(5	NUM
ejpam-811	168	23	)	)	PUNCT
ejpam-811	168	24	.	.	PUNCT
ejpam-811	169	1	then	then	ADV
ejpam-811	169	2	we	we	PRON
ejpam-811	169	3	could	could	AUX
ejpam-811	169	4	constitute	constitute	VERB
ejpam-811	169	5	the	the	DET
ejpam-811	169	6	wolfe	wolfe	PROPN
ejpam-811	169	7	type	type	NOUN
ejpam-811	169	8	dual	dual	ADV
ejpam-811	169	9	as	as	SCONJ
ejpam-811	169	10	the	the	DET
ejpam-811	169	11	dual	dual	ADJ
ejpam-811	169	12	problem	problem	NOUN
ejpam-811	169	13	of	of	ADP
ejpam-811	169	14	(	(	PUNCT
ejpam-811	169	15	p	p	NOUN
ejpam-811	169	16	)	)	PUNCT
ejpam-811	169	17	as	as	ADP
ejpam-811	169	18	the	the	DET
ejpam-811	169	19	following	follow	VERB
ejpam-811	169	20	form	form	NOUN
ejpam-811	169	21	:	:	PUNCT
ejpam-811	169	22	(	(	PUNCT
ejpam-811	169	23	wd	wd	PROPN
ejpam-811	169	24	)	)	PUNCT
ejpam-811	169	25	max	max	NOUN
ejpam-811	169	26	(	(	PUNCT
ejpam-811	169	27	k	k	X
ejpam-811	169	28	,	,	PUNCT
ejpam-811	169	29	eλ	eλ	INTJ
ejpam-811	169	30	,	,	PUNCT
ejpam-811	169	31	eη)∈k(ξ	eη)∈k(ξ	ADJ
ejpam-811	169	32	)	)	PUNCT
ejpam-811	169	33	max	max	PROPN
ejpam-811	169	34	(	(	PUNCT
ejpam-811	169	35	ξ,µ,w1,w2)∈x1(k	ξ,µ,w1,w2)∈x1(k	PROPN
ejpam-811	169	36	,	,	PUNCT
ejpam-811	169	37	eλ	eλ	NOUN
ejpam-811	169	38	,	,	PUNCT
ejpam-811	169	39	eη	eη	NOUN
ejpam-811	169	40	)	)	PUNCT
ejpam-811	169	41	φ(ξ	φ(ξ	PROPN
ejpam-811	169	42	)	)	PUNCT
ejpam-811	169	43	where	where	SCONJ
ejpam-811	169	44	φ(ξ	φ(ξ	NOUN
ejpam-811	169	45	)	)	PUNCT
ejpam-811	169	46	defines	define	VERB
ejpam-811	169	47	a	a	DET
ejpam-811	169	48	fractional	fractional	ADJ
ejpam-811	169	49	functional	functional	ADJ
ejpam-811	169	50	as	as	ADP
ejpam-811	169	51	the	the	DET
ejpam-811	169	52	expression	expression	NOUN
ejpam-811	169	53	(	(	PUNCT
ejpam-811	169	54	7	7	X
ejpam-811	169	55	)	)	PUNCT
ejpam-811	169	56	replace	replace	VERB
ejpam-811	169	57	ζ	ζ	NOUN
ejpam-811	169	58	by	by	ADP
ejpam-811	169	59	ξ	ξ	NOUN
ejpam-811	169	60	.	.	PUNCT
ejpam-811	170	1	here	here	ADV
ejpam-811	170	2	(	(	PUNCT
ejpam-811	170	3	i	i	NOUN
ejpam-811	170	4	)	)	PUNCT
ejpam-811	170	5	k(ξ	k(ξ	X
ejpam-811	170	6	)	)	PUNCT
ejpam-811	170	7	stands	stand	VERB
ejpam-811	170	8	for	for	ADP
ejpam-811	170	9	a	a	DET
ejpam-811	170	10	set	set	NOUN
ejpam-811	170	11	of	of	ADP
ejpam-811	170	12	the	the	DET
ejpam-811	170	13	triplet	triplet	NOUN
ejpam-811	170	14	points	point	NOUN
ejpam-811	170	15	(	(	PUNCT
ejpam-811	170	16	k	k	X
ejpam-811	170	17	,	,	PUNCT
ejpam-811	170	18	λ	λ	PROPN
ejpam-811	170	19	,	,	PUNCT
ejpam-811	170	20	η	η	NOUN
ejpam-811	170	21	)	)	PUNCT
ejpam-811	170	22	satisfying	satisfy	VERB
ejpam-811	170	23	the	the	DET
ejpam-811	170	24	optimality	optimality	NOUN
ejpam-811	170	25	conditions	condition	NOUN
ejpam-811	170	26	of	of	ADP
ejpam-811	170	27	problem	problem	NOUN
ejpam-811	170	28	(	(	PUNCT
ejpam-811	170	29	p	p	NOUN
ejpam-811	170	30	)	)	PUNCT
ejpam-811	170	31	for	for	ADP
ejpam-811	170	32	any	any	DET
ejpam-811	170	33	given	give	VERB
ejpam-811	170	34	feasible	feasible	ADJ
ejpam-811	170	35	solutions	solution	NOUN
ejpam-811	170	36	ξ	ξ	X
ejpam-811	170	37	=	=	SYM
ejpam-811	170	38	(	(	PUNCT
ejpam-811	170	39	α	α	X
ejpam-811	170	40	,	,	PUNCT
ejpam-811	170	41	α	α	NOUN
ejpam-811	170	42	)	)	PUNCT
ejpam-811	170	43	∈	∈	PROPN
ejpam-811	171	1	q	q	NOUN
ejpam-811	171	2	,	,	PUNCT
ejpam-811	171	3	then	then	ADV
ejpam-811	171	4	there	there	PRON
ejpam-811	171	5	exist	exist	VERB
ejpam-811	171	6	a	a	DET
ejpam-811	171	7	nonzero	nonzero	NOUN
ejpam-811	171	8	multiplier	multipli	ADJ
ejpam-811	171	9	µ	µ	PROPN
ejpam-811	171	10	∈	∈	NOUN
ejpam-811	171	11	s∗	s∗	PROPN
ejpam-811	171	12	⊂	⊂	PROPN
ejpam-811	171	13	cp	cp	PROPN
ejpam-811	171	14	,	,	PUNCT
ejpam-811	171	15	the	the	DET
ejpam-811	171	16	dual	dual	ADJ
ejpam-811	171	17	cone	cone	NOUN
ejpam-811	171	18	of	of	ADP
ejpam-811	171	19	the	the	DET
ejpam-811	171	20	polyhedral	polyhedral	ADJ
ejpam-811	171	21	cone	cone	NOUN
ejpam-811	171	22	s	s	X
ejpam-811	171	23	in	in	ADP
ejpam-811	171	24	cp	cp	INTJ
ejpam-811	171	25	such	such	ADJ
ejpam-811	171	26	that	that	SCONJ
ejpam-811	171	27	〈	〈	PROPN
ejpam-811	171	28	v,µ	v,µ	PROPN
ejpam-811	171	29	〉	〉	X
ejpam-811	171	30	≥	≥	X
ejpam-811	171	31	0	0	NUM
ejpam-811	171	32	for	for	ADP
ejpam-811	171	33	any	any	DET
ejpam-811	171	34	v	v	NOUN
ejpam-811	171	35	∈	∈	NOUN
ejpam-811	171	36	s.	s.	PROPN
ejpam-811	171	37	thus	thus	ADV
ejpam-811	171	38	〈	〈	ADV
ejpam-811	171	39	h(ξ),µ	h(ξ),µ	NOUN
ejpam-811	171	40	〉	〉	ADJ
ejpam-811	171	41	≤	≤	NOUN
ejpam-811	171	42	0	0	NUM
ejpam-811	171	43	as	as	ADP
ejpam-811	171	44	−h(ξ	−h(ξ	NOUN
ejpam-811	171	45	)	)	PUNCT
ejpam-811	171	46	∈	∈	PROPN
ejpam-811	171	47	s	s	PART
ejpam-811	171	48	⊂	⊂	PROPN
ejpam-811	171	49	cp	cp	PROPN
ejpam-811	171	50	.	.	PROPN
ejpam-811	171	51	(	(	PUNCT
ejpam-811	171	52	ii	ii	NOUN
ejpam-811	171	53	)	)	PUNCT
ejpam-811	171	54	the	the	DET
ejpam-811	171	55	new	new	ADJ
ejpam-811	171	56	constraint	constraint	NOUN
ejpam-811	171	57	set	set	VERB
ejpam-811	171	58	x1(k	x1(k	PROPN
ejpam-811	171	59	,	,	PUNCT
ejpam-811	171	60	eλ	eλ	INTJ
ejpam-811	171	61	,	,	PUNCT
ejpam-811	171	62	eη	eη	NOUN
ejpam-811	171	63	)	)	PUNCT
ejpam-811	171	64	is	be	AUX
ejpam-811	171	65	the	the	DET
ejpam-811	171	66	set	set	NOUN
ejpam-811	171	67	of	of	ADP
ejpam-811	171	68	all	all	DET
ejpam-811	171	69	feasible	feasible	ADJ
ejpam-811	171	70	solution	solution	NOUN
ejpam-811	171	71	(	(	PUNCT
ejpam-811	171	72	ξ,µ	ξ,µ	NOUN
ejpam-811	171	73	,	,	PUNCT
ejpam-811	171	74	w1	w1	NOUN
ejpam-811	171	75	,	,	PUNCT
ejpam-811	171	76	w2	w2	NOUN
ejpam-811	171	77	)	)	PUNCT
ejpam-811	171	78	of	of	ADP
ejpam-811	171	79	(	(	PUNCT
ejpam-811	171	80	wd	wd	PROPN
ejpam-811	171	81	)	)	PUNCT
ejpam-811	171	82	.	.	PUNCT
ejpam-811	172	1	consequently	consequently	ADV
ejpam-811	172	2	,	,	PUNCT
ejpam-811	172	3	the	the	DET
ejpam-811	172	4	constraints	constraint	NOUN
ejpam-811	172	5	of	of	ADP
ejpam-811	172	6	(	(	PUNCT
ejpam-811	172	7	wd	wd	X
ejpam-811	172	8	)	)	PUNCT
ejpam-811	172	9	are	be	AUX
ejpam-811	172	10	as	as	ADP
ejpam-811	172	11	the	the	DET
ejpam-811	172	12	following	follow	VERB
ejpam-811	172	13	expression	expression	NOUN
ejpam-811	172	14	:	:	PUNCT
ejpam-811	172	15	for	for	ADP
ejpam-811	172	16	ξ=	ξ=	NOUN
ejpam-811	172	17	(	(	PUNCT
ejpam-811	172	18	α	α	NOUN
ejpam-811	172	19	,	,	PUNCT
ejpam-811	172	20	α	α	NOUN
ejpam-811	172	21	)	)	PUNCT
ejpam-811	172	22	∈q	∈q	NOUN
ejpam-811	172	23	⊂	⊂	PROPN
ejpam-811	172	24	c2n	c2n	PROPN
ejpam-811	172	25	,	,	PUNCT
ejpam-811	172	26	�	�	PROPN
ejpam-811	172	27	k∑	k∑	PROPN
ejpam-811	172	28	i=1	i=1	PROPN
ejpam-811	173	1	λi	λi	PROPN
ejpam-811	173	2	�	�	PROPN
ejpam-811	173	3	∇z	∇z	PROPN
ejpam-811	173	4	f	f	PROPN
ejpam-811	173	5	(	(	PUNCT
ejpam-811	173	6	ξ	ξ	PROPN
ejpam-811	173	7	,	,	PUNCT
ejpam-811	173	8	ηi	ηi	X
ejpam-811	173	9	)	)	PUNCT
ejpam-811	173	10	+	+	PROPN
ejpam-811	173	11	∇z	∇z	ADJ
ejpam-811	173	12	f	f	X
ejpam-811	173	13	(	(	PUNCT
ejpam-811	173	14	ξ	ξ	PROPN
ejpam-811	173	15	,	,	PUNCT
ejpam-811	173	16	ηi	ηi	PROPN
ejpam-811	173	17	)	)	PUNCT
ejpam-811	173	18	�	�	PROPN
ejpam-811	174	1	+	+	CCONJ
ejpam-811	174	2	aw1	aw1	PROPN
ejpam-811	174	3	+	+	PROPN
ejpam-811	174	4	µ	µ	PROPN
ejpam-811	174	5	t	t	PROPN
ejpam-811	174	6	∇zh(ξ	∇zh(ξ	PROPN
ejpam-811	174	7	)	)	PUNCT
ejpam-811	174	8	+	+	NOUN
ejpam-811	174	9	µh∇zh(ξ	µh∇zh(ξ	X
ejpam-811	174	10	)	)	PUNCT
ejpam-811	174	11	o	o	NOUN
ejpam-811	174	12	×	×	PROPN
ejpam-811	174	13	�	�	PROPN
ejpam-811	174	14	k∑	k∑	PROPN
ejpam-811	175	1	i=1	i=1	PROPN
ejpam-811	175	2	λi	λi	PROPN
ejpam-811	175	3	[	[	X
ejpam-811	175	4	g(ξ	g(ξ	PROPN
ejpam-811	175	5	,	,	PUNCT
ejpam-811	175	6	ηi)−	ηi)−	PUNCT
ejpam-811	175	7	(	(	PUNCT
ejpam-811	175	8	α	α	PROPN
ejpam-811	175	9	h	h	PROPN
ejpam-811	175	10	bα)1/2	bα)1/2	PROPN
ejpam-811	175	11	]	]	PUNCT
ejpam-811	175	12	�	�	PROPN
ejpam-811	176	1	−	−	PROPN
ejpam-811	176	2	�	�	PROPN
ejpam-811	176	3	k∑	k∑	VERB
ejpam-811	176	4	i=1	i=1	PROPN
ejpam-811	177	1	λi	λi	X
ejpam-811	177	2	[	[	PUNCT
ejpam-811	177	3	f	f	X
ejpam-811	177	4	(	(	PUNCT
ejpam-811	177	5	ξ	ξ	PROPN
ejpam-811	177	6	,	,	PUNCT
ejpam-811	177	7	ηi	ηi	X
ejpam-811	177	8	)	)	PUNCT
ejpam-811	178	1	+	+	CCONJ
ejpam-811	178	2	(	(	PUNCT
ejpam-811	178	3	α	α	PROPN
ejpam-811	178	4	haα)1/2	haα)1/2	PROPN
ejpam-811	178	5	+	+	CCONJ
ejpam-811	178	6	〈	〈	NOUN
ejpam-811	178	7	h(ξ),µ	h(ξ),µ	NOUN
ejpam-811	178	8	〉	〉	NOUN
ejpam-811	178	9	]	]	X
ejpam-811	178	10	�	�	PROPN
ejpam-811	178	11	×	×	PROPN
ejpam-811	178	12	�	�	PROPN
ejpam-811	178	13	k∑	k∑	PROPN
ejpam-811	178	14	i=1	i=1	PROPN
ejpam-811	179	1	λi	λi	ADP
ejpam-811	179	2	�	�	PROPN
ejpam-811	179	3	∇z	∇z	PROPN
ejpam-811	179	4	g(ξ	g(ξ	PROPN
ejpam-811	179	5	,	,	PUNCT
ejpam-811	179	6	ηi	ηi	X
ejpam-811	179	7	)	)	PUNCT
ejpam-811	180	1	+	+	PROPN
ejpam-811	180	2	∇z	∇z	PROPN
ejpam-811	180	3	g(ξ	g(ξ	PROPN
ejpam-811	180	4	,	,	PUNCT
ejpam-811	180	5	ηi	ηi	PROPN
ejpam-811	180	6	)	)	PUNCT
ejpam-811	180	7	�	�	PROPN
ejpam-811	180	8	−	−	PROPN
ejpam-811	180	9	bw2	bw2	PROPN
ejpam-811	180	10	�	�	PROPN
ejpam-811	180	11	=	=	SYM
ejpam-811	180	12	0	0	PROPN
ejpam-811	180	13	,	,	PUNCT
ejpam-811	180	14	(	(	PUNCT
ejpam-811	180	15	8)	8)	NUM
ejpam-811	180	16	re〈h(ξ),µ	re〈h(ξ),µ	X
ejpam-811	180	17	〉	〉	NOUN
ejpam-811	180	18	≥	≥	NUM
ejpam-811	180	19	0	0	NUM
ejpam-811	180	20	,	,	PUNCT
ejpam-811	180	21	µ	µ	X
ejpam-811	180	22	6=	6=	SYM
ejpam-811	180	23	0	0	NUM
ejpam-811	180	24	in	in	ADP
ejpam-811	180	25	s∗	s∗	PROPN
ejpam-811	180	26	,	,	PUNCT
ejpam-811	180	27	(	(	PUNCT
ejpam-811	180	28	9	9	X
ejpam-811	180	29	)	)	PUNCT
ejpam-811	180	30	wh	wh	NOUN
ejpam-811	180	31	1	1	NUM
ejpam-811	180	32	aw1	aw1	PROPN
ejpam-811	180	33	≤	≤	NUM
ejpam-811	180	34	1	1	NUM
ejpam-811	180	35	,	,	PUNCT
ejpam-811	180	36	(	(	PUNCT
ejpam-811	180	37	αhaα)1/2	αhaα)1/2	PROPN
ejpam-811	180	38	=	=	SYM
ejpam-811	180	39	re(αhaw1	re(αhaw1	PROPN
ejpam-811	180	40	)	)	PUNCT
ejpam-811	180	41	,	,	PUNCT
ejpam-811	180	42	(	(	PUNCT
ejpam-811	180	43	10	10	NUM
ejpam-811	180	44	)	)	PUNCT
ejpam-811	180	45	wh	wh	NOUN
ejpam-811	180	46	2	2	NUM
ejpam-811	180	47	bw2	bw2	PROPN
ejpam-811	180	48	≤	≤	PROPN
ejpam-811	180	49	1	1	NUM
ejpam-811	180	50	,	,	PUNCT
ejpam-811	180	51	(	(	PUNCT
ejpam-811	180	52	αh	αh	NOUN
ejpam-811	180	53	bα)1/2	bα)1/2	PROPN
ejpam-811	180	54	=	=	SYM
ejpam-811	180	55	re(αh	re(αh	PROPN
ejpam-811	180	56	bw2	bw2	PROPN
ejpam-811	180	57	)	)	PUNCT
ejpam-811	180	58	,	,	PUNCT
ejpam-811	180	59	(	(	PUNCT
ejpam-811	180	60	11	11	NUM
ejpam-811	180	61	)	)	PUNCT
ejpam-811	180	62	if	if	SCONJ
ejpam-811	180	63	for	for	ADP
ejpam-811	180	64	a	a	DET
ejpam-811	180	65	triplet	triplet	NOUN
ejpam-811	180	66	(	(	PUNCT
ejpam-811	180	67	k	k	X
ejpam-811	180	68	,	,	PUNCT
ejpam-811	180	69	eλ	eλ	INTJ
ejpam-811	180	70	,	,	PUNCT
ejpam-811	180	71	eη	eη	NOUN
ejpam-811	180	72	)	)	PUNCT
ejpam-811	180	73	∈	∈	PROPN
ejpam-811	180	74	k(ξ	k(ξ	PROPN
ejpam-811	180	75	)	)	PUNCT
ejpam-811	180	76	,	,	PUNCT
ejpam-811	180	77	the	the	DET
ejpam-811	180	78	set	set	NOUN
ejpam-811	180	79	x1(k	x1(k	PROPN
ejpam-811	180	80	,	,	PUNCT
ejpam-811	180	81	eλ	eλ	INTJ
ejpam-811	180	82	,	,	PUNCT
ejpam-811	180	83	eη	eη	NOUN
ejpam-811	180	84	)	)	PUNCT
ejpam-811	180	85	=	=	PUNCT
ejpam-811	180	86	;	;	PUNCT
ejpam-811	180	87	,	,	PUNCT
ejpam-811	180	88	then	then	ADV
ejpam-811	180	89	we	we	PRON
ejpam-811	180	90	define	define	VERB
ejpam-811	180	91	the	the	DET
ejpam-811	180	92	supremum	supremum	NOUN
ejpam-811	180	93	over	over	ADP
ejpam-811	180	94	x1(k	x1(k	PROPN
ejpam-811	180	95	,	,	PUNCT
ejpam-811	180	96	eλ	eλ	INTJ
ejpam-811	180	97	,	,	PUNCT
ejpam-811	180	98	eµ	eµ	NOUN
ejpam-811	180	99	)	)	PUNCT
ejpam-811	180	100	to	to	PART
ejpam-811	180	101	be	be	AUX
ejpam-811	180	102	−∞	−∞	X
ejpam-811	180	103	for	for	ADP
ejpam-811	180	104	non	non	ADJ
ejpam-811	180	105	exception	exception	NOUN
ejpam-811	180	106	in	in	ADP
ejpam-811	180	107	the	the	DET
ejpam-811	180	108	formulation	formulation	NOUN
ejpam-811	180	109	of	of	ADP
ejpam-811	180	110	(	(	PUNCT
ejpam-811	180	111	wd	wd	PROPN
ejpam-811	180	112	)	)	PUNCT
ejpam-811	180	113	.	.	PUNCT
ejpam-811	181	1	without	without	ADP
ejpam-811	181	2	loss	loss	NOUN
ejpam-811	181	3	of	of	ADP
ejpam-811	181	4	generality	generality	NOUN
ejpam-811	181	5	,	,	PUNCT
ejpam-811	181	6	we	we	PRON
ejpam-811	181	7	may	may	AUX
ejpam-811	181	8	assume	assume	VERB
ejpam-811	181	9	that	that	SCONJ
ejpam-811	181	10	k∑	k∑	VERB
ejpam-811	181	11	i=1	i=1	PROPN
ejpam-811	181	12	λire	λire	PROPN
ejpam-811	181	13	�	�	PROPN
ejpam-811	181	14	f	f	PROPN
ejpam-811	181	15	(	(	PUNCT
ejpam-811	181	16	ξ	ξ	PROPN
ejpam-811	181	17	,	,	PUNCT
ejpam-811	181	18	ηi	ηi	X
ejpam-811	181	19	)	)	PUNCT
ejpam-811	182	1	+	+	CCONJ
ejpam-811	182	2	(	(	PUNCT
ejpam-811	182	3	α	α	PROPN
ejpam-811	182	4	haα)1/2	haα)1/2	PROPN
ejpam-811	182	5	+	+	CCONJ
ejpam-811	182	6	〈	〈	NOUN
ejpam-811	182	7	h(ξ),µ	h(ξ),µ	ADJ
ejpam-811	182	8	〉	〉	ADJ
ejpam-811	182	9	�	�	PROPN
ejpam-811	182	10	≥	≥	NUM
ejpam-811	182	11	0	0	NUM
ejpam-811	182	12	and	and	CCONJ
ejpam-811	182	13	k∑	k∑	VERB
ejpam-811	182	14	i=1	i=1	PROPN
ejpam-811	182	15	λire	λire	PROPN
ejpam-811	182	16	�	�	PROPN
ejpam-811	182	17	g(ξ	g(ξ	PROPN
ejpam-811	182	18	,	,	PUNCT
ejpam-811	182	19	ηi)−	ηi)−	PUNCT
ejpam-811	182	20	(	(	PUNCT
ejpam-811	182	21	α	α	PROPN
ejpam-811	182	22	h	h	PROPN
ejpam-811	182	23	bα)1/2	bα)1/2	PROPN
ejpam-811	182	24	�	�	PROPN
ejpam-811	182	25	>	>	X
ejpam-811	182	26	0	0	PUNCT
ejpam-811	183	1	h.	h.	PROPN
ejpam-811	183	2	lai	lai	PROPN
ejpam-811	183	3	,	,	PUNCT
ejpam-811	183	4	t.	t.	PROPN
ejpam-811	183	5	huang	huang	PROPN
ejpam-811	183	6	/	/	SYM
ejpam-811	183	7	eur	eur	PROPN
ejpam-811	183	8	.	.	PUNCT
ejpam-811	184	1	j.	j.	PROPN
ejpam-811	184	2	pure	pure	PROPN
ejpam-811	184	3	appl	appl	PROPN
ejpam-811	184	4	.	.	PROPN
ejpam-811	184	5	math	math	PROPN
ejpam-811	184	6	,	,	PUNCT
ejpam-811	184	7	3	3	NUM
ejpam-811	184	8	(	(	PUNCT
ejpam-811	184	9	2010	2010	NUM
ejpam-811	184	10	)	)	PUNCT
ejpam-811	184	11	,	,	PUNCT
ejpam-811	184	12	989	989	NUM
ejpam-811	184	13	-	-	SYM
ejpam-811	184	14	1005	1005	NUM
ejpam-811	184	15	997	997	NUM
ejpam-811	184	16	for	for	ADP
ejpam-811	184	17	each	each	PRON
ejpam-811	184	18	(	(	PUNCT
ejpam-811	184	19	k	k	X
ejpam-811	184	20	,	,	PUNCT
ejpam-811	184	21	eλ	eλ	INTJ
ejpam-811	184	22	,	,	PUNCT
ejpam-811	184	23	eη	eη	NOUN
ejpam-811	184	24	)	)	PUNCT
ejpam-811	184	25	∈	∈	PROPN
ejpam-811	184	26	k(ξ	k(ξ	PROPN
ejpam-811	184	27	)	)	PUNCT
ejpam-811	184	28	,	,	PUNCT
ejpam-811	184	29	(	(	PUNCT
ejpam-811	184	30	ξ,µ	ξ,µ	NOUN
ejpam-811	184	31	,	,	PUNCT
ejpam-811	184	32	w1	w1	NOUN
ejpam-811	184	33	,	,	PUNCT
ejpam-811	184	34	w2	w2	NOUN
ejpam-811	184	35	)	)	PUNCT
ejpam-811	184	36	∈	∈	PROPN
ejpam-811	185	1	x1(k	x1(k	PROPN
ejpam-811	185	2	,	,	PUNCT
ejpam-811	185	3	eλ	eλ	INTJ
ejpam-811	185	4	,	,	PUNCT
ejpam-811	185	5	eη	eη	NOUN
ejpam-811	185	6	)	)	PUNCT
ejpam-811	185	7	.	.	PUNCT
ejpam-811	186	1	how	how	SCONJ
ejpam-811	186	2	we	we	PRON
ejpam-811	186	3	can	can	AUX
ejpam-811	186	4	approve	approve	VERB
ejpam-811	186	5	that	that	DET
ejpam-811	186	6	problem	problem	NOUN
ejpam-811	186	7	(	(	PUNCT
ejpam-811	186	8	wd	wd	X
ejpam-811	186	9	)	)	PUNCT
ejpam-811	186	10	is	be	AUX
ejpam-811	186	11	really	really	ADV
ejpam-811	186	12	a	a	DET
ejpam-811	186	13	dual	dual	ADJ
ejpam-811	186	14	problem	problem	NOUN
ejpam-811	186	15	of	of	ADP
ejpam-811	186	16	the	the	DET
ejpam-811	186	17	problem	problem	NOUN
ejpam-811	186	18	(	(	PUNCT
ejpam-811	186	19	p	p	NOUN
ejpam-811	186	20	)	)	PUNCT
ejpam-811	186	21	?	?	PUNCT
ejpam-811	187	1	to	to	PART
ejpam-811	187	2	confirm	confirm	VERB
ejpam-811	187	3	the	the	DET
ejpam-811	187	4	problems	problem	NOUN
ejpam-811	187	5	(	(	PUNCT
ejpam-811	187	6	wd	wd	PROPN
ejpam-811	187	7	)	)	PUNCT
ejpam-811	187	8	and	and	CCONJ
ejpam-811	187	9	(	(	PUNCT
ejpam-811	187	10	p	p	X
ejpam-811	187	11	)	)	PUNCT
ejpam-811	187	12	are	be	AUX
ejpam-811	187	13	surely	surely	ADV
ejpam-811	187	14	in	in	ADP
ejpam-811	187	15	duality	duality	NOUN
ejpam-811	187	16	relation	relation	NOUN
ejpam-811	187	17	.	.	PUNCT
ejpam-811	188	1	the	the	DET
ejpam-811	188	2	next	next	ADJ
ejpam-811	188	3	three	three	NUM
ejpam-811	188	4	theorems	theorem	NOUN
ejpam-811	188	5	must	must	AUX
ejpam-811	188	6	be	be	AUX
ejpam-811	188	7	established	establish	VERB
ejpam-811	188	8	for	for	ADP
ejpam-811	188	9	non	non	ADJ
ejpam-811	188	10	duality	duality	NOUN
ejpam-811	188	11	gap	gap	NOUN
ejpam-811	188	12	under	under	ADP
ejpam-811	188	13	extra	extra	ADJ
ejpam-811	188	14	assumptions	assumption	NOUN
ejpam-811	188	15	.	.	PUNCT
ejpam-811	189	1	now	now	ADV
ejpam-811	189	2	for	for	ADP
ejpam-811	189	3	simplicity	simplicity	NOUN
ejpam-811	189	4	,	,	PUNCT
ejpam-811	189	5	we	we	PRON
ejpam-811	189	6	denote	denote	VERB
ejpam-811	189	7	the	the	DET
ejpam-811	189	8	function	function	NOUN
ejpam-811	189	9	φ1(•	φ1(•	NOUN
ejpam-811	189	10	)	)	PUNCT
ejpam-811	189	11	=	=	SYM
ejpam-811	189	12	�	�	PROPN
ejpam-811	189	13	k∑	k∑	VERB
ejpam-811	189	14	i=1	i=1	PROPN
ejpam-811	189	15	λire	λire	PROPN
ejpam-811	190	1	�	�	PROPN
ejpam-811	190	2	f	f	PROPN
ejpam-811	190	3	(	(	PUNCT
ejpam-811	190	4	•,ηi	•,ηi	PROPN
ejpam-811	190	5	)	)	PUNCT
ejpam-811	190	6	+	+	CCONJ
ejpam-811	190	7	(	(	PUNCT
ejpam-811	190	8	·	·	PUNCT
ejpam-811	190	9	)	)	PUNCT
ejpam-811	190	10	haw1	haw1	PROPN
ejpam-811	190	11	+	+	CCONJ
ejpam-811	190	12	〈	〈	PROPN
ejpam-811	190	13	h(•),µ	h(•),µ	PROPN
ejpam-811	190	14	〉	〉	NOUN
ejpam-811	190	15	�	�	PROPN
ejpam-811	190	16	�	�	PROPN
ejpam-811	190	17	×	×	PROPN
ejpam-811	190	18	�	�	PROPN
ejpam-811	190	19	k∑	k∑	PROPN
ejpam-811	190	20	i=1	i=1	PROPN
ejpam-811	190	21	λire	λire	PROPN
ejpam-811	190	22	�	�	PROPN
ejpam-811	190	23	g(ξ	g(ξ	PROPN
ejpam-811	190	24	,	,	PUNCT
ejpam-811	190	25	ηi)−α	ηi)−α	PROPN
ejpam-811	190	26	h	h	PROPN
ejpam-811	190	27	bw2	bw2	PROPN
ejpam-811	190	28	�	�	PROPN
ejpam-811	190	29	�	�	PROPN
ejpam-811	190	30	−	−	PROPN
ejpam-811	190	31	�	�	PROPN
ejpam-811	190	32	k∑	k∑	VERB
ejpam-811	190	33	i=1	i=1	PROPN
ejpam-811	190	34	λire	λire	PROPN
ejpam-811	190	35	�	�	PROPN
ejpam-811	190	36	f	f	PROPN
ejpam-811	190	37	(	(	PUNCT
ejpam-811	190	38	ξ	ξ	PROPN
ejpam-811	190	39	,	,	PUNCT
ejpam-811	190	40	ηi	ηi	X
ejpam-811	190	41	)	)	PUNCT
ejpam-811	191	1	+	+	NOUN
ejpam-811	191	2	α	α	NOUN
ejpam-811	191	3	haw1	haw1	NOUN
ejpam-811	191	4	+	+	CCONJ
ejpam-811	191	5	〈	〈	PRON
ejpam-811	191	6	h(ξ),µ	h(ξ),µ	ADJ
ejpam-811	191	7	〉	〉	ADJ
ejpam-811	191	8	�	�	PROPN
ejpam-811	191	9	�	�	PROPN
ejpam-811	191	10	×	×	PROPN
ejpam-811	191	11	�	�	PROPN
ejpam-811	191	12	k∑	k∑	PROPN
ejpam-811	191	13	i=1	i=1	PROPN
ejpam-811	191	14	λire	λire	PROPN
ejpam-811	191	15	�	�	PROPN
ejpam-811	191	16	g(•,ηi)−	g(•,ηi)−	PROPN
ejpam-811	191	17	(	(	PUNCT
ejpam-811	191	18	·	·	PUNCT
ejpam-811	191	19	)	)	PUNCT
ejpam-811	191	20	hbw2	hbw2	PROPN
ejpam-811	191	21	�	�	PROPN
ejpam-811	191	22	�	�	PROPN
ejpam-811	191	23	for	for	ADP
ejpam-811	191	24	•=	•=	NOUN
ejpam-811	191	25	(	(	PUNCT
ejpam-811	191	26	·	·	PUNCT
ejpam-811	191	27	,	,	PUNCT
ejpam-811	191	28	·	·	PUNCT
ejpam-811	191	29	)	)	PUNCT
ejpam-811	191	30	∈	∈	PROPN
ejpam-811	191	31	q	q	X
ejpam-811	192	1	⊂	⊂	NOUN
ejpam-811	192	2	c2n	c2n	NOUN
ejpam-811	192	3	.	.	PUNCT
ejpam-811	193	1	employing	employ	VERB
ejpam-811	193	2	the	the	DET
ejpam-811	193	3	necessary	necessary	ADJ
ejpam-811	193	4	optimality	optimality	NOUN
ejpam-811	193	5	conditions	condition	NOUN
ejpam-811	193	6	(	(	PUNCT
ejpam-811	193	7	2)∼(5	2)∼(5	NUM
ejpam-811	193	8	)	)	PUNCT
ejpam-811	193	9	with	with	ADP
ejpam-811	193	10	some	some	DET
ejpam-811	193	11	generalized	generalized	ADJ
ejpam-811	193	12	convexity	convexity	NOUN
ejpam-811	193	13	,	,	PUNCT
ejpam-811	193	14	we	we	PRON
ejpam-811	193	15	can	can	AUX
ejpam-811	193	16	prove	prove	VERB
ejpam-811	193	17	three	three	NUM
ejpam-811	193	18	theorems	theorem	NOUN
ejpam-811	193	19	:	:	PUNCT
ejpam-811	193	20	the	the	DET
ejpam-811	193	21	weak	weak	ADJ
ejpam-811	193	22	,	,	PUNCT
ejpam-811	193	23	strong	strong	ADJ
ejpam-811	193	24	and	and	CCONJ
ejpam-811	193	25	strict	strict	ADJ
ejpam-811	193	26	converse	converse	NOUN
ejpam-811	193	27	duality	duality	NOUN
ejpam-811	193	28	theorem	theorem	NOUN
ejpam-811	193	29	of	of	ADP
ejpam-811	193	30	problem	problem	NOUN
ejpam-811	193	31	(	(	PUNCT
ejpam-811	193	32	wd	wd	PROPN
ejpam-811	193	33	)	)	PUNCT
ejpam-811	193	34	as	as	SCONJ
ejpam-811	193	35	follows	follow	VERB
ejpam-811	193	36	.	.	PUNCT
ejpam-811	194	1	theorem	theorem	ADJ
ejpam-811	194	2	4	4	NUM
ejpam-811	194	3	.	.	PUNCT
ejpam-811	195	1	[	[	X
ejpam-811	195	2	weak	weak	ADJ
ejpam-811	195	3	duality	duality	NOUN
ejpam-811	195	4	]	]	PUNCT
ejpam-811	195	5	let	let	VERB
ejpam-811	195	6	ζ	ζ	NOUN
ejpam-811	195	7	=	=	SYM
ejpam-811	195	8	(	(	PUNCT
ejpam-811	195	9	z	z	NOUN
ejpam-811	195	10	,	,	PUNCT
ejpam-811	195	11	z	z	NOUN
ejpam-811	195	12	)	)	PUNCT
ejpam-811	195	13	be	be	AUX
ejpam-811	195	14	(	(	PUNCT
ejpam-811	195	15	p)-feasible	p)-feasible	ADJ
ejpam-811	195	16	,	,	PUNCT
ejpam-811	195	17	and	and	CCONJ
ejpam-811	195	18	(	(	PUNCT
ejpam-811	195	19	k	k	X
ejpam-811	195	20	,	,	PUNCT
ejpam-811	195	21	eλ	eλ	INTJ
ejpam-811	195	22	,	,	PUNCT
ejpam-811	195	23	eη	eη	NOUN
ejpam-811	195	24	,	,	PUNCT
ejpam-811	195	25	ξ,µ	ξ,µ	NOUN
ejpam-811	195	26	,	,	PUNCT
ejpam-811	195	27	w1	w1	NOUN
ejpam-811	195	28	,	,	PUNCT
ejpam-811	195	29	w2	w2	NOUN
ejpam-811	195	30	)	)	PUNCT
ejpam-811	195	31	be	be	AUX
ejpam-811	195	32	(	(	PUNCT
ejpam-811	195	33	wd)feasible	wd)feasible	ADJ
ejpam-811	195	34	.	.	PUNCT
ejpam-811	196	1	if	if	SCONJ
ejpam-811	196	2	φ1(ξ	φ1(ξ	PROPN
ejpam-811	196	3	)	)	PUNCT
ejpam-811	196	4	is	be	AUX
ejpam-811	196	5	pseudoconvex	pseudoconvex	NOUN
ejpam-811	196	6	on	on	ADP
ejpam-811	196	7	q	q	NOUN
ejpam-811	196	8	,	,	PUNCT
ejpam-811	196	9	then	then	ADV
ejpam-811	196	10	max	max	PROPN
ejpam-811	196	11	η∈y	η∈y	PROPN
ejpam-811	196	12	re	re	X
ejpam-811	196	13	�	�	PROPN
ejpam-811	196	14	f	f	PROPN
ejpam-811	196	15	(	(	PUNCT
ejpam-811	196	16	ζ	ζ	PROPN
ejpam-811	196	17	,	,	PUNCT
ejpam-811	196	18	η	η	NOUN
ejpam-811	196	19	)	)	PUNCT
ejpam-811	196	20	+	+	CCONJ
ejpam-811	196	21	(	(	PUNCT
ejpam-811	196	22	zhaz)1/2	zhaz)1/2	VERB
ejpam-811	196	23	�	�	PROPN
ejpam-811	196	24	re	re	NOUN
ejpam-811	196	25	�	�	PROPN
ejpam-811	196	26	g(ζ	g(ζ	PROPN
ejpam-811	196	27	,	,	PUNCT
ejpam-811	196	28	η)−	η)−	PROPN
ejpam-811	196	29	(	(	PUNCT
ejpam-811	196	30	zh	zh	PROPN
ejpam-811	196	31	bz)1/2	bz)1/2	PROPN
ejpam-811	196	32	�	�	PROPN
ejpam-811	196	33	≥	≥	PROPN
ejpam-811	196	34	φ(ξ	φ(ξ	PROPN
ejpam-811	196	35	)	)	PUNCT
ejpam-811	196	36	.	.	PUNCT
ejpam-811	197	1	proof	proof	NOUN
ejpam-811	197	2	.	.	PUNCT
ejpam-811	198	1	suppose	suppose	VERB
ejpam-811	198	2	on	on	ADP
ejpam-811	198	3	the	the	DET
ejpam-811	198	4	contrary	contrary	NOUN
ejpam-811	198	5	that	that	PRON
ejpam-811	198	6	max	max	PROPN
ejpam-811	198	7	η∈y	η∈y	PROPN
ejpam-811	198	8	re	re	X
ejpam-811	198	9	�	�	PROPN
ejpam-811	198	10	f	f	PROPN
ejpam-811	198	11	(	(	PUNCT
ejpam-811	198	12	ζ	ζ	PROPN
ejpam-811	198	13	,	,	PUNCT
ejpam-811	198	14	η	η	NOUN
ejpam-811	198	15	)	)	PUNCT
ejpam-811	198	16	+	+	CCONJ
ejpam-811	198	17	(	(	PUNCT
ejpam-811	198	18	zhaz)1/2	zhaz)1/2	VERB
ejpam-811	198	19	�	�	PROPN
ejpam-811	198	20	re	re	NOUN
ejpam-811	198	21	�	�	PROPN
ejpam-811	198	22	g(ζ	g(ζ	PROPN
ejpam-811	198	23	,	,	PUNCT
ejpam-811	198	24	η)−	η)−	PROPN
ejpam-811	198	25	(	(	PUNCT
ejpam-811	198	26	zh	zh	PROPN
ejpam-811	198	27	bz)1/2	bz)1/2	PROPN
ejpam-811	198	28	�	�	PROPN
ejpam-811	198	29	<	<	X
ejpam-811	198	30	φ(ξ	φ(ξ	PROPN
ejpam-811	198	31	)	)	PUNCT
ejpam-811	198	32	=	=	PUNCT
ejpam-811	199	1	∑k	∑k	PROPN
ejpam-811	199	2	i=1λire	i=1λire	VERB
ejpam-811	199	3	�	�	PROPN
ejpam-811	199	4	f	f	PROPN
ejpam-811	199	5	(	(	PUNCT
ejpam-811	199	6	ξ	ξ	PROPN
ejpam-811	199	7	,	,	PUNCT
ejpam-811	199	8	ηi	ηi	X
ejpam-811	199	9	)	)	PUNCT
ejpam-811	200	1	+	+	CCONJ
ejpam-811	200	2	(	(	PUNCT
ejpam-811	200	3	α	α	PROPN
ejpam-811	200	4	haα)1/2	haα)1/2	PROPN
ejpam-811	200	5	+	+	CCONJ
ejpam-811	200	6	〈	〈	NOUN
ejpam-811	200	7	h(ξ),µ	h(ξ),µ	ADJ
ejpam-811	200	8	〉	〉	ADJ
ejpam-811	200	9	�	�	PROPN
ejpam-811	200	10	∑k	∑k	PROPN
ejpam-811	200	11	i=1λire	i=1λire	VERB
ejpam-811	200	12	�	�	PROPN
ejpam-811	200	13	g(ξ	g(ξ	PROPN
ejpam-811	200	14	,	,	PUNCT
ejpam-811	200	15	ηi)−	ηi)−	PUNCT
ejpam-811	200	16	(	(	PUNCT
ejpam-811	200	17	αh	αh	PROPN
ejpam-811	200	18	bα)1/2	bα)1/2	PROPN
ejpam-811	200	19	�	�	PROPN
ejpam-811	200	20	.	.	PUNCT
ejpam-811	201	1	then	then	ADV
ejpam-811	201	2	for	for	ADP
ejpam-811	201	3	each	each	DET
ejpam-811	201	4	η	η	PROPN
ejpam-811	201	5	∈	∈	PROPN
ejpam-811	201	6	y	y	PROPN
ejpam-811	201	7	,	,	PUNCT
ejpam-811	201	8	we	we	PRON
ejpam-811	201	9	get	get	VERB
ejpam-811	201	10	�	�	PROPN
ejpam-811	201	11	re	re	ADJ
ejpam-811	201	12	�	�	PROPN
ejpam-811	201	13	f	f	PROPN
ejpam-811	201	14	(	(	PUNCT
ejpam-811	201	15	ζ	ζ	PROPN
ejpam-811	201	16	,	,	PUNCT
ejpam-811	201	17	η	η	NOUN
ejpam-811	201	18	)	)	PUNCT
ejpam-811	202	1	+	+	CCONJ
ejpam-811	202	2	(	(	PUNCT
ejpam-811	202	3	zhaz)1/2	zhaz)1/2	NUM
ejpam-811	202	4	�	�	PROPN
ejpam-811	202	5	�	�	PROPN
ejpam-811	202	6	×	×	PROPN
ejpam-811	202	7	�	�	PROPN
ejpam-811	202	8	∑k	∑k	PROPN
ejpam-811	202	9	i=1λire	i=1λire	NOUN
ejpam-811	202	10	�	�	PROPN
ejpam-811	202	11	g(ξ	g(ξ	PROPN
ejpam-811	202	12	,	,	PUNCT
ejpam-811	202	13	ηi)−	ηi)−	PUNCT
ejpam-811	202	14	(	(	PUNCT
ejpam-811	202	15	α	α	PROPN
ejpam-811	202	16	h	h	PROPN
ejpam-811	202	17	bα)1/2	bα)1/2	PROPN
ejpam-811	202	18	�	�	PROPN
ejpam-811	202	19	�	�	PROPN
ejpam-811	202	20	<	<	X
ejpam-811	202	21	�	�	PROPN
ejpam-811	202	22	re	re	X
ejpam-811	202	23	�	�	PROPN
ejpam-811	202	24	g(ζ	g(ζ	PROPN
ejpam-811	202	25	,	,	PUNCT
ejpam-811	202	26	η)−	η)−	PROPN
ejpam-811	202	27	(	(	PUNCT
ejpam-811	202	28	zh	zh	PROPN
ejpam-811	202	29	bz)1/2	bz)1/2	PROPN
ejpam-811	202	30	�	�	PROPN
ejpam-811	202	31	�	�	PROPN
ejpam-811	202	32	×	×	PROPN
ejpam-811	202	33	�	�	PROPN
ejpam-811	202	34	∑k	∑k	PROPN
ejpam-811	202	35	i=1λire	i=1λire	VERB
ejpam-811	202	36	�	�	PROPN
ejpam-811	202	37	f	f	PROPN
ejpam-811	202	38	(	(	PUNCT
ejpam-811	202	39	ξ	ξ	PROPN
ejpam-811	202	40	,	,	PUNCT
ejpam-811	202	41	ηi	ηi	X
ejpam-811	202	42	)	)	PUNCT
ejpam-811	202	43	+	+	CCONJ
ejpam-811	202	44	(	(	PUNCT
ejpam-811	202	45	α	α	PROPN
ejpam-811	202	46	haα)1/2	haα)1/2	PROPN
ejpam-811	202	47	+	+	CCONJ
ejpam-811	202	48	〈	〈	NOUN
ejpam-811	202	49	h(ξ),µ	h(ξ),µ	ADJ
ejpam-811	202	50	〉	〉	ADJ
ejpam-811	202	51	�	�	PROPN
ejpam-811	202	52	�	�	PROPN
ejpam-811	202	53	.	.	PUNCT
ejpam-811	203	1	now	now	ADV
ejpam-811	203	2	we	we	PRON
ejpam-811	203	3	are	be	AUX
ejpam-811	203	4	replaced	replace	VERB
ejpam-811	203	5	η	η	PROPN
ejpam-811	203	6	by	by	ADP
ejpam-811	203	7	ηi	ηi	PROPN
ejpam-811	203	8	,	,	PUNCT
ejpam-811	203	9	multiplies	multiplies	PROPN
ejpam-811	203	10	λi	λi	VERB
ejpam-811	203	11	(	(	PUNCT
ejpam-811	203	12	with	with	ADP
ejpam-811	203	13	∑k	∑k	PROPN
ejpam-811	203	14	i=1λi	i=1λi	X
ejpam-811	204	1	=	=	SYM
ejpam-811	204	2	1	1	NUM
ejpam-811	204	3	)	)	PUNCT
ejpam-811	204	4	.	.	PUNCT
ejpam-811	205	1	then	then	ADV
ejpam-811	205	2	it	it	PRON
ejpam-811	205	3	deduce	deduce	VERB
ejpam-811	205	4	to	to	ADP
ejpam-811	205	5	�	�	PROPN
ejpam-811	205	6	k∑	k∑	PROPN
ejpam-811	205	7	i=1	i=1	PROPN
ejpam-811	205	8	λi	λi	X
ejpam-811	205	9	re	re	X
ejpam-811	205	10	�	�	PROPN
ejpam-811	205	11	f	f	PROPN
ejpam-811	205	12	(	(	PUNCT
ejpam-811	205	13	ζ	ζ	PROPN
ejpam-811	205	14	,	,	PUNCT
ejpam-811	205	15	ηi	ηi	PROPN
ejpam-811	205	16	)	)	PUNCT
ejpam-811	206	1	+	+	CCONJ
ejpam-811	206	2	(	(	PUNCT
ejpam-811	206	3	z	z	NOUN
ejpam-811	206	4	haz)1/2	haz)1/2	PROPN
ejpam-811	206	5	�	�	PROPN
ejpam-811	206	6	�	�	PROPN
ejpam-811	206	7	×	×	PROPN
ejpam-811	206	8	�	�	PROPN
ejpam-811	206	9	k∑	k∑	PROPN
ejpam-811	206	10	i=1	i=1	PROPN
ejpam-811	206	11	λire	λire	PROPN
ejpam-811	206	12	�	�	PROPN
ejpam-811	206	13	g(ξ	g(ξ	PROPN
ejpam-811	206	14	,	,	PUNCT
ejpam-811	206	15	ηi)−	ηi)−	PUNCT
ejpam-811	206	16	(	(	PUNCT
ejpam-811	206	17	α	α	PROPN
ejpam-811	206	18	h	h	PROPN
ejpam-811	206	19	bα)1/2	bα)1/2	PROPN
ejpam-811	206	20	�	�	PROPN
ejpam-811	206	21	�	�	PROPN
ejpam-811	206	22	−	−	PROPN
ejpam-811	206	23	�	�	PROPN
ejpam-811	206	24	k∑	k∑	VERB
ejpam-811	206	25	i=1	i=1	PROPN
ejpam-811	206	26	λi	λi	X
ejpam-811	206	27	re	re	X
ejpam-811	206	28	�	�	PROPN
ejpam-811	206	29	g(ζ	g(ζ	PROPN
ejpam-811	206	30	,	,	PUNCT
ejpam-811	206	31	ηi)−	ηi)−	PUNCT
ejpam-811	206	32	(	(	PUNCT
ejpam-811	206	33	z	z	NOUN
ejpam-811	206	34	h	h	PROPN
ejpam-811	206	35	bz)1/2	bz)1/2	PROPN
ejpam-811	206	36	�	�	PROPN
ejpam-811	206	37	�	�	PROPN
ejpam-811	206	38	×	×	PROPN
ejpam-811	206	39	�	�	PROPN
ejpam-811	206	40	k∑	k∑	PROPN
ejpam-811	206	41	i=1	i=1	PROPN
ejpam-811	206	42	λire	λire	PROPN
ejpam-811	206	43	�	�	PROPN
ejpam-811	206	44	f	f	PROPN
ejpam-811	206	45	(	(	PUNCT
ejpam-811	206	46	ξ	ξ	PROPN
ejpam-811	206	47	,	,	PUNCT
ejpam-811	206	48	ηi	ηi	X
ejpam-811	206	49	)	)	PUNCT
ejpam-811	206	50	+	+	CCONJ
ejpam-811	206	51	(	(	PUNCT
ejpam-811	206	52	α	α	PROPN
ejpam-811	206	53	haα)1/2	haα)1/2	PROPN
ejpam-811	206	54	+	+	CCONJ
ejpam-811	206	55	〈	〈	NOUN
ejpam-811	206	56	h(ξ),µ	h(ξ),µ	ADJ
ejpam-811	206	57	〉	〉	NOUN
ejpam-811	206	58	�	�	NOUN
ejpam-811	206	59	�	�	PROPN
ejpam-811	206	60	<	<	X
ejpam-811	206	61	0	0	NUM
ejpam-811	206	62	.	.	PUNCT
ejpam-811	207	1	(	(	PUNCT
ejpam-811	207	2	12	12	NUM
ejpam-811	207	3	)	)	PUNCT
ejpam-811	207	4	h.	h.	PROPN
ejpam-811	207	5	lai	lai	PROPN
ejpam-811	207	6	,	,	PUNCT
ejpam-811	207	7	t.	t.	PROPN
ejpam-811	207	8	huang	huang	PROPN
ejpam-811	207	9	/	/	SYM
ejpam-811	207	10	eur	eur	PROPN
ejpam-811	207	11	.	.	PUNCT
ejpam-811	208	1	j.	j.	PROPN
ejpam-811	208	2	pure	pure	PROPN
ejpam-811	208	3	appl	appl	PROPN
ejpam-811	208	4	.	.	PROPN
ejpam-811	208	5	math	math	PROPN
ejpam-811	208	6	,	,	PUNCT
ejpam-811	208	7	3	3	NUM
ejpam-811	208	8	(	(	PUNCT
ejpam-811	208	9	2010	2010	NUM
ejpam-811	208	10	)	)	PUNCT
ejpam-811	208	11	,	,	PUNCT
ejpam-811	208	12	989	989	NUM
ejpam-811	208	13	-	-	SYM
ejpam-811	208	14	1005	1005	NUM
ejpam-811	208	15	998	998	NUM
ejpam-811	208	16	from	from	ADP
ejpam-811	208	17	inequalities	inequality	NOUN
ejpam-811	208	18	(	(	PUNCT
ejpam-811	208	19	10	10	NUM
ejpam-811	208	20	)	)	PUNCT
ejpam-811	208	21	,	,	PUNCT
ejpam-811	208	22	(	(	PUNCT
ejpam-811	208	23	11	11	NUM
ejpam-811	208	24	)	)	PUNCT
ejpam-811	208	25	and	and	CCONJ
ejpam-811	208	26	generalized	generalize	VERB
ejpam-811	208	27	schwarz	schwarz	PROPN
ejpam-811	208	28	inequality	inequality	NOUN
ejpam-811	208	29	(	(	PUNCT
ejpam-811	208	30	1	1	NUM
ejpam-811	208	31	)	)	PUNCT
ejpam-811	208	32	,	,	PUNCT
ejpam-811	208	33	we	we	PRON
ejpam-811	208	34	obtain	obtain	VERB
ejpam-811	208	35	re(zhaw1)≤	re(zhaw1)≤	NOUN
ejpam-811	209	1	(	(	PUNCT
ejpam-811	209	2	z	z	NOUN
ejpam-811	209	3	haz)1/2(wh	haz)1/2(wh	NOUN
ejpam-811	209	4	1	1	NUM
ejpam-811	209	5	aw1	aw1	PROPN
ejpam-811	209	6	)	)	PUNCT
ejpam-811	209	7	1/2	1/2	NUM
ejpam-811	209	8	≤	≤	NOUN
ejpam-811	209	9	(	(	PUNCT
ejpam-811	209	10	zhaz)1/2	zhaz)1/2	NUM
ejpam-811	209	11	and	and	CCONJ
ejpam-811	209	12	(	(	PUNCT
ejpam-811	209	13	13	13	NUM
ejpam-811	209	14	)	)	PUNCT
ejpam-811	209	15	re(zh	re(zh	NOUN
ejpam-811	209	16	bw2)≤	bw2)≤	NOUN
ejpam-811	209	17	(	(	PUNCT
ejpam-811	209	18	z	z	NOUN
ejpam-811	209	19	h	h	NOUN
ejpam-811	209	20	bz)1/2(wh	bz)1/2(wh	VERB
ejpam-811	209	21	2	2	NUM
ejpam-811	209	22	bw2	bw2	PROPN
ejpam-811	209	23	)	)	PUNCT
ejpam-811	209	24	1/2	1/2	NUM
ejpam-811	209	25	≤	≤	NOUN
ejpam-811	209	26	(	(	PUNCT
ejpam-811	209	27	zh	zh	X
ejpam-811	209	28	bz)1/2	bz)1/2	PROPN
ejpam-811	209	29	,	,	PUNCT
ejpam-811	209	30	(	(	PUNCT
ejpam-811	209	31	14	14	NUM
ejpam-811	209	32	)	)	PUNCT
ejpam-811	209	33	since	since	SCONJ
ejpam-811	209	34	wh	wh	PROPN
ejpam-811	209	35	1	1	NUM
ejpam-811	209	36	aw1	aw1	PROPN
ejpam-811	209	37	≤	≤	NUM
ejpam-811	209	38	1	1	NUM
ejpam-811	209	39	and	and	CCONJ
ejpam-811	209	40	wh	wh	VERB
ejpam-811	209	41	2	2	NUM
ejpam-811	209	42	bw2	bw2	PROPN
ejpam-811	209	43	≤	≤	PROPN
ejpam-811	209	44	1	1	NUM
ejpam-811	209	45	.	.	PUNCT
ejpam-811	209	46	from	from	ADP
ejpam-811	209	47	inequalities	inequality	NOUN
ejpam-811	209	48	(	(	PUNCT
ejpam-811	209	49	12	12	NUM
ejpam-811	209	50	)	)	PUNCT
ejpam-811	209	51	,	,	PUNCT
ejpam-811	209	52	(	(	PUNCT
ejpam-811	209	53	13	13	NUM
ejpam-811	209	54	)	)	PUNCT
ejpam-811	209	55	and	and	CCONJ
ejpam-811	209	56	(	(	PUNCT
ejpam-811	209	57	14	14	NUM
ejpam-811	209	58	)	)	PUNCT
ejpam-811	209	59	,	,	PUNCT
ejpam-811	209	60	we	we	PRON
ejpam-811	209	61	obtain	obtain	VERB
ejpam-811	209	62	φ1(ζ	φ1(ζ	NOUN
ejpam-811	209	63	)	)	PUNCT
ejpam-811	209	64	=	=	SYM
ejpam-811	209	65	�	�	PROPN
ejpam-811	209	66	∑k	∑k	PROPN
ejpam-811	209	67	i=1λire	i=1λire	VERB
ejpam-811	209	68	�	�	PROPN
ejpam-811	209	69	f	f	PROPN
ejpam-811	209	70	(	(	PUNCT
ejpam-811	209	71	ζ	ζ	PROPN
ejpam-811	209	72	,	,	PUNCT
ejpam-811	209	73	ηi	ηi	NOUN
ejpam-811	209	74	)	)	PUNCT
ejpam-811	209	75	+	+	NUM
ejpam-811	209	76	zhaw1	zhaw1	NOUN
ejpam-811	210	1	+	+	CCONJ
ejpam-811	210	2	〈	〈	PROPN
ejpam-811	210	3	h(ζ),µ	h(ζ),µ	NOUN
ejpam-811	210	4	〉	〉	ADJ
ejpam-811	210	5	�	�	PROPN
ejpam-811	210	6	�	�	PROPN
ejpam-811	210	7	×	×	PROPN
ejpam-811	210	8	�	�	PROPN
ejpam-811	210	9	∑k	∑k	PROPN
ejpam-811	210	10	i=1λire	i=1λire	NOUN
ejpam-811	210	11	�	�	PROPN
ejpam-811	210	12	g(ξ	g(ξ	PROPN
ejpam-811	210	13	,	,	PUNCT
ejpam-811	210	14	ηi)−α	ηi)−α	PROPN
ejpam-811	210	15	h	h	PROPN
ejpam-811	210	16	bw2	bw2	PROPN
ejpam-811	210	17	�	�	PROPN
ejpam-811	210	18	�	�	PROPN
ejpam-811	210	19	−	−	PROPN
ejpam-811	210	20	�	�	PROPN
ejpam-811	210	21	∑k	∑k	PROPN
ejpam-811	210	22	i=1λire	i=1λire	VERB
ejpam-811	210	23	�	�	PROPN
ejpam-811	210	24	f	f	PROPN
ejpam-811	210	25	(	(	PUNCT
ejpam-811	210	26	ξ	ξ	PROPN
ejpam-811	210	27	,	,	PUNCT
ejpam-811	210	28	ηi	ηi	X
ejpam-811	210	29	)	)	PUNCT
ejpam-811	211	1	+	+	NOUN
ejpam-811	211	2	α	α	NOUN
ejpam-811	211	3	haw1	haw1	NOUN
ejpam-811	211	4	+	+	CCONJ
ejpam-811	211	5	〈	〈	PRON
ejpam-811	211	6	h(ξ),µ	h(ξ),µ	ADJ
ejpam-811	211	7	〉	〉	ADJ
ejpam-811	211	8	�	�	PROPN
ejpam-811	211	9	�	�	PROPN
ejpam-811	211	10	×	×	PROPN
ejpam-811	211	11	�	�	PROPN
ejpam-811	211	12	∑k	∑k	PROPN
ejpam-811	211	13	i=1λire	i=1λire	NOUN
ejpam-811	211	14	�	�	PROPN
ejpam-811	211	15	g(ζ	g(ζ	PROPN
ejpam-811	211	16	,	,	PUNCT
ejpam-811	211	17	ηi)−	ηi)−	PUNCT
ejpam-811	211	18	zh	zh	PROPN
ejpam-811	211	19	bw2	bw2	PROPN
ejpam-811	211	20	�	�	PROPN
ejpam-811	211	21	�	�	PROPN
ejpam-811	211	22	<	<	X
ejpam-811	211	23	�	�	PROPN
ejpam-811	212	1	∑k	∑k	PROPN
ejpam-811	212	2	i=1λire	i=1λire	NOUN
ejpam-811	212	3	�	�	PROPN
ejpam-811	212	4	f	f	PROPN
ejpam-811	212	5	(	(	PUNCT
ejpam-811	212	6	ζ	ζ	PROPN
ejpam-811	212	7	,	,	PUNCT
ejpam-811	212	8	ηi	ηi	PROPN
ejpam-811	212	9	)	)	PUNCT
ejpam-811	213	1	+	+	CCONJ
ejpam-811	213	2	(	(	PUNCT
ejpam-811	213	3	z	z	NOUN
ejpam-811	213	4	haz)1/2	haz)1/2	PROPN
ejpam-811	213	5	+	+	CCONJ
ejpam-811	213	6	〈	〈	PROPN
ejpam-811	213	7	h(ζ),µ	h(ζ),µ	NOUN
ejpam-811	213	8	〉	〉	ADJ
ejpam-811	213	9	�	�	PROPN
ejpam-811	213	10	�	�	PROPN
ejpam-811	213	11	×	×	PROPN
ejpam-811	213	12	�	�	PROPN
ejpam-811	213	13	∑k	∑k	PROPN
ejpam-811	213	14	i=1λire	i=1λire	NOUN
ejpam-811	213	15	�	�	PROPN
ejpam-811	213	16	g(ξ	g(ξ	PROPN
ejpam-811	213	17	,	,	PUNCT
ejpam-811	213	18	ηi)−α	ηi)−α	PROPN
ejpam-811	213	19	h	h	PROPN
ejpam-811	213	20	bw2	bw2	PROPN
ejpam-811	213	21	�	�	PROPN
ejpam-811	213	22	�	�	PROPN
ejpam-811	213	23	−	−	PROPN
ejpam-811	213	24	�	�	PROPN
ejpam-811	213	25	∑k	∑k	PROPN
ejpam-811	213	26	i=1λire	i=1λire	VERB
ejpam-811	213	27	�	�	PROPN
ejpam-811	213	28	f	f	PROPN
ejpam-811	213	29	(	(	PUNCT
ejpam-811	213	30	ξ	ξ	PROPN
ejpam-811	213	31	,	,	PUNCT
ejpam-811	213	32	ηi	ηi	X
ejpam-811	213	33	)	)	PUNCT
ejpam-811	214	1	+	+	NOUN
ejpam-811	214	2	α	α	NOUN
ejpam-811	214	3	haw1	haw1	NOUN
ejpam-811	214	4	+	+	CCONJ
ejpam-811	214	5	〈	〈	PRON
ejpam-811	214	6	h(ξ),µ	h(ξ),µ	ADJ
ejpam-811	214	7	〉	〉	ADJ
ejpam-811	214	8	�	�	PROPN
ejpam-811	214	9	�	�	PROPN
ejpam-811	214	10	×	×	PROPN
ejpam-811	214	11	�	�	PROPN
ejpam-811	214	12	∑k	∑k	PROPN
ejpam-811	214	13	i=1λire	i=1λire	NOUN
ejpam-811	214	14	�	�	PROPN
ejpam-811	214	15	g(ζ	g(ζ	PROPN
ejpam-811	214	16	,	,	PUNCT
ejpam-811	214	17	ηi)−	ηi)−	PUNCT
ejpam-811	214	18	(	(	PUNCT
ejpam-811	214	19	z	z	NOUN
ejpam-811	214	20	h	h	PROPN
ejpam-811	214	21	bz)1/2	bz)1/2	PROPN
ejpam-811	214	22	�	�	PROPN
ejpam-811	214	23	�	�	PROPN
ejpam-811	214	24	<	<	X
ejpam-811	214	25	0	0	NUM
ejpam-811	214	26	+	+	CCONJ
ejpam-811	214	27	re	re	NOUN
ejpam-811	214	28	〈	〈	NOUN
ejpam-811	214	29	h(ζ),µ	h(ζ),µ	NOUN
ejpam-811	214	30	〉	〉	ADJ
ejpam-811	214	31	×	×	PROPN
ejpam-811	214	32	�	�	PROPN
ejpam-811	214	33	∑k	∑k	PROPN
ejpam-811	214	34	i=1λire	i=1λire	NOUN
ejpam-811	214	35	�	�	PROPN
ejpam-811	214	36	g(ζ	g(ζ	PROPN
ejpam-811	214	37	,	,	PUNCT
ejpam-811	214	38	ηi)−α	ηi)−α	PROPN
ejpam-811	214	39	h	h	PROPN
ejpam-811	214	40	bw2	bw2	PROPN
ejpam-811	214	41	�	�	PROPN
ejpam-811	214	42	�	�	PROPN
ejpam-811	214	43	.	.	PUNCT
ejpam-811	215	1	since	since	SCONJ
ejpam-811	215	2	re	re	VERB
ejpam-811	215	3	〈	〈	NOUN
ejpam-811	215	4	h(ζ),µ	h(ζ),µ	NOUN
ejpam-811	215	5	〉	〉	NOUN
ejpam-811	215	6	<	<	X
ejpam-811	215	7	0	0	NUM
ejpam-811	215	8	and	and	CCONJ
ejpam-811	215	9	�	�	PROPN
ejpam-811	215	10	∑k	∑k	PROPN
ejpam-811	215	11	i=1λire	i=1λire	NOUN
ejpam-811	215	12	�	�	PROPN
ejpam-811	215	13	g(ξ	g(ξ	PROPN
ejpam-811	215	14	,	,	PUNCT
ejpam-811	215	15	ηi	ηi	PROPN
ejpam-811	215	16	)	)	PUNCT
ejpam-811	215	17	−	−	PROPN
ejpam-811	216	1	α	α	PRON
ejpam-811	216	2	h	h	PROPN
ejpam-811	216	3	bw2	bw2	PROPN
ejpam-811	216	4	�	�	PROPN
ejpam-811	216	5	�	�	PROPN
ejpam-811	216	6	>	>	X
ejpam-811	216	7	0	0	PROPN
ejpam-811	216	8	,	,	PUNCT
ejpam-811	216	9	the	the	DET
ejpam-811	216	10	above	above	ADJ
ejpam-811	216	11	inequality	inequality	NOUN
ejpam-811	216	12	implies	imply	VERB
ejpam-811	216	13	that	that	SCONJ
ejpam-811	216	14	φ1(ζ	φ1(ζ	VERB
ejpam-811	216	15	)	)	PUNCT
ejpam-811	216	16	<	<	X
ejpam-811	216	17	0=	0=	NUM
ejpam-811	216	18	φ1(ξ	φ1(ξ	PROPN
ejpam-811	216	19	)	)	PUNCT
ejpam-811	216	20	.	.	PUNCT
ejpam-811	217	1	by	by	ADP
ejpam-811	217	2	hypothesis	hypothesis	NOUN
ejpam-811	217	3	φ1	φ1	NOUN
ejpam-811	217	4	is	be	AUX
ejpam-811	217	5	pseudoconvex	pseudoconvex	NOUN
ejpam-811	217	6	and	and	CCONJ
ejpam-811	217	7	φ1(ζ)−φ1(ξ	φ1(ζ)−φ1(ξ	NOUN
ejpam-811	217	8	)	)	PUNCT
ejpam-811	217	9	<	<	X
ejpam-811	217	10	0	0	NUM
ejpam-811	217	11	,	,	PUNCT
ejpam-811	217	12	we	we	PRON
ejpam-811	217	13	get	get	VERB
ejpam-811	217	14	�	�	PROPN
ejpam-811	217	15	k∑	k∑	PROPN
ejpam-811	217	16	i=1	i=1	PROPN
ejpam-811	217	17	λi	λi	PROPN
ejpam-811	217	18	�	�	PROPN
ejpam-811	218	1	∇z	∇z	PROPN
ejpam-811	218	2	f	f	PROPN
ejpam-811	218	3	(	(	PUNCT
ejpam-811	218	4	ξ	ξ	PROPN
ejpam-811	218	5	,	,	PUNCT
ejpam-811	218	6	ηi	ηi	X
ejpam-811	218	7	)	)	PUNCT
ejpam-811	218	8	+	+	PROPN
ejpam-811	218	9	∇z	∇z	ADJ
ejpam-811	218	10	f	f	X
ejpam-811	218	11	(	(	PUNCT
ejpam-811	218	12	ξ	ξ	PROPN
ejpam-811	218	13	,	,	PUNCT
ejpam-811	218	14	ηi	ηi	PROPN
ejpam-811	218	15	)	)	PUNCT
ejpam-811	218	16	�	�	PROPN
ejpam-811	218	17	+	+	CCONJ
ejpam-811	218	18	aw1	aw1	PROPN
ejpam-811	218	19	+	+	PROPN
ejpam-811	218	20	µ	µ	PROPN
ejpam-811	218	21	t	t	PROPN
ejpam-811	218	22	∇zh(ξ	∇zh(ξ	PROPN
ejpam-811	218	23	)	)	PUNCT
ejpam-811	218	24	+	+	NOUN
ejpam-811	218	25	µh∇zh(ξ	µh∇zh(ξ	X
ejpam-811	218	26	)	)	PUNCT
ejpam-811	218	27	�	�	PROPN
ejpam-811	218	28	·	·	PUNCT
ejpam-811	218	29	�	�	PROPN
ejpam-811	218	30	k∑	k∑	VERB
ejpam-811	218	31	i=1	i=1	PROPN
ejpam-811	219	1	λi	λi	PROPN
ejpam-811	219	2	[	[	X
ejpam-811	219	3	g(ξ	g(ξ	PROPN
ejpam-811	219	4	,	,	PUNCT
ejpam-811	219	5	ηi)−	ηi)−	PUNCT
ejpam-811	219	6	(	(	PUNCT
ejpam-811	219	7	α	α	PROPN
ejpam-811	219	8	h	h	PROPN
ejpam-811	219	9	bα)1/2	bα)1/2	PROPN
ejpam-811	219	10	]	]	PUNCT
ejpam-811	219	11	�	�	PROPN
ejpam-811	220	1	−	−	PROPN
ejpam-811	220	2	�	�	PROPN
ejpam-811	220	3	k∑	k∑	VERB
ejpam-811	220	4	i=1	i=1	PROPN
ejpam-811	221	1	λi	λi	X
ejpam-811	221	2	[	[	PUNCT
ejpam-811	221	3	f	f	X
ejpam-811	221	4	(	(	PUNCT
ejpam-811	221	5	ξ	ξ	PROPN
ejpam-811	221	6	,	,	PUNCT
ejpam-811	221	7	ηi	ηi	X
ejpam-811	221	8	)	)	PUNCT
ejpam-811	222	1	+	+	CCONJ
ejpam-811	222	2	(	(	PUNCT
ejpam-811	222	3	α	α	PROPN
ejpam-811	222	4	haα)1/2	haα)1/2	PROPN
ejpam-811	222	5	+	+	CCONJ
ejpam-811	222	6	〈	〈	NOUN
ejpam-811	222	7	h(ξ),µ	h(ξ),µ	NOUN
ejpam-811	222	8	〉	〉	NOUN
ejpam-811	222	9	]	]	X
ejpam-811	222	10	�	�	PROPN
ejpam-811	222	11	·	·	PUNCT
ejpam-811	222	12	�	�	PROPN
ejpam-811	222	13	k∑	k∑	PROPN
ejpam-811	222	14	i=1	i=1	PROPN
ejpam-811	222	15	λi	λi	ADP
ejpam-811	222	16	�	�	PROPN
ejpam-811	222	17	∇z	∇z	PROPN
ejpam-811	222	18	g(ξ	g(ξ	PROPN
ejpam-811	222	19	,	,	PUNCT
ejpam-811	222	20	ηi	ηi	X
ejpam-811	222	21	)	)	PUNCT
ejpam-811	222	22	+	+	PROPN
ejpam-811	222	23	∇z	∇z	PROPN
ejpam-811	222	24	g(ξ	g(ξ	PROPN
ejpam-811	222	25	,	,	PUNCT
ejpam-811	222	26	ηi	ηi	PROPN
ejpam-811	222	27	)	)	PUNCT
ejpam-811	222	28	�	�	PROPN
ejpam-811	222	29	−	−	PROPN
ejpam-811	222	30	bw2	bw2	PROPN
ejpam-811	222	31	�	�	PROPN
ejpam-811	222	32	<	<	X
ejpam-811	222	33	0	0	PROPN
ejpam-811	222	34	.	.	PUNCT
ejpam-811	223	1	this	this	PRON
ejpam-811	223	2	contradicts	contradict	VERB
ejpam-811	223	3	the	the	DET
ejpam-811	223	4	equality	equality	NOUN
ejpam-811	223	5	of	of	ADP
ejpam-811	223	6	(	(	PUNCT
ejpam-811	223	7	8)	8)	NUM
ejpam-811	223	8	.	.	PUNCT
ejpam-811	224	1	hence	hence	ADV
ejpam-811	224	2	the	the	DET
ejpam-811	224	3	proof	proof	NOUN
ejpam-811	224	4	is	be	AUX
ejpam-811	224	5	complete	complete	ADJ
ejpam-811	224	6	.	.	PUNCT
ejpam-811	225	1	�	�	PROPN
ejpam-811	225	2	theorem	theorem	VERB
ejpam-811	225	3	5	5	NUM
ejpam-811	225	4	.	.	PUNCT
ejpam-811	226	1	[	[	X
ejpam-811	226	2	strong	strong	ADJ
ejpam-811	226	3	duality	duality	NOUN
ejpam-811	226	4	]	]	PUNCT
ejpam-811	226	5	let	let	AUX
ejpam-811	226	6	ζ0	ζ0	NOUN
ejpam-811	226	7	=	=	SYM
ejpam-811	226	8	(	(	PUNCT
ejpam-811	226	9	z0	z0	PROPN
ejpam-811	226	10	,	,	PUNCT
ejpam-811	226	11	z0	z0	PROPN
ejpam-811	226	12	)	)	PUNCT
ejpam-811	226	13	be	be	VERB
ejpam-811	226	14	an	an	DET
ejpam-811	226	15	optimal	optimal	ADJ
ejpam-811	226	16	solution	solution	NOUN
ejpam-811	226	17	of	of	ADP
ejpam-811	226	18	problem	problem	NOUN
ejpam-811	226	19	(	(	PUNCT
ejpam-811	226	20	p	p	X
ejpam-811	226	21	)	)	PUNCT
ejpam-811	226	22	satisfying	satisfy	VERB
ejpam-811	226	23	the	the	DET
ejpam-811	226	24	hypothesis	hypothesis	NOUN
ejpam-811	226	25	of	of	ADP
ejpam-811	226	26	theorem	theorem	NOUN
ejpam-811	226	27	1	1	NUM
ejpam-811	226	28	.	.	PUNCT
ejpam-811	227	1	then	then	ADV
ejpam-811	227	2	there	there	PRON
ejpam-811	227	3	exist	exist	VERB
ejpam-811	227	4	(	(	PUNCT
ejpam-811	227	5	k	k	X
ejpam-811	227	6	,	,	PUNCT
ejpam-811	227	7	eλ	eλ	INTJ
ejpam-811	227	8	,	,	PUNCT
ejpam-811	227	9	eη	eη	NOUN
ejpam-811	227	10	)	)	PUNCT
ejpam-811	227	11	∈	∈	PROPN
ejpam-811	227	12	k(ζ0	k(ζ0	NOUN
ejpam-811	227	13	)	)	PUNCT
ejpam-811	227	14	and	and	CCONJ
ejpam-811	227	15	(	(	PUNCT
ejpam-811	227	16	ζ0,µ	ζ0,µ	PROPN
ejpam-811	227	17	,	,	PUNCT
ejpam-811	227	18	w1	w1	NOUN
ejpam-811	227	19	,	,	PUNCT
ejpam-811	227	20	w2	w2	NOUN
ejpam-811	227	21	)	)	PUNCT
ejpam-811	227	22	∈	∈	PROPN
ejpam-811	228	1	x1(k	x1(k	PROPN
ejpam-811	228	2	,	,	PUNCT
ejpam-811	228	3	eλ	eλ	INTJ
ejpam-811	228	4	,	,	PUNCT
ejpam-811	228	5	eη	eη	NOUN
ejpam-811	228	6	)	)	PUNCT
ejpam-811	228	7	such	such	ADJ
ejpam-811	228	8	that	that	SCONJ
ejpam-811	228	9	(	(	PUNCT
ejpam-811	228	10	k	k	X
ejpam-811	228	11	,	,	PUNCT
ejpam-811	228	12	eλ	eλ	INTJ
ejpam-811	228	13	,	,	PUNCT
ejpam-811	228	14	eη	eη	NOUN
ejpam-811	228	15	,	,	PUNCT
ejpam-811	228	16	ζ0,µ	ζ0,µ	PROPN
ejpam-811	228	17	,	,	PUNCT
ejpam-811	228	18	w1	w1	NOUN
ejpam-811	228	19	,	,	PUNCT
ejpam-811	228	20	w2	w2	NOUN
ejpam-811	228	21	)	)	PUNCT
ejpam-811	228	22	is	be	AUX
ejpam-811	228	23	a	a	DET
ejpam-811	228	24	feasible	feasible	ADJ
ejpam-811	228	25	solution	solution	NOUN
ejpam-811	228	26	of	of	ADP
ejpam-811	228	27	the	the	DET
ejpam-811	228	28	dual	dual	ADJ
ejpam-811	228	29	problem	problem	NOUN
ejpam-811	228	30	(	(	PUNCT
ejpam-811	228	31	wd	wd	PROPN
ejpam-811	228	32	)	)	PUNCT
ejpam-811	228	33	.	.	PUNCT
ejpam-811	229	1	if	if	SCONJ
ejpam-811	229	2	the	the	DET
ejpam-811	229	3	hypotheses	hypothesis	NOUN
ejpam-811	229	4	of	of	ADP
ejpam-811	229	5	theorem	theorem	NOUN
ejpam-811	229	6	4	4	NUM
ejpam-811	229	7	are	be	AUX
ejpam-811	229	8	fulfilled	fulfil	VERB
ejpam-811	229	9	,	,	PUNCT
ejpam-811	229	10	then	then	ADV
ejpam-811	229	11	(	(	PUNCT
ejpam-811	229	12	k	k	X
ejpam-811	229	13	,	,	PUNCT
ejpam-811	229	14	eλ	eλ	INTJ
ejpam-811	229	15	,	,	PUNCT
ejpam-811	229	16	eη	eη	NOUN
ejpam-811	229	17	,	,	PUNCT
ejpam-811	229	18	ζ0,µ	ζ0,µ	PROPN
ejpam-811	229	19	,	,	PUNCT
ejpam-811	229	20	w1	w1	NOUN
ejpam-811	229	21	,	,	PUNCT
ejpam-811	229	22	w2	w2	NOUN
ejpam-811	229	23	)	)	PUNCT
ejpam-811	229	24	is	be	AUX
ejpam-811	229	25	an	an	DET
ejpam-811	229	26	optimal	optimal	ADJ
ejpam-811	229	27	solution	solution	NOUN
ejpam-811	229	28	of	of	ADP
ejpam-811	229	29	(	(	PUNCT
ejpam-811	229	30	wd	wd	PROPN
ejpam-811	229	31	)	)	PUNCT
ejpam-811	229	32	,	,	PUNCT
ejpam-811	229	33	and	and	CCONJ
ejpam-811	229	34	the	the	DET
ejpam-811	229	35	two	two	NUM
ejpam-811	229	36	problems	problem	NOUN
ejpam-811	229	37	(	(	PUNCT
ejpam-811	229	38	p	p	NOUN
ejpam-811	229	39	)	)	PUNCT
ejpam-811	229	40	and	and	CCONJ
ejpam-811	229	41	(	(	PUNCT
ejpam-811	229	42	wd	wd	X
ejpam-811	229	43	)	)	PUNCT
ejpam-811	229	44	have	have	VERB
ejpam-811	229	45	the	the	DET
ejpam-811	229	46	same	same	ADJ
ejpam-811	229	47	optimal	optimal	ADJ
ejpam-811	229	48	values	value	NOUN
ejpam-811	229	49	.	.	PUNCT
ejpam-811	230	1	h.	h.	PROPN
ejpam-811	230	2	lai	lai	PROPN
ejpam-811	230	3	,	,	PUNCT
ejpam-811	230	4	t.	t.	PROPN
ejpam-811	230	5	huang	huang	PROPN
ejpam-811	230	6	/	/	SYM
ejpam-811	230	7	eur	eur	PROPN
ejpam-811	230	8	.	.	PUNCT
ejpam-811	231	1	j.	j.	PROPN
ejpam-811	231	2	pure	pure	PROPN
ejpam-811	231	3	appl	appl	PROPN
ejpam-811	231	4	.	.	PROPN
ejpam-811	231	5	math	math	PROPN
ejpam-811	231	6	,	,	PUNCT
ejpam-811	231	7	3	3	NUM
ejpam-811	231	8	(	(	PUNCT
ejpam-811	231	9	2010	2010	NUM
ejpam-811	231	10	)	)	PUNCT
ejpam-811	231	11	,	,	PUNCT
ejpam-811	231	12	989	989	NUM
ejpam-811	231	13	-	-	PUNCT
ejpam-811	231	14	1005	1005	NUM
ejpam-811	231	15	999	999	NUM
ejpam-811	231	16	proof	proof	NOUN
ejpam-811	231	17	.	.	PUNCT
ejpam-811	232	1	if	if	SCONJ
ejpam-811	232	2	ζ0	ζ0	NOUN
ejpam-811	232	3	=	=	SYM
ejpam-811	232	4	(	(	PUNCT
ejpam-811	232	5	z0	z0	PROPN
ejpam-811	232	6	,	,	PUNCT
ejpam-811	232	7	z0	z0	PROPN
ejpam-811	232	8	)	)	PUNCT
ejpam-811	232	9	∈q	∈q	NOUN
ejpam-811	232	10	be	be	VERB
ejpam-811	232	11	an	an	DET
ejpam-811	232	12	optimal	optimal	ADJ
ejpam-811	232	13	solution	solution	NOUN
ejpam-811	232	14	of	of	ADP
ejpam-811	232	15	problem	problem	NOUN
ejpam-811	232	16	(	(	PUNCT
ejpam-811	232	17	p	p	NOUN
ejpam-811	232	18	)	)	PUNCT
ejpam-811	232	19	with	with	ADP
ejpam-811	232	20	optimal	optimal	ADJ
ejpam-811	232	21	value	value	NOUN
ejpam-811	232	22	v∗	v∗	NOUN
ejpam-811	232	23	=	=	SYM
ejpam-811	232	24	ϕ(ζ0	ϕ(ζ0	NOUN
ejpam-811	232	25	)	)	PUNCT
ejpam-811	233	1	=	=	SYM
ejpam-811	234	1	∑k	∑k	PROPN
ejpam-811	234	2	i=1λire	i=1λire	NOUN
ejpam-811	234	3	[	[	PUNCT
ejpam-811	234	4	f	f	X
ejpam-811	234	5	(	(	PUNCT
ejpam-811	234	6	ζ0,ηi	ζ0,ηi	PROPN
ejpam-811	234	7	)	)	PUNCT
ejpam-811	234	8	+	+	CCONJ
ejpam-811	234	9	(	(	PUNCT
ejpam-811	234	10	z	z	NOUN
ejpam-811	234	11	h	h	NOUN
ejpam-811	234	12	0	0	NUM
ejpam-811	234	13	az0	az0	NOUN
ejpam-811	234	14	)	)	PUNCT
ejpam-811	234	15	1/2	1/2	NUM
ejpam-811	234	16	]	]	PUNCT
ejpam-811	235	1	∑k	∑k	PROPN
ejpam-811	235	2	i=1λire[g(ζ0,ηi)−	i=1λire[g(ζ0,ηi)−	PROPN
ejpam-811	235	3	(	(	PUNCT
ejpam-811	235	4	z	z	NOUN
ejpam-811	235	5	h	h	NOUN
ejpam-811	235	6	0	0	NUM
ejpam-811	235	7	bz0	bz0	NUM
ejpam-811	235	8	)	)	PUNCT
ejpam-811	235	9	1/2	1/2	NUM
ejpam-811	235	10	]	]	PUNCT
ejpam-811	235	11	,	,	PUNCT
ejpam-811	235	12	then	then	ADV
ejpam-811	235	13	by	by	ADP
ejpam-811	235	14	theorem	theorem	NOUN
ejpam-811	235	15	1	1	NUM
ejpam-811	235	16	,	,	PUNCT
ejpam-811	235	17	there	there	PRON
ejpam-811	235	18	exist	exist	VERB
ejpam-811	235	19	0	0	NUM
ejpam-811	235	20	6=	6=	NUM
ejpam-811	235	21	µ	µ	X
ejpam-811	235	22	∈	∈	NOUN
ejpam-811	235	23	s∗	s∗	PROPN
ejpam-811	235	24	⊂	⊂	PROPN
ejpam-811	235	25	cp	cp	PROPN
ejpam-811	235	26	,	,	PUNCT
ejpam-811	235	27	w1	w1	NOUN
ejpam-811	235	28	,	,	PUNCT
ejpam-811	235	29	w2	w2	NOUN
ejpam-811	235	30	∈	∈	PROPN
ejpam-811	235	31	c	c	PROPN
ejpam-811	235	32	n	n	NOUN
ejpam-811	235	33	and	and	CCONJ
ejpam-811	235	34	positive	positive	ADJ
ejpam-811	235	35	integer	integer	NOUN
ejpam-811	235	36	k	k	PROPN
ejpam-811	235	37	to	to	PART
ejpam-811	235	38	satisfy	satisfy	VERB
ejpam-811	235	39	the	the	DET
ejpam-811	235	40	following	follow	VERB
ejpam-811	235	41	equality	equality	NOUN
ejpam-811	235	42	:	:	PUNCT
ejpam-811	235	43	�	�	PROPN
ejpam-811	235	44	k∑	k∑	VERB
ejpam-811	235	45	i=1	i=1	PROPN
ejpam-811	235	46	λi	λi	PROPN
ejpam-811	235	47	�	�	PROPN
ejpam-811	235	48	∇z	∇z	PROPN
ejpam-811	235	49	f	f	PROPN
ejpam-811	235	50	(	(	PUNCT
ejpam-811	235	51	ζ0,ηi	ζ0,ηi	PROPN
ejpam-811	235	52	)	)	PUNCT
ejpam-811	236	1	+	+	PROPN
ejpam-811	236	2	∇z	∇z	ADJ
ejpam-811	236	3	f	f	X
ejpam-811	236	4	(	(	PUNCT
ejpam-811	236	5	ζ0,ηi	ζ0,ηi	PROPN
ejpam-811	236	6	)	)	PUNCT
ejpam-811	236	7	�	�	PROPN
ejpam-811	237	1	+	+	CCONJ
ejpam-811	237	2	aw1	aw1	PROPN
ejpam-811	237	3	+	+	PROPN
ejpam-811	237	4	µ	µ	X
ejpam-811	237	5	t	t	PROPN
ejpam-811	237	6	∇zh(ζ0	∇zh(ζ0	PROPN
ejpam-811	237	7	)	)	PUNCT
ejpam-811	237	8	+	+	PROPN
ejpam-811	237	9	µ	µ	X
ejpam-811	237	10	h∇zh(ζ0	h∇zh(ζ0	PROPN
ejpam-811	237	11	)	)	PUNCT
ejpam-811	237	12	�	�	PROPN
ejpam-811	237	13	×	×	PROPN
ejpam-811	237	14	�	�	PROPN
ejpam-811	237	15	k∑	k∑	PROPN
ejpam-811	238	1	i=1	i=1	PROPN
ejpam-811	238	2	λi	λi	X
ejpam-811	239	1	[	[	X
ejpam-811	239	2	g(ζ0,ηi)−	g(ζ0,ηi)−	NOUN
ejpam-811	239	3	(	(	PUNCT
ejpam-811	239	4	z	z	NOUN
ejpam-811	239	5	h	h	NOUN
ejpam-811	239	6	0	0	NUM
ejpam-811	239	7	bz0	bz0	NUM
ejpam-811	239	8	)	)	PUNCT
ejpam-811	239	9	1/2	1/2	NUM
ejpam-811	239	10	]	]	PUNCT
ejpam-811	239	11	�	�	PROPN
ejpam-811	239	12	−	−	PROPN
ejpam-811	239	13	�	�	PROPN
ejpam-811	239	14	k∑	k∑	VERB
ejpam-811	239	15	i=1	i=1	PROPN
ejpam-811	240	1	λi	λi	X
ejpam-811	240	2	[	[	PUNCT
ejpam-811	240	3	f	f	X
ejpam-811	240	4	(	(	PUNCT
ejpam-811	240	5	ζ0,ηi	ζ0,ηi	PROPN
ejpam-811	240	6	)	)	PUNCT
ejpam-811	241	1	+	+	CCONJ
ejpam-811	241	2	(	(	PUNCT
ejpam-811	241	3	z	z	NOUN
ejpam-811	241	4	h	h	NOUN
ejpam-811	241	5	0	0	NUM
ejpam-811	241	6	az0	az0	NOUN
ejpam-811	241	7	)	)	PUNCT
ejpam-811	241	8	1/2	1/2	NUM
ejpam-811	242	1	+	+	NUM
ejpam-811	242	2	〈	〈	PROPN
ejpam-811	242	3	h(ζ0),µ	h(ζ0),µ	PROPN
ejpam-811	242	4	〉	〉	NOUN
ejpam-811	242	5	]	]	X
ejpam-811	242	6	�	�	PROPN
ejpam-811	242	7	×	×	PROPN
ejpam-811	242	8	�	�	PROPN
ejpam-811	242	9	k∑	k∑	PROPN
ejpam-811	242	10	i=1	i=1	PROPN
ejpam-811	242	11	λi	λi	PROPN
ejpam-811	242	12	�	�	PROPN
ejpam-811	242	13	∇z	∇z	PROPN
ejpam-811	242	14	g(ζ0,ηi	g(ζ0,ηi	NUM
ejpam-811	242	15	)	)	PUNCT
ejpam-811	243	1	+	+	PUNCT
ejpam-811	243	2	∇z	∇z	NOUN
ejpam-811	243	3	g(ζ0,ηi	g(ζ0,ηi	NUM
ejpam-811	243	4	)	)	PUNCT
ejpam-811	243	5	�	�	PROPN
ejpam-811	243	6	−	−	PROPN
ejpam-811	243	7	bw2	bw2	PROPN
ejpam-811	243	8	�	�	PROPN
ejpam-811	243	9	=	=	SYM
ejpam-811	243	10	0	0	PROPN
ejpam-811	243	11	.	.	PUNCT
ejpam-811	244	1	it	it	PRON
ejpam-811	244	2	follows	follow	VERB
ejpam-811	244	3	that	that	SCONJ
ejpam-811	244	4	(	(	PUNCT
ejpam-811	244	5	k	k	X
ejpam-811	244	6	,	,	PUNCT
ejpam-811	244	7	eλ	eλ	INTJ
ejpam-811	244	8	,	,	PUNCT
ejpam-811	244	9	eη	eη	NOUN
ejpam-811	244	10	)	)	PUNCT
ejpam-811	244	11	∈	∈	PROPN
ejpam-811	244	12	k(ζ0	k(ζ0	NOUN
ejpam-811	244	13	)	)	PUNCT
ejpam-811	244	14	and	and	CCONJ
ejpam-811	244	15	(	(	PUNCT
ejpam-811	244	16	ζ0,µ	ζ0,µ	PROPN
ejpam-811	244	17	,	,	PUNCT
ejpam-811	244	18	w1	w1	NOUN
ejpam-811	244	19	,	,	PUNCT
ejpam-811	244	20	w2	w2	NOUN
ejpam-811	244	21	)	)	PUNCT
ejpam-811	244	22	∈	∈	PROPN
ejpam-811	244	23	x	x	X
ejpam-811	244	24	(	(	PUNCT
ejpam-811	244	25	k	k	X
ejpam-811	244	26	,	,	PUNCT
ejpam-811	244	27	eλ	eλ	INTJ
ejpam-811	244	28	,	,	PUNCT
ejpam-811	244	29	eη	eη	NOUN
ejpam-811	244	30	)	)	PUNCT
ejpam-811	244	31	such	such	ADJ
ejpam-811	244	32	that	that	SCONJ
ejpam-811	244	33	(	(	PUNCT
ejpam-811	244	34	k	k	X
ejpam-811	244	35	,	,	PUNCT
ejpam-811	244	36	eλ	eλ	INTJ
ejpam-811	244	37	,	,	PUNCT
ejpam-811	244	38	eη	eη	NOUN
ejpam-811	244	39	,	,	PUNCT
ejpam-811	244	40	ζ0,µ	ζ0,µ	PROPN
ejpam-811	244	41	,	,	PUNCT
ejpam-811	244	42	w1	w1	NOUN
ejpam-811	244	43	,	,	PUNCT
ejpam-811	244	44	w2	w2	NOUN
ejpam-811	244	45	)	)	PUNCT
ejpam-811	244	46	is	be	AUX
ejpam-811	244	47	a	a	DET
ejpam-811	244	48	feasible	feasible	ADJ
ejpam-811	244	49	solution	solution	NOUN
ejpam-811	244	50	of	of	ADP
ejpam-811	244	51	the	the	DET
ejpam-811	244	52	dual	dual	ADJ
ejpam-811	244	53	problem	problem	NOUN
ejpam-811	244	54	(	(	PUNCT
ejpam-811	244	55	wd	wd	PROPN
ejpam-811	244	56	)	)	PUNCT
ejpam-811	244	57	.	.	PUNCT
ejpam-811	245	1	if	if	SCONJ
ejpam-811	245	2	the	the	DET
ejpam-811	245	3	hypotheses	hypothesis	NOUN
ejpam-811	245	4	of	of	ADP
ejpam-811	245	5	theorem	theorem	NOUN
ejpam-811	245	6	4	4	NUM
ejpam-811	245	7	are	be	AUX
ejpam-811	245	8	also	also	ADV
ejpam-811	245	9	fulfilled	fulfil	VERB
ejpam-811	245	10	,	,	PUNCT
ejpam-811	245	11	then	then	ADV
ejpam-811	245	12	(	(	PUNCT
ejpam-811	245	13	k	k	X
ejpam-811	245	14	,	,	PUNCT
ejpam-811	245	15	eλ	eλ	INTJ
ejpam-811	245	16	,	,	PUNCT
ejpam-811	245	17	eη	eη	NOUN
ejpam-811	245	18	,	,	PUNCT
ejpam-811	245	19	ζ0,µ	ζ0,µ	PROPN
ejpam-811	245	20	,	,	PUNCT
ejpam-811	245	21	w1	w1	NOUN
ejpam-811	245	22	,	,	PUNCT
ejpam-811	245	23	w2	w2	NOUN
ejpam-811	245	24	)	)	PUNCT
ejpam-811	245	25	is	be	AUX
ejpam-811	245	26	an	an	DET
ejpam-811	245	27	optimal	optimal	ADJ
ejpam-811	245	28	solution	solution	NOUN
ejpam-811	245	29	of	of	ADP
ejpam-811	245	30	the	the	DET
ejpam-811	245	31	dual	dual	ADJ
ejpam-811	245	32	problem	problem	NOUN
ejpam-811	245	33	(	(	PUNCT
ejpam-811	245	34	wd	wd	PROPN
ejpam-811	245	35	)	)	PUNCT
ejpam-811	245	36	.	.	PUNCT
ejpam-811	246	1	�	�	PROPN
ejpam-811	246	2	now	now	ADV
ejpam-811	246	3	we	we	PRON
ejpam-811	246	4	consider	consider	VERB
ejpam-811	246	5	φ1(•	φ1(•	NOUN
ejpam-811	246	6	)	)	PUNCT
ejpam-811	246	7	as	as	ADP
ejpam-811	246	8	a	a	DET
ejpam-811	246	9	strictly	strictly	ADV
ejpam-811	246	10	pseudoconvex	pseudoconvex	NOUN
ejpam-811	246	11	on	on	ADP
ejpam-811	246	12	q	q	PROPN
ejpam-811	246	13	instead	instead	ADV
ejpam-811	246	14	of	of	ADP
ejpam-811	246	15	pseudoconvex	pseudoconvex	NOUN
ejpam-811	246	16	.	.	PUNCT
ejpam-811	247	1	then	then	ADV
ejpam-811	247	2	we	we	PRON
ejpam-811	247	3	have	have	VERB
ejpam-811	247	4	the	the	DET
ejpam-811	247	5	strict	strict	ADJ
ejpam-811	247	6	converse	converse	NOUN
ejpam-811	247	7	duality	duality	NOUN
ejpam-811	247	8	theorem	theorem	VERB
ejpam-811	247	9	as	as	SCONJ
ejpam-811	247	10	follows	follow	VERB
ejpam-811	247	11	.	.	PUNCT
ejpam-811	248	1	theorem	theorem	ADJ
ejpam-811	248	2	6	6	NUM
ejpam-811	248	3	.	.	PUNCT
ejpam-811	249	1	[	[	X
ejpam-811	249	2	strict	strict	ADJ
ejpam-811	249	3	converse	converse	NOUN
ejpam-811	249	4	duality	duality	NOUN
ejpam-811	249	5	]	]	PUNCT
ejpam-811	249	6	let	let	VERB
ejpam-811	249	7	bζ	bζ	PROPN
ejpam-811	249	8	and	and	CCONJ
ejpam-811	249	9	(	(	PUNCT
ejpam-811	249	10	bk	bk	INTJ
ejpam-811	249	11	,	,	PUNCT
ejpam-811	249	12	bλ	bλ	PROPN
ejpam-811	249	13	,	,	PUNCT
ejpam-811	249	14	bη	bη	VERB
ejpam-811	249	15	,	,	PUNCT
ejpam-811	249	16	bξ	bξ	PROPN
ejpam-811	249	17	,	,	PUNCT
ejpam-811	249	18	bµ,cw1	bµ,cw1	NOUN
ejpam-811	249	19	,	,	PUNCT
ejpam-811	249	20	,	,	PUNCT
ejpam-811	249	21	cw1	cw1	PROPN
ejpam-811	249	22	)	)	PUNCT
ejpam-811	249	23	be	be	AUX
ejpam-811	249	24	optimal	optimal	ADJ
ejpam-811	249	25	solutions	solution	NOUN
ejpam-811	249	26	of	of	ADP
ejpam-811	249	27	(	(	PUNCT
ejpam-811	249	28	p	p	NOUN
ejpam-811	249	29	)	)	PUNCT
ejpam-811	249	30	and	and	CCONJ
ejpam-811	249	31	(	(	PUNCT
ejpam-811	249	32	wd	wd	PROPN
ejpam-811	249	33	)	)	PUNCT
ejpam-811	249	34	,	,	PUNCT
ejpam-811	249	35	respectively	respectively	ADV
ejpam-811	249	36	,	,	PUNCT
ejpam-811	249	37	and	and	CCONJ
ejpam-811	249	38	assume	assume	VERB
ejpam-811	249	39	that	that	SCONJ
ejpam-811	249	40	the	the	DET
ejpam-811	249	41	assumptions	assumption	NOUN
ejpam-811	249	42	of	of	ADP
ejpam-811	249	43	theorem	theorem	ADJ
ejpam-811	249	44	5	5	NUM
ejpam-811	249	45	are	be	AUX
ejpam-811	249	46	fulfilled	fulfil	VERB
ejpam-811	249	47	.	.	PUNCT
ejpam-811	250	1	if	if	SCONJ
ejpam-811	250	2	φ1(•	φ1(•	NOUN
ejpam-811	250	3	)	)	PUNCT
ejpam-811	250	4	is	be	AUX
ejpam-811	250	5	strictly	strictly	ADV
ejpam-811	250	6	pseudoconvex	pseudoconvex	NOUN
ejpam-811	250	7	on	on	ADP
ejpam-811	250	8	q	q	NOUN
ejpam-811	250	9	,	,	PUNCT
ejpam-811	250	10	then	then	ADV
ejpam-811	250	11	bζ=	bζ=	PROPN
ejpam-811	250	12	bξ	bξ	PROPN
ejpam-811	250	13	;	;	PUNCT
ejpam-811	250	14	and	and	CCONJ
ejpam-811	250	15	the	the	DET
ejpam-811	250	16	optimal	optimal	ADJ
ejpam-811	250	17	values	value	NOUN
ejpam-811	250	18	of	of	ADP
ejpam-811	250	19	(	(	PUNCT
ejpam-811	250	20	p	p	NOUN
ejpam-811	250	21	)	)	PUNCT
ejpam-811	250	22	and	and	CCONJ
ejpam-811	250	23	(	(	PUNCT
ejpam-811	250	24	wd	wd	X
ejpam-811	250	25	)	)	PUNCT
ejpam-811	250	26	are	be	AUX
ejpam-811	250	27	equal	equal	ADJ
ejpam-811	250	28	.	.	PUNCT
ejpam-811	251	1	proof	proof	NOUN
ejpam-811	251	2	.	.	PUNCT
ejpam-811	252	1	assume	assume	VERB
ejpam-811	252	2	that	that	SCONJ
ejpam-811	252	3	(	(	PUNCT
ejpam-811	252	4	bz	bz	PROPN
ejpam-811	252	5	,	,	PUNCT
ejpam-811	252	6	bz	bz	PROPN
ejpam-811	252	7	)	)	PUNCT
ejpam-811	252	8	=	=	SYM
ejpam-811	252	9	bζ	bζ	PROPN
ejpam-811	252	10	6=	6=	NOUN
ejpam-811	252	11	bξ	bξ	PROPN
ejpam-811	252	12	=	=	SYM
ejpam-811	252	13	(	(	PUNCT
ejpam-811	252	14	bα	bα	PROPN
ejpam-811	252	15	,	,	PUNCT
ejpam-811	252	16	bα	bα	PROPN
ejpam-811	252	17	)	)	PUNCT
ejpam-811	252	18	,	,	PUNCT
ejpam-811	252	19	and	and	CCONJ
ejpam-811	252	20	reach	reach	VERB
ejpam-811	252	21	a	a	DET
ejpam-811	252	22	contradiction	contradiction	NOUN
ejpam-811	252	23	.	.	PUNCT
ejpam-811	253	1	by	by	ADP
ejpam-811	253	2	theorem	theorem	NOUN
ejpam-811	253	3	5	5	NUM
ejpam-811	253	4	,	,	PUNCT
ejpam-811	253	5	we	we	PRON
ejpam-811	253	6	know	know	VERB
ejpam-811	253	7	that	that	SCONJ
ejpam-811	253	8	max	max	PROPN
ejpam-811	253	9	η∈y	η∈y	PROPN
ejpam-811	253	10	re	re	PROPN
ejpam-811	253	11	[	[	PUNCT
ejpam-811	253	12	f	f	X
ejpam-811	253	13	(	(	PUNCT
ejpam-811	253	14	bζ	bζ	PROPN
ejpam-811	253	15	,	,	PUNCT
ejpam-811	253	16	η	η	PROPN
ejpam-811	253	17	)	)	PUNCT
ejpam-811	253	18	+	+	CCONJ
ejpam-811	253	19	(	(	PUNCT
ejpam-811	253	20	bzhabz)1/2	bzhabz)1/2	PROPN
ejpam-811	253	21	]	]	X
ejpam-811	253	22	re[g(bζ	re[g(bζ	PROPN
ejpam-811	253	23	,	,	PUNCT
ejpam-811	253	24	η)−	η)−	PROPN
ejpam-811	253	25	(	(	PUNCT
ejpam-811	253	26	bzh	bzh	X
ejpam-811	253	27	bbz)1/2	bbz)1/2	PROPN
ejpam-811	253	28	]	]	X
ejpam-811	253	29	=	=	SYM
ejpam-811	253	30	∑bk	∑bk	ADP
ejpam-811	253	31	i=1	i=1	PROPN
ejpam-811	253	32	bλire	bλire	PROPN
ejpam-811	253	33	�	�	PROPN
ejpam-811	253	34	f	f	PROPN
ejpam-811	253	35	(	(	PUNCT
ejpam-811	253	36	bξ	bξ	PROPN
ejpam-811	253	37	,	,	PUNCT
ejpam-811	253	38	bηi	bηi	NOUN
ejpam-811	253	39	)	)	PUNCT
ejpam-811	253	40	+	+	CCONJ
ejpam-811	253	41	(	(	PUNCT
ejpam-811	253	42	bαhabα)1/2	bαhabα)1/2	NOUN
ejpam-811	253	43	+	+	CCONJ
ejpam-811	253	44	〈	〈	NOUN
ejpam-811	253	45	h(bξ	h(bξ	NOUN
ejpam-811	253	46	)	)	PUNCT
ejpam-811	253	47	,	,	PUNCT
ejpam-811	253	48	bµ	bµ	PROPN
ejpam-811	253	49	〉	〉	X
ejpam-811	253	50	�	�	PROPN
ejpam-811	253	51	∑bk	∑bk	ADP
ejpam-811	253	52	i=1	i=1	PROPN
ejpam-811	253	53	bλire	bλire	PROPN
ejpam-811	253	54	�	�	PROPN
ejpam-811	253	55	g(bξ	g(bξ	PROPN
ejpam-811	253	56	,	,	PUNCT
ejpam-811	253	57	bηi)−	bηi)−	PROPN
ejpam-811	253	58	(	(	PUNCT
ejpam-811	253	59	bαh	bαh	PRON
ejpam-811	253	60	bbα)1/2	bbα)1/2	PROPN
ejpam-811	253	61	�	�	PROPN
ejpam-811	253	62	.	.	PUNCT
ejpam-811	254	1	then	then	ADV
ejpam-811	254	2	for	for	ADP
ejpam-811	254	3	each	each	DET
ejpam-811	254	4	η	η	PROPN
ejpam-811	254	5	∈	∈	PROPN
ejpam-811	254	6	y	y	PROPN
ejpam-811	254	7	,	,	PUNCT
ejpam-811	254	8	re	re	PROPN
ejpam-811	254	9	[	[	PUNCT
ejpam-811	254	10	f	f	X
ejpam-811	254	11	(	(	PUNCT
ejpam-811	254	12	bζ	bζ	PROPN
ejpam-811	254	13	,	,	PUNCT
ejpam-811	254	14	η	η	PROPN
ejpam-811	254	15	)	)	PUNCT
ejpam-811	254	16	+	+	CCONJ
ejpam-811	254	17	(	(	PUNCT
ejpam-811	254	18	bzhabz)1/2	bzhabz)1/2	PROPN
ejpam-811	254	19	]	]	X
ejpam-811	254	20	re[g(bζ	re[g(bζ	PROPN
ejpam-811	254	21	,	,	PUNCT
ejpam-811	254	22	η)−	η)−	PROPN
ejpam-811	254	23	(	(	PUNCT
ejpam-811	254	24	bzh	bzh	X
ejpam-811	254	25	bbz)1/2	bbz)1/2	PROPN
ejpam-811	254	26	]	]	X
ejpam-811	254	27	≤	≤	NUM
ejpam-811	254	28	∑bk	∑bk	ADP
ejpam-811	254	29	i=1	i=1	PROPN
ejpam-811	254	30	bλire	bλire	PROPN
ejpam-811	254	31	�	�	PROPN
ejpam-811	254	32	f	f	PROPN
ejpam-811	254	33	(	(	PUNCT
ejpam-811	254	34	bξ	bξ	PROPN
ejpam-811	254	35	,	,	PUNCT
ejpam-811	254	36	bηi	bηi	NOUN
ejpam-811	254	37	)	)	PUNCT
ejpam-811	254	38	+	+	CCONJ
ejpam-811	254	39	(	(	PUNCT
ejpam-811	254	40	bαhabα)1/2	bαhabα)1/2	NOUN
ejpam-811	254	41	+	+	CCONJ
ejpam-811	254	42	〈	〈	NOUN
ejpam-811	254	43	h(bξ	h(bξ	NOUN
ejpam-811	254	44	)	)	PUNCT
ejpam-811	254	45	,	,	PUNCT
ejpam-811	254	46	bµ	bµ	X
ejpam-811	254	47	〉	〉	X
ejpam-811	254	48	�	�	PROPN
ejpam-811	254	49	∑bk	∑bk	ADP
ejpam-811	254	50	i=1	i=1	PROPN
ejpam-811	254	51	bλire	bλire	PROPN
ejpam-811	254	52	�	�	PROPN
ejpam-811	254	53	g(bξ	g(bξ	PROPN
ejpam-811	254	54	,	,	PUNCT
ejpam-811	254	55	bηi)−	bηi)−	PROPN
ejpam-811	254	56	(	(	PUNCT
ejpam-811	254	57	bαh	bαh	PRON
ejpam-811	254	58	bbα)1/2	bbα)1/2	NOUN
ejpam-811	254	59	�	�	PROPN
ejpam-811	254	60	.	.	PUNCT
ejpam-811	255	1	that	that	PRON
ejpam-811	255	2	is	be	AUX
ejpam-811	255	3	,	,	PUNCT
ejpam-811	255	4	for	for	ADP
ejpam-811	255	5	each	each	DET
ejpam-811	255	6	η	η	PROPN
ejpam-811	255	7	∈	∈	PROPN
ejpam-811	255	8	y	y	PROPN
ejpam-811	255	9	,	,	PUNCT
ejpam-811	255	10	�	�	PROPN
ejpam-811	255	11	re	re	SYM
ejpam-811	255	12	[	[	PUNCT
ejpam-811	255	13	f	f	X
ejpam-811	255	14	(	(	PUNCT
ejpam-811	255	15	bζ	bζ	PROPN
ejpam-811	255	16	,	,	PUNCT
ejpam-811	255	17	η	η	PROPN
ejpam-811	255	18	)	)	PUNCT
ejpam-811	255	19	+	+	CCONJ
ejpam-811	255	20	(	(	PUNCT
ejpam-811	255	21	bzhabz)1/2	bzhabz)1/2	X
ejpam-811	255	22	�	�	PROPN
ejpam-811	255	23	×	×	PROPN
ejpam-811	255	24	�	�	PROPN
ejpam-811	255	25	bk∑	bk∑	PROPN
ejpam-811	255	26	i=1	i=1	PROPN
ejpam-811	255	27	bλire	bλire	NOUN
ejpam-811	255	28	�	�	PROPN
ejpam-811	255	29	g(bξ	g(bξ	PROPN
ejpam-811	255	30	,	,	PUNCT
ejpam-811	255	31	bηi)−	bηi)−	PROPN
ejpam-811	255	32	(	(	PUNCT
ejpam-811	255	33	bαh	bαh	PROPN
ejpam-811	255	34	bbα)1/2	bbα)1/2	PROPN
ejpam-811	255	35	�	�	PROPN
ejpam-811	255	36	�	�	PROPN
ejpam-811	255	37	h.	h.	PROPN
ejpam-811	255	38	lai	lai	PROPN
ejpam-811	255	39	,	,	PUNCT
ejpam-811	255	40	t.	t.	PROPN
ejpam-811	255	41	huang	huang	PROPN
ejpam-811	255	42	/	/	SYM
ejpam-811	255	43	eur	eur	PROPN
ejpam-811	255	44	.	.	PUNCT
ejpam-811	256	1	j.	j.	PROPN
ejpam-811	256	2	pure	pure	PROPN
ejpam-811	256	3	appl	appl	PROPN
ejpam-811	256	4	.	.	PROPN
ejpam-811	256	5	math	math	PROPN
ejpam-811	256	6	,	,	PUNCT
ejpam-811	256	7	3	3	NUM
ejpam-811	256	8	(	(	PUNCT
ejpam-811	256	9	2010	2010	NUM
ejpam-811	256	10	)	)	PUNCT
ejpam-811	256	11	,	,	PUNCT
ejpam-811	256	12	989	989	NUM
ejpam-811	256	13	-	-	SYM
ejpam-811	256	14	1005	1005	NUM
ejpam-811	256	15	1000	1000	NUM
ejpam-811	256	16	−	−	PROPN
ejpam-811	256	17	�	�	PROPN
ejpam-811	256	18	re[g(bζ	re[g(bζ	PROPN
ejpam-811	256	19	,	,	PUNCT
ejpam-811	256	20	η)−	η)−	PROPN
ejpam-811	256	21	(	(	PUNCT
ejpam-811	256	22	bzh	bzh	PROPN
ejpam-811	256	23	bbz)1/2	bbz)1/2	PROPN
ejpam-811	256	24	]	]	X
ejpam-811	256	25	�	�	PROPN
ejpam-811	256	26	×	×	PROPN
ejpam-811	256	27	�	�	PROPN
ejpam-811	256	28	bk∑	bk∑	PROPN
ejpam-811	256	29	i=1	i=1	PROPN
ejpam-811	256	30	bλire	bλire	NOUN
ejpam-811	256	31	�	�	PROPN
ejpam-811	256	32	f	f	PROPN
ejpam-811	256	33	(	(	PUNCT
ejpam-811	256	34	bξ	bξ	PROPN
ejpam-811	256	35	,	,	PUNCT
ejpam-811	256	36	bηi	bηi	NOUN
ejpam-811	256	37	)	)	PUNCT
ejpam-811	257	1	+	+	CCONJ
ejpam-811	257	2	(	(	PUNCT
ejpam-811	257	3	bαhabα)1/2	bαhabα)1/2	NOUN
ejpam-811	257	4	+	+	CCONJ
ejpam-811	257	5	〈	〈	NOUN
ejpam-811	257	6	h(bξ	h(bξ	NOUN
ejpam-811	257	7	)	)	PUNCT
ejpam-811	257	8	,	,	PUNCT
ejpam-811	257	9	bµ	bµ	PROPN
ejpam-811	257	10	〉	〉	X
ejpam-811	257	11	�	�	PROPN
ejpam-811	257	12	�	�	PROPN
ejpam-811	257	13	≤	≤	PROPN
ejpam-811	257	14	0	0	NUM
ejpam-811	257	15	.	.	PUNCT
ejpam-811	258	1	it	it	PRON
ejpam-811	258	2	implies	imply	VERB
ejpam-811	258	3	that	that	SCONJ
ejpam-811	258	4	�	�	PROPN
ejpam-811	258	5	bk∑	bk∑	PROPN
ejpam-811	258	6	i=1	i=1	PROPN
ejpam-811	258	7	bλire	bλire	NOUN
ejpam-811	258	8	[	[	PUNCT
ejpam-811	258	9	f	f	PROPN
ejpam-811	258	10	(	(	PUNCT
ejpam-811	258	11	bζ	bζ	NOUN
ejpam-811	258	12	,	,	PUNCT
ejpam-811	258	13	bηi	bηi	NOUN
ejpam-811	258	14	)	)	PUNCT
ejpam-811	258	15	+	+	CCONJ
ejpam-811	258	16	(	(	PUNCT
ejpam-811	258	17	bzhabz)1/2	bzhabz)1/2	PROPN
ejpam-811	258	18	]	]	X
ejpam-811	258	19	�	�	PROPN
ejpam-811	258	20	×	×	PROPN
ejpam-811	258	21	�	�	PROPN
ejpam-811	258	22	bk∑	bk∑	PROPN
ejpam-811	258	23	i=1	i=1	PROPN
ejpam-811	258	24	bλire	bλire	NOUN
ejpam-811	258	25	�	�	PROPN
ejpam-811	258	26	g(bξ	g(bξ	PROPN
ejpam-811	258	27	,	,	PUNCT
ejpam-811	258	28	bηi)−	bηi)−	PROPN
ejpam-811	258	29	(	(	PUNCT
ejpam-811	258	30	bαh	bαh	PRON
ejpam-811	258	31	bbα)1/2	bbα)1/2	PROPN
ejpam-811	258	32	�	�	PROPN
ejpam-811	258	33	�	�	PROPN
ejpam-811	258	34	−	−	PROPN
ejpam-811	258	35	�	�	PROPN
ejpam-811	258	36	bk∑	bk∑	VERB
ejpam-811	258	37	i=1	i=1	PROPN
ejpam-811	259	1	bλire[g(bζ	bλire[g(bζ	PROPN
ejpam-811	259	2	,	,	PUNCT
ejpam-811	259	3	bηi)−	bηi)−	PROPN
ejpam-811	259	4	(	(	PUNCT
ejpam-811	259	5	bzh	bzh	X
ejpam-811	259	6	bbz)1/2	bbz)1/2	PROPN
ejpam-811	259	7	]	]	X
ejpam-811	259	8	�	�	PROPN
ejpam-811	259	9	×	×	PROPN
ejpam-811	259	10	�	�	PROPN
ejpam-811	259	11	bk∑	bk∑	PROPN
ejpam-811	259	12	i=1	i=1	PROPN
ejpam-811	259	13	bλire	bλire	NOUN
ejpam-811	259	14	�	�	PROPN
ejpam-811	259	15	f	f	PROPN
ejpam-811	259	16	(	(	PUNCT
ejpam-811	259	17	bξ	bξ	PROPN
ejpam-811	259	18	,	,	PUNCT
ejpam-811	259	19	bηi	bηi	NOUN
ejpam-811	259	20	)	)	PUNCT
ejpam-811	260	1	+	+	CCONJ
ejpam-811	260	2	(	(	PUNCT
ejpam-811	260	3	bαhabα)1/2	bαhabα)1/2	NOUN
ejpam-811	260	4	+	+	CCONJ
ejpam-811	260	5	〈	〈	NOUN
ejpam-811	260	6	h(bξ	h(bξ	NOUN
ejpam-811	260	7	)	)	PUNCT
ejpam-811	260	8	,	,	PUNCT
ejpam-811	260	9	bµ	bµ	PROPN
ejpam-811	260	10	〉	〉	X
ejpam-811	260	11	�	�	NOUN
ejpam-811	260	12	�	�	PROPN
ejpam-811	260	13	≤	≤	NOUN
ejpam-811	260	14	0	0	NUM
ejpam-811	260	15	.	.	PUNCT
ejpam-811	261	1	(	(	PUNCT
ejpam-811	261	2	15	15	NUM
ejpam-811	261	3	)	)	PUNCT
ejpam-811	261	4	from	from	ADP
ejpam-811	261	5	inequality	inequality	NOUN
ejpam-811	261	6	(	(	PUNCT
ejpam-811	261	7	15	15	NUM
ejpam-811	261	8	)	)	PUNCT
ejpam-811	261	9	,	,	PUNCT
ejpam-811	261	10	we	we	PRON
ejpam-811	261	11	use	use	VERB
ejpam-811	261	12	the	the	DET
ejpam-811	261	13	same	same	ADJ
ejpam-811	261	14	line	line	NOUN
ejpam-811	261	15	as	as	ADP
ejpam-811	261	16	the	the	DET
ejpam-811	261	17	proof	proof	NOUN
ejpam-811	261	18	of	of	ADP
ejpam-811	261	19	theorem	theorem	ADJ
ejpam-811	261	20	4	4	NUM
ejpam-811	261	21	,	,	PUNCT
ejpam-811	261	22	one	one	PRON
ejpam-811	261	23	can	can	AUX
ejpam-811	261	24	easily	easily	ADV
ejpam-811	261	25	obtain	obtain	VERB
ejpam-811	261	26	φ1	φ1	PROPN
ejpam-811	261	27	(	(	PUNCT
ejpam-811	261	28	bζ)≤	bζ)≤	NOUN
ejpam-811	261	29	φ1	φ1	PROPN
ejpam-811	261	30	(	(	PUNCT
ejpam-811	261	31	bξ	bξ	PROPN
ejpam-811	261	32	)	)	PUNCT
ejpam-811	261	33	.	.	PUNCT
ejpam-811	262	1	since	since	SCONJ
ejpam-811	262	2	hypothesis	hypothesis	NOUN
ejpam-811	262	3	φ1(•	φ1(•	NOUN
ejpam-811	262	4	)	)	PUNCT
ejpam-811	262	5	is	be	AUX
ejpam-811	262	6	strictly	strictly	ADV
ejpam-811	262	7	pseudoconvex	pseudoconvex	NOUN
ejpam-811	262	8	on	on	ADP
ejpam-811	262	9	q	q	X
ejpam-811	262	10	,	,	PUNCT
ejpam-811	262	11	it	it	PRON
ejpam-811	262	12	implies	imply	VERB
ejpam-811	262	13	that	that	SCONJ
ejpam-811	262	14	�	�	PROPN
ejpam-811	262	15	bk∑	bk∑	PROPN
ejpam-811	262	16	i=1	i=1	PROPN
ejpam-811	262	17	bλi	bλi	PROPN
ejpam-811	262	18	�	�	PROPN
ejpam-811	262	19	∇z	∇z	PROPN
ejpam-811	262	20	f	f	PROPN
ejpam-811	262	21	(	(	PUNCT
ejpam-811	262	22	bξ	bξ	PROPN
ejpam-811	262	23	,	,	PUNCT
ejpam-811	262	24	bηi	bηi	NOUN
ejpam-811	262	25	)	)	PUNCT
ejpam-811	263	1	+	+	PROPN
ejpam-811	263	2	∇z	∇z	ADJ
ejpam-811	263	3	f	f	X
ejpam-811	263	4	(	(	PUNCT
ejpam-811	263	5	bξ	bξ	PROPN
ejpam-811	263	6	,	,	PUNCT
ejpam-811	263	7	bηi	bηi	NOUN
ejpam-811	263	8	)	)	PUNCT
ejpam-811	263	9	�	�	PROPN
ejpam-811	263	10	+	+	CCONJ
ejpam-811	263	11	abw1	abw1	ADJ
ejpam-811	263	12	+	+	CCONJ
ejpam-811	263	13	bµt	bµt	PROPN
ejpam-811	263	14	∇zh(bξ	∇zh(bξ	NOUN
ejpam-811	263	15	)	)	PUNCT
ejpam-811	264	1	+	+	X
ejpam-811	264	2	bµh∇zh(bξ	bµh∇zh(bξ	NOUN
ejpam-811	264	3	)	)	PUNCT
ejpam-811	264	4	�	�	PROPN
ejpam-811	264	5	·	·	PUNCT
ejpam-811	264	6	�	�	PROPN
ejpam-811	264	7	bk∑	bk∑	PROPN
ejpam-811	264	8	i=1	i=1	PROPN
ejpam-811	264	9	bλi	bλi	PROPN
ejpam-811	265	1	[	[	X
ejpam-811	265	2	g	g	X
ejpam-811	265	3	(	(	PUNCT
ejpam-811	265	4	bξ	bξ	PROPN
ejpam-811	265	5	,	,	PUNCT
ejpam-811	265	6	bηi)−	bηi)−	PROPN
ejpam-811	265	7	(	(	PUNCT
ejpam-811	265	8	bαh	bαh	PRON
ejpam-811	265	9	bbα)1/2	bbα)1/2	PROPN
ejpam-811	265	10	]	]	X
ejpam-811	265	11	�	�	PROPN
ejpam-811	265	12	−	−	PROPN
ejpam-811	265	13	�	�	PROPN
ejpam-811	265	14	bk∑	bk∑	PROPN
ejpam-811	265	15	i=1	i=1	PROPN
ejpam-811	266	1	bλi	bλi	PROPN
ejpam-811	266	2	[	[	PUNCT
ejpam-811	266	3	f	f	X
ejpam-811	266	4	(	(	PUNCT
ejpam-811	266	5	bξ	bξ	PROPN
ejpam-811	266	6	,	,	PUNCT
ejpam-811	266	7	bηi	bηi	NOUN
ejpam-811	266	8	)	)	PUNCT
ejpam-811	267	1	+	+	CCONJ
ejpam-811	267	2	(	(	PUNCT
ejpam-811	267	3	bαhabα)1/2	bαhabα)1/2	NOUN
ejpam-811	267	4	+	+	CCONJ
ejpam-811	267	5	〈	〈	NOUN
ejpam-811	267	6	h(bξ	h(bξ	NOUN
ejpam-811	267	7	)	)	PUNCT
ejpam-811	267	8	,	,	PUNCT
ejpam-811	267	9	bµ	bµ	PROPN
ejpam-811	267	10	〉	〉	NOUN
ejpam-811	267	11	]	]	X
ejpam-811	267	12	�	�	PROPN
ejpam-811	267	13	·	·	PUNCT
ejpam-811	267	14	�	�	PROPN
ejpam-811	267	15	bk∑	bk∑	PROPN
ejpam-811	267	16	i=1	i=1	PROPN
ejpam-811	267	17	bλi	bλi	PROPN
ejpam-811	267	18	�	�	PROPN
ejpam-811	267	19	∇z	∇z	PROPN
ejpam-811	267	20	g(bξ	g(bξ	PROPN
ejpam-811	267	21	,	,	PUNCT
ejpam-811	267	22	bηi	bηi	NOUN
ejpam-811	267	23	)	)	PUNCT
ejpam-811	268	1	+	+	SYM
ejpam-811	268	2	∇z	∇z	PROPN
ejpam-811	268	3	g(bξ	g(bξ	NOUN
ejpam-811	268	4	,	,	PUNCT
ejpam-811	268	5	bηi	bηi	NOUN
ejpam-811	268	6	)	)	PUNCT
ejpam-811	268	7	�	�	PROPN
ejpam-811	268	8	−	−	PROPN
ejpam-811	268	9	b	b	PROPN
ejpam-811	268	10	bw2	bw2	PROPN
ejpam-811	268	11	�	�	PROPN
ejpam-811	268	12	<	<	X
ejpam-811	268	13	0	0	NUM
ejpam-811	268	14	which	which	PRON
ejpam-811	268	15	contradicts	contradict	VERB
ejpam-811	268	16	the	the	DET
ejpam-811	268	17	equality	equality	NOUN
ejpam-811	268	18	of	of	ADP
ejpam-811	268	19	(	(	PUNCT
ejpam-811	268	20	8)	8)	NUM
ejpam-811	268	21	.	.	PUNCT
ejpam-811	269	1	hence	hence	ADV
ejpam-811	269	2	the	the	DET
ejpam-811	269	3	proof	proof	NOUN
ejpam-811	269	4	is	be	AUX
ejpam-811	269	5	complete	complete	ADJ
ejpam-811	269	6	.	.	PUNCT
ejpam-811	270	1	�	�	PROPN
ejpam-811	270	2	6	6	NUM
ejpam-811	270	3	.	.	PUNCT
ejpam-811	271	1	mond	mond	PROPN
ejpam-811	271	2	-	-	PUNCT
ejpam-811	271	3	weir	weir	PROPN
ejpam-811	271	4	dual	dual	ADJ
ejpam-811	271	5	problem	problem	NOUN
ejpam-811	271	6	and	and	CCONJ
ejpam-811	271	7	its	its	PRON
ejpam-811	271	8	duality	duality	NOUN
ejpam-811	271	9	theorems	theorem	VERB
ejpam-811	271	10	the	the	DET
ejpam-811	271	11	minimax	minimax	NOUN
ejpam-811	271	12	fractional	fractional	ADJ
ejpam-811	271	13	problem	problem	NOUN
ejpam-811	271	14	(	(	PUNCT
ejpam-811	271	15	p	p	NOUN
ejpam-811	271	16	)	)	PUNCT
ejpam-811	271	17	,	,	PUNCT
ejpam-811	271	18	actually	actually	ADV
ejpam-811	271	19	is	be	AUX
ejpam-811	271	20	a	a	DET
ejpam-811	271	21	minimization	minimization	NOUN
ejpam-811	271	22	problem	problem	NOUN
ejpam-811	271	23	with	with	ADP
ejpam-811	271	24	objective	objective	ADJ
ejpam-811	271	25	function	function	NOUN
ejpam-811	271	26	ϕ(ζ	ϕ(ζ	X
ejpam-811	271	27	)	)	PUNCT
ejpam-811	272	1	=	=	PUNCT
ejpam-811	273	1	∑k	∑k	PROPN
ejpam-811	273	2	i=1λire	i=1λire	VERB
ejpam-811	273	3	�	�	PROPN
ejpam-811	273	4	f	f	PROPN
ejpam-811	273	5	(	(	PUNCT
ejpam-811	273	6	ζ	ζ	PROPN
ejpam-811	273	7	,	,	PUNCT
ejpam-811	273	8	ηi	ηi	PROPN
ejpam-811	273	9	)	)	PUNCT
ejpam-811	274	1	+	+	CCONJ
ejpam-811	274	2	(	(	PUNCT
ejpam-811	274	3	z	z	NOUN
ejpam-811	274	4	haz)1/2	haz)1/2	PROPN
ejpam-811	274	5	�	�	PROPN
ejpam-811	274	6	∑k	∑k	PROPN
ejpam-811	274	7	i=1λire	i=1λire	NOUN
ejpam-811	274	8	�	�	PROPN
ejpam-811	274	9	g(ζ	g(ζ	PROPN
ejpam-811	274	10	,	,	PUNCT
ejpam-811	274	11	ηi)−	ηi)−	PUNCT
ejpam-811	274	12	(	(	PUNCT
ejpam-811	274	13	zh	zh	X
ejpam-811	274	14	bz)1/2	bz)1/2	PROPN
ejpam-811	274	15	�	�	PROPN
ejpam-811	274	16	.	.	PUNCT
ejpam-811	275	1	thus	thus	ADV
ejpam-811	275	2	the	the	DET
ejpam-811	275	3	mond	mond	PROPN
ejpam-811	275	4	-	-	PUNCT
ejpam-811	275	5	weir	weir	PROPN
ejpam-811	275	6	type	type	PROPN
ejpam-811	275	7	dual	dual	ADJ
ejpam-811	275	8	problem	problem	NOUN
ejpam-811	275	9	(	(	PUNCT
ejpam-811	275	10	d	d	X
ejpam-811	275	11	)	)	PUNCT
ejpam-811	275	12	can	can	AUX
ejpam-811	275	13	be	be	AUX
ejpam-811	275	14	regarded	regard	VERB
ejpam-811	275	15	as	as	ADP
ejpam-811	275	16	a	a	DET
ejpam-811	275	17	maximization	maximization	NOUN
ejpam-811	275	18	problem	problem	NOUN
ejpam-811	275	19	with	with	ADP
ejpam-811	275	20	objective	objective	ADJ
ejpam-811	275	21	function	function	NOUN
ejpam-811	275	22	ϕ(ξ	ϕ(ξ	PROPN
ejpam-811	275	23	)	)	PUNCT
ejpam-811	276	1	=	=	PUNCT
ejpam-811	277	1	∑k	∑k	PROPN
ejpam-811	277	2	i=1λire	i=1λire	VERB
ejpam-811	277	3	�	�	PROPN
ejpam-811	277	4	f	f	PROPN
ejpam-811	277	5	(	(	PUNCT
ejpam-811	277	6	ξ	ξ	PROPN
ejpam-811	277	7	,	,	PUNCT
ejpam-811	277	8	ηi	ηi	X
ejpam-811	277	9	)	)	PUNCT
ejpam-811	278	1	+	+	CCONJ
ejpam-811	278	2	(	(	PUNCT
ejpam-811	278	3	α	α	PROPN
ejpam-811	278	4	haα)1/2	haα)1/2	PROPN
ejpam-811	278	5	�	�	PROPN
ejpam-811	278	6	∑k	∑k	PROPN
ejpam-811	278	7	i=1λire	i=1λire	VERB
ejpam-811	278	8	�	�	PROPN
ejpam-811	278	9	g(ξ	g(ξ	PROPN
ejpam-811	278	10	,	,	PUNCT
ejpam-811	278	11	ηi)−	ηi)−	PUNCT
ejpam-811	278	12	(	(	PUNCT
ejpam-811	278	13	αh	αh	PROPN
ejpam-811	278	14	bα)1/2	bα)1/2	PROPN
ejpam-811	278	15	�	�	PROPN
ejpam-811	278	16	which	which	PRON
ejpam-811	278	17	is	be	AUX
ejpam-811	278	18	obtained	obtain	VERB
ejpam-811	278	19	by	by	ADP
ejpam-811	278	20	using	use	VERB
ejpam-811	278	21	the	the	DET
ejpam-811	278	22	original	original	ADJ
ejpam-811	278	23	variable	variable	ADJ
ejpam-811	278	24	ζ	ζ	NOUN
ejpam-811	278	25	=	=	SYM
ejpam-811	278	26	(	(	PUNCT
ejpam-811	278	27	z	z	NOUN
ejpam-811	278	28	,	,	PUNCT
ejpam-811	278	29	z	z	NOUN
ejpam-811	278	30	)	)	PUNCT
ejpam-811	278	31	∈q	∈q	NOUN
ejpam-811	278	32	of	of	ADP
ejpam-811	278	33	ϕ(ζ	ϕ(ζ	PROPN
ejpam-811	278	34	)	)	PUNCT
ejpam-811	278	35	replaced	replace	VERB
ejpam-811	278	36	by	by	ADP
ejpam-811	278	37	ξ	ξ	PROPN
ejpam-811	278	38	=	=	SYM
ejpam-811	278	39	(	(	PUNCT
ejpam-811	278	40	α	α	X
ejpam-811	278	41	,	,	PUNCT
ejpam-811	278	42	α	α	NOUN
ejpam-811	278	43	)	)	PUNCT
ejpam-811	278	44	∈q	∈q	NOUN
ejpam-811	278	45	in	in	ADP
ejpam-811	278	46	the	the	DET
ejpam-811	278	47	same	same	ADJ
ejpam-811	278	48	fractional	fractional	ADJ
ejpam-811	278	49	functional	functional	ADJ
ejpam-811	278	50	to	to	PART
ejpam-811	278	51	be	be	AUX
ejpam-811	278	52	ϕ(ξ	ϕ(ξ	PROPN
ejpam-811	278	53	)	)	PUNCT
ejpam-811	278	54	.	.	PUNCT
ejpam-811	279	1	h.	h.	PROPN
ejpam-811	279	2	lai	lai	PROPN
ejpam-811	279	3	,	,	PUNCT
ejpam-811	279	4	t.	t.	PROPN
ejpam-811	279	5	huang	huang	PROPN
ejpam-811	279	6	/	/	SYM
ejpam-811	279	7	eur	eur	PROPN
ejpam-811	279	8	.	.	PUNCT
ejpam-811	280	1	j.	j.	PROPN
ejpam-811	280	2	pure	pure	PROPN
ejpam-811	280	3	appl	appl	PROPN
ejpam-811	280	4	.	.	PROPN
ejpam-811	280	5	math	math	PROPN
ejpam-811	280	6	,	,	PUNCT
ejpam-811	280	7	3	3	NUM
ejpam-811	280	8	(	(	PUNCT
ejpam-811	280	9	2010	2010	NUM
ejpam-811	280	10	)	)	PUNCT
ejpam-811	280	11	,	,	PUNCT
ejpam-811	280	12	989	989	NUM
ejpam-811	280	13	-	-	SYM
ejpam-811	280	14	1005	1005	NUM
ejpam-811	280	15	1001	1001	NUM
ejpam-811	280	16	the	the	DET
ejpam-811	280	17	main	main	ADJ
ejpam-811	280	18	task	task	NOUN
ejpam-811	280	19	for	for	ADP
ejpam-811	280	20	the	the	DET
ejpam-811	280	21	dual	dual	ADJ
ejpam-811	280	22	model	model	NOUN
ejpam-811	280	23	(	(	PUNCT
ejpam-811	280	24	d	d	X
ejpam-811	280	25	)	)	PUNCT
ejpam-811	280	26	is	be	AUX
ejpam-811	280	27	to	to	PART
ejpam-811	280	28	establish	establish	VERB
ejpam-811	280	29	the	the	DET
ejpam-811	280	30	constraints	constraint	NOUN
ejpam-811	280	31	of	of	ADP
ejpam-811	280	32	(	(	PUNCT
ejpam-811	280	33	d	d	NOUN
ejpam-811	280	34	)	)	PUNCT
ejpam-811	280	35	and	and	CCONJ
ejpam-811	280	36	search	search	VERB
ejpam-811	280	37	the	the	DET
ejpam-811	280	38	conditions	condition	NOUN
ejpam-811	280	39	to	to	PART
ejpam-811	280	40	approve	approve	VERB
ejpam-811	280	41	the	the	DET
ejpam-811	280	42	problem	problem	NOUN
ejpam-811	280	43	(	(	PUNCT
ejpam-811	280	44	d	d	X
ejpam-811	280	45	)	)	PUNCT
ejpam-811	280	46	is	be	AUX
ejpam-811	280	47	surely	surely	ADV
ejpam-811	280	48	a	a	DET
ejpam-811	280	49	dual	dual	ADJ
ejpam-811	280	50	problem	problem	NOUN
ejpam-811	280	51	with	with	ADP
ejpam-811	280	52	respect	respect	NOUN
ejpam-811	280	53	to	to	ADP
ejpam-811	280	54	the	the	DET
ejpam-811	280	55	primal	primal	ADJ
ejpam-811	280	56	problem	problem	NOUN
ejpam-811	280	57	(	(	PUNCT
ejpam-811	280	58	p	p	NOUN
ejpam-811	280	59	)	)	PUNCT
ejpam-811	280	60	.	.	PUNCT
ejpam-811	281	1	moreover	moreover	ADV
ejpam-811	281	2	to	to	PART
ejpam-811	281	3	prove	prove	VERB
ejpam-811	281	4	there	there	PRON
ejpam-811	281	5	are	be	VERB
ejpam-811	281	6	no	no	DET
ejpam-811	281	7	duality	duality	NOUN
ejpam-811	281	8	gap	gap	NOUN
ejpam-811	281	9	between	between	ADP
ejpam-811	281	10	(	(	PUNCT
ejpam-811	281	11	d	d	NOUN
ejpam-811	281	12	)	)	PUNCT
ejpam-811	281	13	and	and	CCONJ
ejpam-811	281	14	(	(	PUNCT
ejpam-811	281	15	p	p	NOUN
ejpam-811	281	16	)	)	PUNCT
ejpam-811	281	17	.	.	PUNCT
ejpam-811	282	1	that	that	PRON
ejpam-811	282	2	is	be	AUX
ejpam-811	282	3	,	,	PUNCT
ejpam-811	282	4	they	they	PRON
ejpam-811	282	5	have	have	VERB
ejpam-811	282	6	the	the	DET
ejpam-811	282	7	same	same	ADJ
ejpam-811	282	8	optimal	optimal	ADJ
ejpam-811	282	9	values	value	NOUN
ejpam-811	282	10	.	.	PUNCT
ejpam-811	283	1	in	in	ADP
ejpam-811	283	2	other	other	ADJ
ejpam-811	283	3	word	word	NOUN
ejpam-811	283	4	,	,	PUNCT
ejpam-811	283	5	min	min	NOUN
ejpam-811	283	6	ζ	ζ	X
ejpam-811	283	7	(	(	PUNCT
ejpam-811	283	8	p	p	NOUN
ejpam-811	283	9	)	)	PUNCT
ejpam-811	283	10	=	=	NOUN
ejpam-811	283	11	max	max	X
ejpam-811	283	12	ξ	ξ	X
ejpam-811	283	13	(	(	PUNCT
ejpam-811	283	14	d	d	NOUN
ejpam-811	283	15	)	)	PUNCT
ejpam-811	283	16	is	be	AUX
ejpam-811	283	17	approved	approve	VERB
ejpam-811	283	18	.	.	PUNCT
ejpam-811	284	1	this	this	PRON
ejpam-811	284	2	is	be	AUX
ejpam-811	284	3	the	the	DET
ejpam-811	284	4	main	main	ADJ
ejpam-811	284	5	thought	thought	NOUN
ejpam-811	284	6	.	.	PUNCT
ejpam-811	285	1	fortunately	fortunately	ADV
ejpam-811	285	2	,	,	PUNCT
ejpam-811	285	3	from	from	ADP
ejpam-811	285	4	necessary	necessary	ADJ
ejpam-811	285	5	optimality	optimality	NOUN
ejpam-811	285	6	conditions	condition	NOUN
ejpam-811	285	7	(	(	PUNCT
ejpam-811	285	8	2)∼(5	2)∼(5	NUM
ejpam-811	285	9	)	)	PUNCT
ejpam-811	285	10	is	be	AUX
ejpam-811	285	11	used	use	VERB
ejpam-811	285	12	to	to	ADP
ejpam-811	285	13	the	the	DET
ejpam-811	285	14	assumptions	assumption	NOUN
ejpam-811	285	15	for	for	ADP
ejpam-811	285	16	sufficient	sufficient	ADJ
ejpam-811	285	17	optimality	optimality	NOUN
ejpam-811	285	18	conditions	condition	NOUN
ejpam-811	285	19	.	.	PUNCT
ejpam-811	286	1	consequently	consequently	ADV
ejpam-811	286	2	one	one	PRON
ejpam-811	286	3	can	can	AUX
ejpam-811	286	4	find	find	VERB
ejpam-811	286	5	the	the	DET
ejpam-811	286	6	existence	existence	NOUN
ejpam-811	286	7	of	of	ADP
ejpam-811	286	8	optimal	optimal	ADJ
ejpam-811	286	9	solution	solution	NOUN
ejpam-811	286	10	for	for	ADP
ejpam-811	286	11	problem	problem	NOUN
ejpam-811	286	12	(	(	PUNCT
ejpam-811	286	13	p	p	NOUN
ejpam-811	286	14	)	)	PUNCT
ejpam-811	286	15	,	,	PUNCT
ejpam-811	286	16	besides	besides	SCONJ
ejpam-811	286	17	a	a	DET
ejpam-811	286	18	feasible	feasible	ADJ
ejpam-811	286	19	solution	solution	NOUN
ejpam-811	286	20	satisfying	satisfy	VERB
ejpam-811	286	21	conditions	condition	NOUN
ejpam-811	286	22	(	(	PUNCT
ejpam-811	286	23	2)∼(5	2)∼(5	NUM
ejpam-811	286	24	)	)	PUNCT
ejpam-811	286	25	,	,	PUNCT
ejpam-811	286	26	it	it	PRON
ejpam-811	286	27	needs	need	VERB
ejpam-811	286	28	extra	extra	ADJ
ejpam-811	286	29	assumptions	assumption	NOUN
ejpam-811	286	30	(	(	PUNCT
ejpam-811	286	31	for	for	ADP
ejpam-811	286	32	instance	instance	NOUN
ejpam-811	286	33	,	,	PUNCT
ejpam-811	286	34	generalized	generalized	ADJ
ejpam-811	286	35	convexity	convexity	NOUN
ejpam-811	286	36	)	)	PUNCT
ejpam-811	286	37	to	to	PART
ejpam-811	286	38	obtain	obtain	VERB
ejpam-811	286	39	a	a	DET
ejpam-811	286	40	sufficient	sufficient	ADJ
ejpam-811	286	41	optimality	optimality	NOUN
ejpam-811	286	42	condition	condition	NOUN
ejpam-811	286	43	.	.	PUNCT
ejpam-811	287	1	caused	cause	VERB
ejpam-811	287	2	from	from	ADP
ejpam-811	287	3	this	this	DET
ejpam-811	287	4	reason	reason	NOUN
ejpam-811	287	5	,	,	PUNCT
ejpam-811	287	6	we	we	PRON
ejpam-811	287	7	establish	establish	VERB
ejpam-811	287	8	the	the	DET
ejpam-811	287	9	mond	mond	PROPN
ejpam-811	287	10	-	-	PUNCT
ejpam-811	287	11	weir	weir	PROPN
ejpam-811	287	12	type	type	PROPN
ejpam-811	287	13	dual	dual	ADJ
ejpam-811	287	14	problem	problem	NOUN
ejpam-811	287	15	(	(	PUNCT
ejpam-811	287	16	mwd	mwd	PROPN
ejpam-811	287	17	)	)	PUNCT
ejpam-811	287	18	as	as	ADP
ejpam-811	287	19	the	the	DET
ejpam-811	287	20	following	follow	VERB
ejpam-811	287	21	form	form	NOUN
ejpam-811	287	22	:	:	PUNCT
ejpam-811	287	23	(	(	PUNCT
ejpam-811	287	24	mwd	mwd	PROPN
ejpam-811	287	25	)	)	PUNCT
ejpam-811	287	26	max	max	PROPN
ejpam-811	287	27	(	(	PUNCT
ejpam-811	287	28	k	k	X
ejpam-811	287	29	,	,	PUNCT
ejpam-811	287	30	eλ	eλ	INTJ
ejpam-811	287	31	,	,	PUNCT
ejpam-811	287	32	eη)∈k(ξ	eη)∈k(ξ	ADJ
ejpam-811	287	33	)	)	PUNCT
ejpam-811	287	34	max	max	PROPN
ejpam-811	287	35	(	(	PUNCT
ejpam-811	287	36	ξ,µ,w1,w2)∈x2(k	ξ,µ,w1,w2)∈x2(k	NOUN
ejpam-811	287	37	,	,	PUNCT
ejpam-811	287	38	eλ	eλ	NOUN
ejpam-811	287	39	,	,	PUNCT
ejpam-811	287	40	eη	eη	NOUN
ejpam-811	287	41	)	)	PUNCT
ejpam-811	287	42	ϕ(ξ	ϕ(ξ	PROPN
ejpam-811	287	43	)	)	PUNCT
ejpam-811	287	44	where	where	SCONJ
ejpam-811	287	45	ξ	ξ	X
ejpam-811	287	46	=	=	SYM
ejpam-811	287	47	(	(	PUNCT
ejpam-811	287	48	α	α	X
ejpam-811	287	49	,	,	PUNCT
ejpam-811	287	50	α	α	NOUN
ejpam-811	287	51	)	)	PUNCT
ejpam-811	287	52	∈	∈	PROPN
ejpam-811	287	53	q	q	X
ejpam-811	288	1	⊂	⊂	PUNCT
ejpam-811	288	2	c2n	c2n	NOUN
ejpam-811	288	3	is	be	AUX
ejpam-811	288	4	given	give	VERB
ejpam-811	288	5	as	as	ADP
ejpam-811	288	6	any	any	DET
ejpam-811	288	7	feasible	feasible	ADJ
ejpam-811	288	8	point	point	NOUN
ejpam-811	288	9	satisfying	satisfy	VERB
ejpam-811	288	10	the	the	DET
ejpam-811	288	11	conditions	condition	NOUN
ejpam-811	288	12	(	(	PUNCT
ejpam-811	288	13	2)∼(5	2)∼(5	NUM
ejpam-811	288	14	)	)	PUNCT
ejpam-811	288	15	in	in	ADP
ejpam-811	288	16	theorem	theorem	NOUN
ejpam-811	288	17	1	1	NUM
ejpam-811	288	18	,	,	PUNCT
ejpam-811	288	19	it	it	PRON
ejpam-811	288	20	corresponds	correspond	VERB
ejpam-811	288	21	to	to	ADP
ejpam-811	288	22	k	k	PROPN
ejpam-811	288	23	∈	∈	PROPN
ejpam-811	288	24	n	n	CCONJ
ejpam-811	288	25	,	,	PUNCT
ejpam-811	288	26	eλ	eλ	X
ejpam-811	288	27	=	=	SYM
ejpam-811	288	28	(	(	PUNCT
ejpam-811	288	29	λ1	λ1	ADJ
ejpam-811	288	30	,	,	PUNCT
ejpam-811	288	31	·	·	PUNCT
ejpam-811	288	32	·	·	PUNCT
ejpam-811	288	33	·	·	PUNCT
ejpam-811	288	34	,	,	PUNCT
ejpam-811	288	35	λk	λk	X
ejpam-811	288	36	)	)	PUNCT
ejpam-811	288	37	,	,	PUNCT
ejpam-811	288	38	λi	λi	X
ejpam-811	288	39	>	>	X
ejpam-811	288	40	0	0	PUNCT
ejpam-811	288	41	with	with	ADP
ejpam-811	288	42	∑k	∑k	PROPN
ejpam-811	288	43	i=1λi	i=1λi	X
ejpam-811	288	44	=	=	SYM
ejpam-811	288	45	1	1	NUM
ejpam-811	288	46	and	and	CCONJ
ejpam-811	288	47	eη	eη	NOUN
ejpam-811	288	48	=	=	SYM
ejpam-811	288	49	(	(	PUNCT
ejpam-811	288	50	η1	η1	NOUN
ejpam-811	288	51	,	,	PUNCT
ejpam-811	288	52	·	·	PUNCT
ejpam-811	288	53	·	·	PUNCT
ejpam-811	288	54	·	·	PUNCT
ejpam-811	288	55	,	,	PUNCT
ejpam-811	288	56	ηk	ηk	PROPN
ejpam-811	288	57	)	)	PUNCT
ejpam-811	288	58	of	of	ADP
ejpam-811	288	59	ηi	ηi	PROPN
ejpam-811	288	60	∈	∈	PROPN
ejpam-811	288	61	y	y	PROPN
ejpam-811	288	62	(	(	PUNCT
ejpam-811	288	63	ξ	ξ	PROPN
ejpam-811	288	64	)	)	PUNCT
ejpam-811	288	65	⊂	⊂	PROPN
ejpam-811	289	1	y	y	PROPN
ejpam-811	289	2	.	.	PUNCT
ejpam-811	290	1	we	we	PRON
ejpam-811	290	2	use	use	VERB
ejpam-811	290	3	k(ξ	k(ξ	ADJ
ejpam-811	290	4	)	)	PUNCT
ejpam-811	290	5	to	to	PART
ejpam-811	290	6	denote	denote	VERB
ejpam-811	290	7	the	the	DET
ejpam-811	290	8	set	set	NOUN
ejpam-811	290	9	of	of	ADP
ejpam-811	290	10	all	all	DET
ejpam-811	290	11	triplet	triplet	NOUN
ejpam-811	290	12	points	point	NOUN
ejpam-811	290	13	(	(	PUNCT
ejpam-811	290	14	k	k	X
ejpam-811	290	15	,	,	PUNCT
ejpam-811	290	16	eλ	eλ	INTJ
ejpam-811	290	17	,	,	PUNCT
ejpam-811	290	18	eη	eη	NOUN
ejpam-811	290	19	)	)	PUNCT
ejpam-811	290	20	depending	depend	VERB
ejpam-811	290	21	on	on	ADP
ejpam-811	290	22	ξ	ξ	PROPN
ejpam-811	290	23	.	.	PUNCT
ejpam-811	291	1	then	then	ADV
ejpam-811	291	2	by	by	ADP
ejpam-811	291	3	the	the	DET
ejpam-811	291	4	triplet	triplet	NOUN
ejpam-811	291	5	points	point	NOUN
ejpam-811	291	6	(	(	PUNCT
ejpam-811	291	7	k	k	X
ejpam-811	291	8	,	,	PUNCT
ejpam-811	291	9	eλ	eλ	PROPN
ejpam-811	291	10	,	,	PUNCT
ejpam-811	291	11	η	η	NOUN
ejpam-811	291	12	)	)	PUNCT
ejpam-811	291	13	corresponding	correspond	VERB
ejpam-811	291	14	to	to	ADP
ejpam-811	291	15	all	all	DET
ejpam-811	291	16	points	point	NOUN
ejpam-811	291	17	(	(	PUNCT
ejpam-811	291	18	ξ,µ	ξ,µ	NOUN
ejpam-811	291	19	,	,	PUNCT
ejpam-811	291	20	w1	w1	NOUN
ejpam-811	291	21	,	,	PUNCT
ejpam-811	291	22	w2	w2	NOUN
ejpam-811	291	23	)	)	PUNCT
ejpam-811	291	24	∈	∈	PROPN
ejpam-811	291	25	c	c	NOUN
ejpam-811	291	26	2n×cp×cn×cn	2n×cp×cn×cn	NOUN
ejpam-811	291	27	in	in	ADP
ejpam-811	291	28	the	the	DET
ejpam-811	291	29	fractional	fractional	ADJ
ejpam-811	291	30	functional	functional	ADJ
ejpam-811	291	31	ϕ(ξ	ϕ(ξ	PROPN
ejpam-811	291	32	)	)	PUNCT
ejpam-811	291	33	and	and	CCONJ
ejpam-811	291	34	maximizing	maximize	VERB
ejpam-811	291	35	the	the	DET
ejpam-811	291	36	real	real	ADJ
ejpam-811	291	37	number	number	NOUN
ejpam-811	291	38	over	over	ADP
ejpam-811	291	39	ξ	ξ	PROPN
ejpam-811	291	40	under	under	ADP
ejpam-811	291	41	the	the	DET
ejpam-811	291	42	complex	complex	ADJ
ejpam-811	291	43	variables	variable	NOUN
ejpam-811	291	44	.	.	PUNCT
ejpam-811	292	1	we	we	PRON
ejpam-811	292	2	denote	denote	VERB
ejpam-811	292	3	x2(k	x2(k	PROPN
ejpam-811	292	4	,	,	PUNCT
ejpam-811	292	5	eλ	eλ	INTJ
ejpam-811	292	6	,	,	PUNCT
ejpam-811	292	7	eη	eη	NOUN
ejpam-811	292	8	)	)	PUNCT
ejpam-811	292	9	as	as	ADP
ejpam-811	292	10	the	the	DET
ejpam-811	292	11	set	set	NOUN
ejpam-811	292	12	of	of	ADP
ejpam-811	292	13	all	all	DET
ejpam-811	292	14	points	point	NOUN
ejpam-811	292	15	(	(	PUNCT
ejpam-811	292	16	ξ,µ	ξ,µ	NOUN
ejpam-811	292	17	,	,	PUNCT
ejpam-811	292	18	w1	w1	NOUN
ejpam-811	292	19	,	,	PUNCT
ejpam-811	292	20	w2	w2	NOUN
ejpam-811	292	21	)	)	PUNCT
ejpam-811	292	22	in	in	ADP
ejpam-811	292	23	problem	problem	NOUN
ejpam-811	292	24	(	(	PUNCT
ejpam-811	292	25	mwd	mwd	PROPN
ejpam-811	292	26	)	)	PUNCT
ejpam-811	292	27	.	.	PUNCT
ejpam-811	293	1	consequently	consequently	ADV
ejpam-811	293	2	,	,	PUNCT
ejpam-811	293	3	from	from	ADP
ejpam-811	293	4	the	the	DET
ejpam-811	293	5	above	above	ADJ
ejpam-811	293	6	preparation	preparation	NOUN
ejpam-811	293	7	,	,	PUNCT
ejpam-811	293	8	the	the	DET
ejpam-811	293	9	mond	mond	PROPN
ejpam-811	293	10	-	-	PUNCT
ejpam-811	293	11	weir	weir	PROPN
ejpam-811	293	12	type	type	PROPN
ejpam-811	293	13	dual	dual	ADJ
ejpam-811	293	14	problem	problem	NOUN
ejpam-811	293	15	is	be	AUX
ejpam-811	293	16	then	then	ADV
ejpam-811	293	17	formulated	formulate	VERB
ejpam-811	293	18	by	by	ADP
ejpam-811	293	19	(	(	PUNCT
ejpam-811	293	20	mwd	mwd	PROPN
ejpam-811	293	21	)	)	PUNCT
ejpam-811	293	22	maxξ∈x	maxξ∈x	PROPN
ejpam-811	293	23	maxη∈y	maxη∈y	PROPN
ejpam-811	293	24	re	re	PROPN
ejpam-811	293	25	[	[	PUNCT
ejpam-811	293	26	f	f	X
ejpam-811	293	27	(	(	PUNCT
ejpam-811	293	28	ξ	ξ	PROPN
ejpam-811	293	29	,	,	PUNCT
ejpam-811	293	30	η)+(αh	η)+(αh	NOUN
ejpam-811	293	31	aα)1/2	aα)1/2	VERB
ejpam-811	293	32	]	]	PUNCT
ejpam-811	294	1	re[g(ξ	re[g(ξ	PROPN
ejpam-811	294	2	,	,	PUNCT
ejpam-811	294	3	η)−(αh	η)−(αh	X
ejpam-811	294	4	bα)1/2	bα)1/2	PROPN
ejpam-811	294	5	]	]	X
ejpam-811	294	6	�	�	PROPN
ejpam-811	294	7	=	=	SYM
ejpam-811	294	8	maxξ∈x	maxξ∈x	PROPN
ejpam-811	294	9	ϕ(ξ	ϕ(ξ	PROPN
ejpam-811	294	10	)	)	PUNCT
ejpam-811	295	1	=	=	PUNCT
ejpam-811	295	2	maxξ∈x	maxξ∈x	PROPN
ejpam-811	295	3	∑k	∑k	PROPN
ejpam-811	295	4	i=1	i=1	PROPN
ejpam-811	295	5	λire	λire	VERB
ejpam-811	295	6	�	�	PROPN
ejpam-811	295	7	f	f	PROPN
ejpam-811	295	8	(	(	PUNCT
ejpam-811	295	9	ξ	ξ	PROPN
ejpam-811	295	10	,	,	PUNCT
ejpam-811	295	11	ηi)+(α	ηi)+(α	PROPN
ejpam-811	295	12	h	h	PROPN
ejpam-811	295	13	aα)1/2	aα)1/2	PROPN
ejpam-811	295	14	�	�	PROPN
ejpam-811	296	1	∑k	∑k	PROPN
ejpam-811	296	2	i=1	i=1	PROPN
ejpam-811	296	3	λire	λire	VERB
ejpam-811	296	4	�	�	PROPN
ejpam-811	296	5	g(ξ	g(ξ	PROPN
ejpam-811	296	6	,	,	PUNCT
ejpam-811	296	7	ηi)−(αh	ηi)−(αh	PROPN
ejpam-811	296	8	bα)1/2	bα)1/2	PROPN
ejpam-811	296	9	�	�	PROPN
ejpam-811	296	10	=	=	SYM
ejpam-811	296	11	max	max	PROPN
ejpam-811	296	12	(	(	PUNCT
ejpam-811	296	13	k	k	X
ejpam-811	296	14	,	,	PUNCT
ejpam-811	296	15	eλ	eλ	INTJ
ejpam-811	296	16	,	,	PUNCT
ejpam-811	296	17	eη)∈k(ξ	eη)∈k(ξ	ADJ
ejpam-811	296	18	)	)	PUNCT
ejpam-811	296	19	max	max	PROPN
ejpam-811	296	20	(	(	PUNCT
ejpam-811	296	21	ξ,µ,w1,w2)∈x2(k	ξ,µ,w1,w2)∈x2(k	NOUN
ejpam-811	296	22	,	,	PUNCT
ejpam-811	296	23	eλ	eλ	NOUN
ejpam-811	296	24	,	,	PUNCT
ejpam-811	296	25	eη	eη	NOUN
ejpam-811	296	26	)	)	PUNCT
ejpam-811	296	27	ϕ(ξ	ϕ(ξ	PROPN
ejpam-811	296	28	)	)	PUNCT
ejpam-811	296	29	�	�	PROPN
ejpam-811	296	30	subject	subject	ADJ
ejpam-811	296	31	to	to	ADP
ejpam-811	296	32	ξ=	ξ=	PROPN
ejpam-811	296	33	(	(	PUNCT
ejpam-811	296	34	α	α	NOUN
ejpam-811	296	35	,	,	PUNCT
ejpam-811	296	36	α	α	NOUN
ejpam-811	296	37	)	)	PUNCT
ejpam-811	296	38	∈q	∈q	NOUN
ejpam-811	296	39	⊂	⊂	PROPN
ejpam-811	296	40	c2n	c2n	PROPN
ejpam-811	296	41	and	and	CCONJ
ejpam-811	296	42	�	�	PROPN
ejpam-811	296	43	k∑	k∑	VERB
ejpam-811	296	44	i=1	i=1	PROPN
ejpam-811	296	45	λi	λi	PROPN
ejpam-811	296	46	�	�	PROPN
ejpam-811	296	47	∇z	∇z	PROPN
ejpam-811	296	48	f	f	PROPN
ejpam-811	296	49	(	(	PUNCT
ejpam-811	296	50	ξ	ξ	PROPN
ejpam-811	296	51	,	,	PUNCT
ejpam-811	296	52	ηi	ηi	X
ejpam-811	296	53	)	)	PUNCT
ejpam-811	296	54	+	+	PROPN
ejpam-811	296	55	∇z	∇z	ADJ
ejpam-811	296	56	f	f	X
ejpam-811	296	57	(	(	PUNCT
ejpam-811	296	58	ξ	ξ	PROPN
ejpam-811	296	59	,	,	PUNCT
ejpam-811	296	60	ηi	ηi	PROPN
ejpam-811	296	61	)	)	PUNCT
ejpam-811	296	62	�	�	PROPN
ejpam-811	296	63	+	+	CCONJ
ejpam-811	296	64	aw1	aw1	PROPN
ejpam-811	296	65	�	�	PROPN
ejpam-811	296	66	×	×	PROPN
ejpam-811	296	67	�	�	PROPN
ejpam-811	296	68	k∑	k∑	PROPN
ejpam-811	296	69	i=1	i=1	PROPN
ejpam-811	296	70	λi	λi	X
ejpam-811	296	71	re	re	VERB
ejpam-811	296	72	[	[	X
ejpam-811	296	73	g(ξ	g(ξ	PROPN
ejpam-811	296	74	,	,	PUNCT
ejpam-811	296	75	ηi)−	ηi)−	PUNCT
ejpam-811	296	76	(	(	PUNCT
ejpam-811	296	77	α	α	PROPN
ejpam-811	296	78	h	h	PROPN
ejpam-811	296	79	bα)1/2	bα)1/2	PROPN
ejpam-811	296	80	]	]	PUNCT
ejpam-811	296	81	�	�	PROPN
ejpam-811	296	82	−	−	PROPN
ejpam-811	296	83	�	�	PROPN
ejpam-811	296	84	k∑	k∑	VERB
ejpam-811	296	85	i=1	i=1	PROPN
ejpam-811	296	86	λire	λire	NOUN
ejpam-811	296	87	[	[	PUNCT
ejpam-811	296	88	f	f	X
ejpam-811	296	89	(	(	PUNCT
ejpam-811	296	90	ξ	ξ	PROPN
ejpam-811	296	91	,	,	PUNCT
ejpam-811	296	92	ηi	ηi	X
ejpam-811	296	93	)	)	PUNCT
ejpam-811	297	1	+	+	CCONJ
ejpam-811	297	2	(	(	PUNCT
ejpam-811	297	3	α	α	PROPN
ejpam-811	297	4	haα)1/2	haα)1/2	PROPN
ejpam-811	297	5	]	]	X
ejpam-811	297	6	�	�	PROPN
ejpam-811	297	7	×	×	PROPN
ejpam-811	297	8	�	�	PROPN
ejpam-811	297	9	k∑	k∑	PROPN
ejpam-811	297	10	i=1	i=1	PROPN
ejpam-811	297	11	λi	λi	ADP
ejpam-811	297	12	�	�	PROPN
ejpam-811	297	13	∇z	∇z	PROPN
ejpam-811	297	14	g(ξ	g(ξ	PROPN
ejpam-811	297	15	,	,	PUNCT
ejpam-811	297	16	ηi	ηi	X
ejpam-811	297	17	)	)	PUNCT
ejpam-811	297	18	+	+	PROPN
ejpam-811	297	19	∇z	∇z	PROPN
ejpam-811	297	20	g(ξ	g(ξ	PROPN
ejpam-811	297	21	,	,	PUNCT
ejpam-811	297	22	ηi	ηi	PROPN
ejpam-811	297	23	)	)	PUNCT
ejpam-811	297	24	�	�	PROPN
ejpam-811	297	25	−	−	PROPN
ejpam-811	297	26	bw2	bw2	PROPN
ejpam-811	297	27	�	�	PROPN
ejpam-811	298	1	+	+	PROPN
ejpam-811	298	2	µt	µt	PROPN
ejpam-811	298	3	∇zh(ξ	∇zh(ξ	PROPN
ejpam-811	298	4	)	)	PUNCT
ejpam-811	298	5	+	+	NOUN
ejpam-811	298	6	µh∇zh(ξ	µh∇zh(ξ	X
ejpam-811	298	7	)	)	PUNCT
ejpam-811	298	8	=	=	SYM
ejpam-811	298	9	0	0	NUM
ejpam-811	298	10	,	,	PUNCT
ejpam-811	298	11	(	(	PUNCT
ejpam-811	298	12	16	16	NUM
ejpam-811	298	13	)	)	PUNCT
ejpam-811	298	14	re〈h(ξ),µ	re〈h(ξ),µ	VERB
ejpam-811	298	15	〉	〉	X
ejpam-811	298	16	≥	≥	NUM
ejpam-811	298	17	0	0	NUM
ejpam-811	298	18	,	,	PUNCT
ejpam-811	298	19	µ	µ	X
ejpam-811	298	20	6=	6=	SYM
ejpam-811	298	21	0	0	NUM
ejpam-811	298	22	in	in	ADP
ejpam-811	298	23	s∗	s∗	PROPN
ejpam-811	298	24	,	,	PUNCT
ejpam-811	298	25	(	(	PUNCT
ejpam-811	298	26	17	17	NUM
ejpam-811	298	27	)	)	PUNCT
ejpam-811	298	28	h.	h.	PROPN
ejpam-811	298	29	lai	lai	PROPN
ejpam-811	298	30	,	,	PUNCT
ejpam-811	298	31	t.	t.	PROPN
ejpam-811	298	32	huang	huang	PROPN
ejpam-811	298	33	/	/	SYM
ejpam-811	298	34	eur	eur	PROPN
ejpam-811	298	35	.	.	PUNCT
ejpam-811	299	1	j.	j.	PROPN
ejpam-811	299	2	pure	pure	PROPN
ejpam-811	299	3	appl	appl	PROPN
ejpam-811	299	4	.	.	PROPN
ejpam-811	299	5	math	math	PROPN
ejpam-811	299	6	,	,	PUNCT
ejpam-811	299	7	3	3	NUM
ejpam-811	299	8	(	(	PUNCT
ejpam-811	299	9	2010	2010	NUM
ejpam-811	299	10	)	)	PUNCT
ejpam-811	299	11	,	,	PUNCT
ejpam-811	299	12	989	989	NUM
ejpam-811	299	13	-	-	SYM
ejpam-811	299	14	1005	1005	NUM
ejpam-811	299	15	1002	1002	NUM
ejpam-811	299	16	wh	wh	NOUN
ejpam-811	299	17	1	1	NUM
ejpam-811	299	18	aw1	aw1	PROPN
ejpam-811	299	19	≤	≤	NUM
ejpam-811	299	20	1	1	NUM
ejpam-811	299	21	,	,	PUNCT
ejpam-811	299	22	(	(	PUNCT
ejpam-811	299	23	αhaα)1/2	αhaα)1/2	PROPN
ejpam-811	299	24	=	=	SYM
ejpam-811	299	25	re(αhaw1	re(αhaw1	PROPN
ejpam-811	299	26	)	)	PUNCT
ejpam-811	299	27	,	,	PUNCT
ejpam-811	299	28	(	(	PUNCT
ejpam-811	299	29	18	18	NUM
ejpam-811	299	30	)	)	PUNCT
ejpam-811	299	31	wh	wh	NOUN
ejpam-811	299	32	2	2	NUM
ejpam-811	299	33	bw2	bw2	PROPN
ejpam-811	299	34	≤	≤	PROPN
ejpam-811	299	35	1	1	NUM
ejpam-811	299	36	,	,	PUNCT
ejpam-811	299	37	(	(	PUNCT
ejpam-811	299	38	αh	αh	NOUN
ejpam-811	299	39	bα)1/2	bα)1/2	PROPN
ejpam-811	299	40	=	=	SYM
ejpam-811	299	41	re(αh	re(αh	PROPN
ejpam-811	299	42	bw2	bw2	PROPN
ejpam-811	299	43	)	)	PUNCT
ejpam-811	299	44	.	.	PUNCT
ejpam-811	300	1	(	(	PUNCT
ejpam-811	300	2	19	19	NUM
ejpam-811	300	3	)	)	PUNCT
ejpam-811	300	4	for	for	ADP
ejpam-811	300	5	convenient	convenient	ADJ
ejpam-811	300	6	,	,	PUNCT
ejpam-811	300	7	we	we	PRON
ejpam-811	300	8	denote	denote	VERB
ejpam-811	300	9	the	the	DET
ejpam-811	300	10	function	function	NOUN
ejpam-811	300	11	φ2(•	φ2(•	ADV
ejpam-811	300	12	)	)	PUNCT
ejpam-811	300	13	=	=	SYM
ejpam-811	300	14	�	�	PROPN
ejpam-811	300	15	∑k	∑k	PROPN
ejpam-811	300	16	i=1λire	i=1λire	VERB
ejpam-811	300	17	�	�	PROPN
ejpam-811	300	18	f	f	PROPN
ejpam-811	300	19	(	(	PUNCT
ejpam-811	300	20	•,ηi	•,ηi	PROPN
ejpam-811	300	21	)	)	PUNCT
ejpam-811	301	1	+	+	CCONJ
ejpam-811	301	2	(	(	PUNCT
ejpam-811	301	3	·	·	PUNCT
ejpam-811	301	4	)	)	PUNCT
ejpam-811	301	5	haw1	haw1	PROPN
ejpam-811	301	6	�	�	PROPN
ejpam-811	301	7	�	�	PROPN
ejpam-811	301	8	×	×	PROPN
ejpam-811	301	9	�	�	PROPN
ejpam-811	301	10	∑k	∑k	PROPN
ejpam-811	301	11	i=1λire	i=1λire	NOUN
ejpam-811	301	12	�	�	PROPN
ejpam-811	301	13	g(ξ	g(ξ	PROPN
ejpam-811	301	14	,	,	PUNCT
ejpam-811	301	15	ηi)−α	ηi)−α	PROPN
ejpam-811	301	16	h	h	PROPN
ejpam-811	301	17	bw2	bw2	PROPN
ejpam-811	301	18	�	�	PROPN
ejpam-811	301	19	�	�	PROPN
ejpam-811	301	20	−	−	PROPN
ejpam-811	301	21	�	�	PROPN
ejpam-811	301	22	∑k	∑k	PROPN
ejpam-811	301	23	i=1λire	i=1λire	VERB
ejpam-811	301	24	�	�	PROPN
ejpam-811	301	25	f	f	PROPN
ejpam-811	301	26	(	(	PUNCT
ejpam-811	301	27	ξ	ξ	PROPN
ejpam-811	301	28	,	,	PUNCT
ejpam-811	301	29	ηi	ηi	X
ejpam-811	301	30	)	)	PUNCT
ejpam-811	302	1	+	+	NOUN
ejpam-811	302	2	α	α	PROPN
ejpam-811	302	3	haw1	haw1	PROPN
ejpam-811	302	4	�	�	PROPN
ejpam-811	302	5	�	�	PROPN
ejpam-811	302	6	×	×	PROPN
ejpam-811	302	7	�	�	PROPN
ejpam-811	302	8	∑k	∑k	PROPN
ejpam-811	302	9	i=1λire	i=1λire	NOUN
ejpam-811	302	10	�	�	PROPN
ejpam-811	302	11	g(•,ηi)−	g(•,ηi)−	PROPN
ejpam-811	302	12	(	(	PUNCT
ejpam-811	302	13	·	·	PUNCT
ejpam-811	302	14	)	)	PUNCT
ejpam-811	302	15	hbw2	hbw2	PROPN
ejpam-811	302	16	�	�	PROPN
ejpam-811	302	17	�	�	PROPN
ejpam-811	302	18	for	for	ADP
ejpam-811	302	19	•=	•=	NOUN
ejpam-811	302	20	(	(	PUNCT
ejpam-811	302	21	·	·	PUNCT
ejpam-811	302	22	,	,	PUNCT
ejpam-811	302	23	·	·	PUNCT
ejpam-811	302	24	)	)	PUNCT
ejpam-811	302	25	∈	∈	PROPN
ejpam-811	302	26	q	q	X
ejpam-811	302	27	⊂	⊂	PROPN
ejpam-811	302	28	c2n	c2n	NOUN
ejpam-811	302	29	.	.	PUNCT
ejpam-811	303	1	in	in	ADP
ejpam-811	303	2	order	order	NOUN
ejpam-811	303	3	to	to	PART
ejpam-811	303	4	show	show	VERB
ejpam-811	303	5	that	that	SCONJ
ejpam-811	303	6	the	the	DET
ejpam-811	303	7	problem	problem	NOUN
ejpam-811	303	8	(	(	PUNCT
ejpam-811	303	9	mwd	mwd	PROPN
ejpam-811	303	10	)	)	PUNCT
ejpam-811	303	11	is	be	AUX
ejpam-811	303	12	a	a	DET
ejpam-811	303	13	dual	dual	ADJ
ejpam-811	303	14	problem	problem	NOUN
ejpam-811	303	15	of	of	ADP
ejpam-811	303	16	(	(	PUNCT
ejpam-811	303	17	p	p	NOUN
ejpam-811	303	18	)	)	PUNCT
ejpam-811	303	19	,	,	PUNCT
ejpam-811	303	20	we	we	PRON
ejpam-811	303	21	need	need	VERB
ejpam-811	303	22	to	to	PART
ejpam-811	303	23	establish	establish	VERB
ejpam-811	303	24	the	the	DET
ejpam-811	303	25	following	follow	VERB
ejpam-811	303	26	duality	duality	NOUN
ejpam-811	303	27	theorems	theorem	NOUN
ejpam-811	303	28	:	:	PUNCT
ejpam-811	303	29	weak	weak	ADJ
ejpam-811	303	30	,	,	PUNCT
ejpam-811	303	31	strong	strong	ADJ
ejpam-811	303	32	and	and	CCONJ
ejpam-811	303	33	strict	strict	ADJ
ejpam-811	303	34	converse	converse	NOUN
ejpam-811	303	35	duality	duality	NOUN
ejpam-811	303	36	theorem	theorem	VERB
ejpam-811	303	37	for	for	ADP
ejpam-811	303	38	problem	problem	NOUN
ejpam-811	303	39	(	(	PUNCT
ejpam-811	303	40	mwd	mwd	PROPN
ejpam-811	303	41	)	)	PUNCT
ejpam-811	303	42	,	,	PUNCT
ejpam-811	303	43	mutatis	mutatis	NOUN
ejpam-811	303	44	mutandis	mutandis	PROPN
ejpam-811	303	45	,	,	PUNCT
ejpam-811	303	46	the	the	DET
ejpam-811	303	47	same	same	ADJ
ejpam-811	303	48	as	as	ADP
ejpam-811	303	49	the	the	DET
ejpam-811	303	50	proof	proof	NOUN
ejpam-811	303	51	of	of	ADP
ejpam-811	303	52	the	the	DET
ejpam-811	303	53	weak	weak	ADJ
ejpam-811	303	54	,	,	PUNCT
ejpam-811	303	55	strong	strong	ADJ
ejpam-811	303	56	and	and	CCONJ
ejpam-811	303	57	strict	strict	ADJ
ejpam-811	303	58	converse	converse	NOUN
ejpam-811	303	59	duality	duality	NOUN
ejpam-811	303	60	theorem	theorem	VERB
ejpam-811	303	61	for	for	ADP
ejpam-811	303	62	problem	problem	NOUN
ejpam-811	303	63	(	(	PUNCT
ejpam-811	303	64	wd	wd	PROPN
ejpam-811	303	65	)	)	PUNCT
ejpam-811	303	66	.	.	PUNCT
ejpam-811	304	1	theorem	theorem	ADJ
ejpam-811	304	2	7	7	NUM
ejpam-811	304	3	(	(	PUNCT
ejpam-811	304	4	weak	weak	ADJ
ejpam-811	304	5	duality	duality	NOUN
ejpam-811	304	6	)	)	PUNCT
ejpam-811	304	7	.	.	PUNCT
ejpam-811	305	1	let	let	VERB
ejpam-811	305	2	ζ	ζ	NOUN
ejpam-811	305	3	=	=	SYM
ejpam-811	305	4	(	(	PUNCT
ejpam-811	305	5	z	z	NOUN
ejpam-811	305	6	,	,	PUNCT
ejpam-811	305	7	z	z	NOUN
ejpam-811	305	8	)	)	PUNCT
ejpam-811	305	9	be	be	AUX
ejpam-811	305	10	(	(	PUNCT
ejpam-811	305	11	p)-feasible	p)-feasible	ADJ
ejpam-811	305	12	,	,	PUNCT
ejpam-811	305	13	and	and	CCONJ
ejpam-811	305	14	(	(	PUNCT
ejpam-811	305	15	k	k	X
ejpam-811	305	16	,	,	PUNCT
ejpam-811	305	17	eλ	eλ	INTJ
ejpam-811	305	18	,	,	PUNCT
ejpam-811	305	19	eη	eη	NOUN
ejpam-811	305	20	,	,	PUNCT
ejpam-811	305	21	ξ,µ	ξ,µ	NOUN
ejpam-811	305	22	,	,	PUNCT
ejpam-811	305	23	w1	w1	NOUN
ejpam-811	305	24	,	,	PUNCT
ejpam-811	305	25	w2	w2	NOUN
ejpam-811	305	26	)	)	PUNCT
ejpam-811	305	27	be	be	AUX
ejpam-811	305	28	(	(	PUNCT
ejpam-811	305	29	wd)feasible	wd)feasible	ADJ
ejpam-811	305	30	.	.	PUNCT
ejpam-811	305	31	suppose	suppose	VERB
ejpam-811	305	32	that	that	SCONJ
ejpam-811	305	33	any	any	DET
ejpam-811	305	34	one	one	NUM
ejpam-811	305	35	of	of	ADP
ejpam-811	305	36	the	the	DET
ejpam-811	305	37	following	follow	VERB
ejpam-811	305	38	conditions	condition	NOUN
ejpam-811	305	39	(	(	PUNCT
ejpam-811	305	40	i	i	NOUN
ejpam-811	305	41	)	)	PUNCT
ejpam-811	305	42	and	and	CCONJ
ejpam-811	305	43	(	(	PUNCT
ejpam-811	305	44	ii	ii	NOUN
ejpam-811	305	45	)	)	PUNCT
ejpam-811	305	46	holds	hold	VERB
ejpam-811	305	47	:	:	PUNCT
ejpam-811	305	48	(	(	PUNCT
ejpam-811	305	49	i	i	NOUN
ejpam-811	305	50	)	)	PUNCT
ejpam-811	305	51	φ2(•	φ2(•	ADV
ejpam-811	305	52	)	)	PUNCT
ejpam-811	305	53	is	be	AUX
ejpam-811	305	54	pseudoconvex	pseudoconvex	NOUN
ejpam-811	305	55	on	on	ADP
ejpam-811	305	56	q	q	PROPN
ejpam-811	305	57	and	and	CCONJ
ejpam-811	305	58	〈	〈	PROPN
ejpam-811	305	59	h(•),µ	h(•),µ	PROPN
ejpam-811	305	60	〉	〉	NOUN
ejpam-811	305	61	is	be	AUX
ejpam-811	305	62	quasiconvex	quasiconvex	NOUN
ejpam-811	305	63	on	on	ADP
ejpam-811	305	64	q	q	NOUN
ejpam-811	305	65	,	,	PUNCT
ejpam-811	305	66	(	(	PUNCT
ejpam-811	305	67	ii	ii	NOUN
ejpam-811	305	68	)	)	PUNCT
ejpam-811	305	69	φ2(•	φ2(•	ADV
ejpam-811	305	70	)	)	PUNCT
ejpam-811	305	71	is	be	AUX
ejpam-811	305	72	quasiconvex	quasiconvex	NOUN
ejpam-811	305	73	on	on	ADP
ejpam-811	305	74	q	q	PROPN
ejpam-811	305	75	and	and	CCONJ
ejpam-811	305	76	〈	〈	PROPN
ejpam-811	305	77	h(•),µ	h(•),µ	PROPN
ejpam-811	305	78	〉	〉	NOUN
ejpam-811	305	79	is	be	AUX
ejpam-811	305	80	strictly	strictly	ADV
ejpam-811	305	81	pseudoconvex	pseudoconvex	NOUN
ejpam-811	305	82	on	on	ADP
ejpam-811	305	83	q	q	NOUN
ejpam-811	306	1	,	,	PUNCT
ejpam-811	306	2	then	then	ADV
ejpam-811	306	3	max	max	PROPN
ejpam-811	306	4	η∈y	η∈y	PROPN
ejpam-811	306	5	re	re	X
ejpam-811	306	6	�	�	PROPN
ejpam-811	306	7	f	f	PROPN
ejpam-811	306	8	(	(	PUNCT
ejpam-811	306	9	ζ	ζ	PROPN
ejpam-811	306	10	,	,	PUNCT
ejpam-811	306	11	η	η	NOUN
ejpam-811	306	12	)	)	PUNCT
ejpam-811	306	13	+	+	CCONJ
ejpam-811	306	14	(	(	PUNCT
ejpam-811	306	15	zhaz)1/2	zhaz)1/2	VERB
ejpam-811	306	16	�	�	PROPN
ejpam-811	306	17	re	re	NOUN
ejpam-811	306	18	�	�	PROPN
ejpam-811	306	19	g(ζ	g(ζ	PROPN
ejpam-811	306	20	,	,	PUNCT
ejpam-811	306	21	η)−	η)−	PROPN
ejpam-811	306	22	(	(	PUNCT
ejpam-811	306	23	zh	zh	PROPN
ejpam-811	306	24	bz)1/2	bz)1/2	PROPN
ejpam-811	306	25	�	�	PROPN
ejpam-811	306	26	≥	≥	PROPN
ejpam-811	306	27	ϕ(ξ	ϕ(ξ	PROPN
ejpam-811	306	28	)	)	PUNCT
ejpam-811	306	29	.	.	PUNCT
ejpam-811	307	1	proof	proof	NOUN
ejpam-811	307	2	.	.	PUNCT
ejpam-811	308	1	suppose	suppose	VERB
ejpam-811	308	2	on	on	ADP
ejpam-811	308	3	the	the	DET
ejpam-811	308	4	contrary	contrary	NOUN
ejpam-811	309	1	that	that	PRON
ejpam-811	309	2	max	max	PROPN
ejpam-811	309	3	η∈y	η∈y	PROPN
ejpam-811	309	4	re	re	X
ejpam-811	309	5	�	�	PROPN
ejpam-811	309	6	f	f	PROPN
ejpam-811	309	7	(	(	PUNCT
ejpam-811	309	8	ζ	ζ	PROPN
ejpam-811	309	9	,	,	PUNCT
ejpam-811	309	10	η	η	NOUN
ejpam-811	309	11	)	)	PUNCT
ejpam-811	309	12	+	+	CCONJ
ejpam-811	309	13	(	(	PUNCT
ejpam-811	309	14	zhaz)1/2	zhaz)1/2	VERB
ejpam-811	309	15	�	�	PROPN
ejpam-811	309	16	re	re	NOUN
ejpam-811	309	17	�	�	PROPN
ejpam-811	309	18	g(ζ	g(ζ	PROPN
ejpam-811	309	19	,	,	PUNCT
ejpam-811	309	20	η)−	η)−	PROPN
ejpam-811	309	21	(	(	PUNCT
ejpam-811	309	22	zh	zh	PROPN
ejpam-811	309	23	bz)1/2	bz)1/2	PROPN
ejpam-811	309	24	�	�	PROPN
ejpam-811	309	25	<	<	X
ejpam-811	309	26	ϕ(ξ	ϕ(ξ	PROPN
ejpam-811	309	27	)	)	PUNCT
ejpam-811	310	1	=	=	PUNCT
ejpam-811	311	1	∑k	∑k	PROPN
ejpam-811	311	2	i=1λire	i=1λire	VERB
ejpam-811	311	3	�	�	PROPN
ejpam-811	311	4	f	f	PROPN
ejpam-811	311	5	(	(	PUNCT
ejpam-811	311	6	ξ	ξ	PROPN
ejpam-811	311	7	,	,	PUNCT
ejpam-811	311	8	ηi	ηi	X
ejpam-811	311	9	)	)	PUNCT
ejpam-811	312	1	+	+	CCONJ
ejpam-811	312	2	(	(	PUNCT
ejpam-811	312	3	α	α	PROPN
ejpam-811	312	4	haα)1/2	haα)1/2	PROPN
ejpam-811	312	5	�	�	PROPN
ejpam-811	312	6	∑k	∑k	PROPN
ejpam-811	312	7	i=1λire	i=1λire	VERB
ejpam-811	312	8	�	�	PROPN
ejpam-811	312	9	g(ξ	g(ξ	PROPN
ejpam-811	312	10	,	,	PUNCT
ejpam-811	312	11	ηi)−	ηi)−	PUNCT
ejpam-811	312	12	(	(	PUNCT
ejpam-811	312	13	αh	αh	PROPN
ejpam-811	312	14	bα)1/2	bα)1/2	PROPN
ejpam-811	312	15	�	�	PROPN
ejpam-811	312	16	.	.	PUNCT
ejpam-811	313	1	then	then	ADV
ejpam-811	313	2	for	for	ADP
ejpam-811	313	3	each	each	DET
ejpam-811	313	4	η	η	PROPN
ejpam-811	313	5	∈	∈	PROPN
ejpam-811	313	6	y	y	PROPN
ejpam-811	313	7	,	,	PUNCT
ejpam-811	313	8	we	we	PRON
ejpam-811	313	9	get	get	VERB
ejpam-811	313	10	�	�	PROPN
ejpam-811	313	11	re	re	ADJ
ejpam-811	313	12	�	�	PROPN
ejpam-811	313	13	f	f	PROPN
ejpam-811	313	14	(	(	PUNCT
ejpam-811	313	15	ζ	ζ	PROPN
ejpam-811	313	16	,	,	PUNCT
ejpam-811	313	17	η	η	NOUN
ejpam-811	313	18	)	)	PUNCT
ejpam-811	314	1	+	+	CCONJ
ejpam-811	314	2	(	(	PUNCT
ejpam-811	314	3	zhaz)1/2	zhaz)1/2	NUM
ejpam-811	314	4	�	�	PROPN
ejpam-811	314	5	�	�	PROPN
ejpam-811	314	6	×	×	PROPN
ejpam-811	314	7	�	�	PROPN
ejpam-811	314	8	∑k	∑k	PROPN
ejpam-811	314	9	i=1λire	i=1λire	NOUN
ejpam-811	314	10	�	�	PROPN
ejpam-811	314	11	g(ξ	g(ξ	PROPN
ejpam-811	314	12	,	,	PUNCT
ejpam-811	314	13	ηi)−	ηi)−	PUNCT
ejpam-811	314	14	(	(	PUNCT
ejpam-811	314	15	α	α	PROPN
ejpam-811	314	16	h	h	PROPN
ejpam-811	314	17	bα)1/2	bα)1/2	PROPN
ejpam-811	314	18	�	�	PROPN
ejpam-811	314	19	�	�	PROPN
ejpam-811	314	20	<	<	X
ejpam-811	314	21	�	�	PROPN
ejpam-811	314	22	re	re	X
ejpam-811	314	23	�	�	PROPN
ejpam-811	314	24	g(ζ	g(ζ	PROPN
ejpam-811	314	25	,	,	PUNCT
ejpam-811	314	26	η)−	η)−	PROPN
ejpam-811	314	27	(	(	PUNCT
ejpam-811	314	28	zh	zh	PROPN
ejpam-811	314	29	bz)1/2	bz)1/2	PROPN
ejpam-811	314	30	�	�	PROPN
ejpam-811	314	31	�	�	PROPN
ejpam-811	314	32	×	×	PROPN
ejpam-811	314	33	�	�	PROPN
ejpam-811	314	34	∑k	∑k	PROPN
ejpam-811	314	35	i=1λire	i=1λire	VERB
ejpam-811	314	36	�	�	PROPN
ejpam-811	314	37	f	f	PROPN
ejpam-811	314	38	(	(	PUNCT
ejpam-811	314	39	ξ	ξ	PROPN
ejpam-811	314	40	,	,	PUNCT
ejpam-811	314	41	ηi	ηi	X
ejpam-811	314	42	)	)	PUNCT
ejpam-811	314	43	+	+	CCONJ
ejpam-811	314	44	(	(	PUNCT
ejpam-811	314	45	α	α	PROPN
ejpam-811	314	46	haα)1/2	haα)1/2	PROPN
ejpam-811	314	47	�	�	PROPN
ejpam-811	314	48	�	�	PROPN
ejpam-811	314	49	.	.	PUNCT
ejpam-811	315	1	now	now	ADV
ejpam-811	315	2	we	we	PRON
ejpam-811	315	3	are	be	AUX
ejpam-811	315	4	replaced	replace	VERB
ejpam-811	315	5	η	η	PROPN
ejpam-811	315	6	by	by	ADP
ejpam-811	315	7	ηi	ηi	PROPN
ejpam-811	315	8	,	,	PUNCT
ejpam-811	315	9	multiplies	multiplies	PROPN
ejpam-811	315	10	λi	λi	VERB
ejpam-811	315	11	(	(	PUNCT
ejpam-811	315	12	with	with	ADP
ejpam-811	315	13	∑k	∑k	PROPN
ejpam-811	315	14	i=1λi	i=1λi	X
ejpam-811	316	1	=	=	SYM
ejpam-811	316	2	1	1	NUM
ejpam-811	316	3	)	)	PUNCT
ejpam-811	316	4	.	.	PUNCT
ejpam-811	317	1	it	it	PRON
ejpam-811	317	2	reduces	reduce	VERB
ejpam-811	317	3	to	to	AUX
ejpam-811	317	4	�	�	PROPN
ejpam-811	317	5	k∑	k∑	PROPN
ejpam-811	317	6	i=1	i=1	PROPN
ejpam-811	317	7	λi	λi	X
ejpam-811	317	8	re	re	X
ejpam-811	317	9	�	�	PROPN
ejpam-811	317	10	f	f	PROPN
ejpam-811	317	11	(	(	PUNCT
ejpam-811	317	12	ζ	ζ	PROPN
ejpam-811	317	13	,	,	PUNCT
ejpam-811	317	14	ηi	ηi	PROPN
ejpam-811	317	15	)	)	PUNCT
ejpam-811	317	16	+	+	CCONJ
ejpam-811	317	17	(	(	PUNCT
ejpam-811	317	18	z	z	NOUN
ejpam-811	317	19	haz)1/2	haz)1/2	PROPN
ejpam-811	317	20	�	�	PROPN
ejpam-811	317	21	�	�	PROPN
ejpam-811	317	22	×	×	PROPN
ejpam-811	317	23	�	�	PROPN
ejpam-811	317	24	k∑	k∑	PROPN
ejpam-811	317	25	i=1	i=1	PROPN
ejpam-811	317	26	λire	λire	PROPN
ejpam-811	317	27	�	�	PROPN
ejpam-811	317	28	g(ξ	g(ξ	PROPN
ejpam-811	317	29	,	,	PUNCT
ejpam-811	317	30	ηi)−	ηi)−	PUNCT
ejpam-811	317	31	(	(	PUNCT
ejpam-811	317	32	α	α	PROPN
ejpam-811	317	33	h	h	PROPN
ejpam-811	317	34	bα)1/2	bα)1/2	PROPN
ejpam-811	317	35	�	�	PROPN
ejpam-811	317	36	�	�	PROPN
ejpam-811	317	37	−	−	PROPN
ejpam-811	317	38	�	�	PROPN
ejpam-811	317	39	k∑	k∑	VERB
ejpam-811	317	40	i=1	i=1	PROPN
ejpam-811	317	41	λi	λi	X
ejpam-811	317	42	re	re	X
ejpam-811	317	43	�	�	PROPN
ejpam-811	317	44	g(ζ	g(ζ	PROPN
ejpam-811	317	45	,	,	PUNCT
ejpam-811	317	46	ηi)−	ηi)−	PUNCT
ejpam-811	317	47	(	(	PUNCT
ejpam-811	317	48	z	z	NOUN
ejpam-811	317	49	h	h	PROPN
ejpam-811	317	50	bz)1/2	bz)1/2	PROPN
ejpam-811	317	51	�	�	PROPN
ejpam-811	317	52	�	�	PROPN
ejpam-811	317	53	×	×	PROPN
ejpam-811	317	54	�	�	PROPN
ejpam-811	317	55	k∑	k∑	PROPN
ejpam-811	317	56	i=1	i=1	PROPN
ejpam-811	317	57	λire	λire	PROPN
ejpam-811	317	58	�	�	PROPN
ejpam-811	317	59	f	f	PROPN
ejpam-811	317	60	(	(	PUNCT
ejpam-811	317	61	ξ	ξ	PROPN
ejpam-811	317	62	,	,	PUNCT
ejpam-811	317	63	ηi	ηi	X
ejpam-811	317	64	)	)	PUNCT
ejpam-811	318	1	+	+	CCONJ
ejpam-811	318	2	(	(	PUNCT
ejpam-811	318	3	α	α	PROPN
ejpam-811	318	4	haα)1/2	haα)1/2	PROPN
ejpam-811	318	5	�	�	PROPN
ejpam-811	318	6	�	�	PROPN
ejpam-811	318	7	h.	h.	PROPN
ejpam-811	318	8	lai	lai	PROPN
ejpam-811	318	9	,	,	PUNCT
ejpam-811	318	10	t.	t.	PROPN
ejpam-811	318	11	huang	huang	PROPN
ejpam-811	318	12	/	/	SYM
ejpam-811	318	13	eur	eur	PROPN
ejpam-811	318	14	.	.	PUNCT
ejpam-811	319	1	j.	j.	PROPN
ejpam-811	319	2	pure	pure	PROPN
ejpam-811	319	3	appl	appl	PROPN
ejpam-811	319	4	.	.	PROPN
ejpam-811	319	5	math	math	PROPN
ejpam-811	319	6	,	,	PUNCT
ejpam-811	319	7	3	3	NUM
ejpam-811	319	8	(	(	PUNCT
ejpam-811	319	9	2010	2010	NUM
ejpam-811	319	10	)	)	PUNCT
ejpam-811	319	11	,	,	PUNCT
ejpam-811	319	12	989	989	NUM
ejpam-811	319	13	-	-	SYM
ejpam-811	319	14	1005	1005	NUM
ejpam-811	319	15	1003	1003	NUM
ejpam-811	319	16	<	<	X
ejpam-811	319	17	0	0	NUM
ejpam-811	319	18	.	.	PUNCT
ejpam-811	320	1	(	(	PUNCT
ejpam-811	320	2	20	20	NUM
ejpam-811	320	3	)	)	PUNCT
ejpam-811	320	4	from	from	ADP
ejpam-811	320	5	inequality	inequality	NOUN
ejpam-811	320	6	(	(	PUNCT
ejpam-811	320	7	18	18	NUM
ejpam-811	320	8	)	)	PUNCT
ejpam-811	320	9	,	,	PUNCT
ejpam-811	320	10	(	(	PUNCT
ejpam-811	320	11	19	19	NUM
ejpam-811	320	12	)	)	PUNCT
ejpam-811	320	13	and	and	CCONJ
ejpam-811	320	14	generalized	generalize	VERB
ejpam-811	320	15	schwarz	schwarz	PROPN
ejpam-811	320	16	inequality	inequality	NOUN
ejpam-811	320	17	(	(	PUNCT
ejpam-811	320	18	1	1	NUM
ejpam-811	320	19	)	)	PUNCT
ejpam-811	320	20	,	,	PUNCT
ejpam-811	320	21	we	we	PRON
ejpam-811	320	22	obtain	obtain	VERB
ejpam-811	320	23	re(zhaw1)≤	re(zhaw1)≤	NOUN
ejpam-811	321	1	(	(	PUNCT
ejpam-811	321	2	z	z	NOUN
ejpam-811	321	3	haz)1/2(wh	haz)1/2(wh	NOUN
ejpam-811	321	4	1	1	NUM
ejpam-811	321	5	aw1	aw1	PROPN
ejpam-811	321	6	)	)	PUNCT
ejpam-811	321	7	1/2	1/2	NUM
ejpam-811	321	8	≤	≤	NOUN
ejpam-811	321	9	(	(	PUNCT
ejpam-811	321	10	zhaz)1/2	zhaz)1/2	NUM
ejpam-811	321	11	and	and	CCONJ
ejpam-811	321	12	(	(	PUNCT
ejpam-811	321	13	21	21	NUM
ejpam-811	321	14	)	)	PUNCT
ejpam-811	321	15	re(zh	re(zh	NOUN
ejpam-811	321	16	bw2)≤	bw2)≤	NOUN
ejpam-811	321	17	(	(	PUNCT
ejpam-811	321	18	z	z	NOUN
ejpam-811	321	19	h	h	NOUN
ejpam-811	321	20	bz)1/2(wh	bz)1/2(wh	VERB
ejpam-811	321	21	2	2	NUM
ejpam-811	321	22	bw2	bw2	PROPN
ejpam-811	321	23	)	)	PUNCT
ejpam-811	321	24	1/2	1/2	NUM
ejpam-811	321	25	≤	≤	NOUN
ejpam-811	321	26	(	(	PUNCT
ejpam-811	321	27	zh	zh	X
ejpam-811	321	28	bz)1/2	bz)1/2	PROPN
ejpam-811	321	29	.	.	PUNCT
ejpam-811	322	1	(	(	PUNCT
ejpam-811	322	2	22	22	NUM
ejpam-811	322	3	)	)	PUNCT
ejpam-811	322	4	from	from	ADP
ejpam-811	322	5	inequalities(19	inequalities(19	NOUN
ejpam-811	322	6	)	)	PUNCT
ejpam-811	322	7	,	,	PUNCT
ejpam-811	322	8	(	(	PUNCT
ejpam-811	322	9	20	20	NUM
ejpam-811	322	10	)	)	PUNCT
ejpam-811	322	11	,	,	PUNCT
ejpam-811	322	12	(	(	PUNCT
ejpam-811	322	13	21	21	NUM
ejpam-811	322	14	)	)	PUNCT
ejpam-811	322	15	and	and	CCONJ
ejpam-811	322	16	(	(	PUNCT
ejpam-811	322	17	22	22	NUM
ejpam-811	322	18	)	)	PUNCT
ejpam-811	322	19	,	,	PUNCT
ejpam-811	322	20	φ2(ζ	φ2(ζ	X
ejpam-811	322	21	)	)	PUNCT
ejpam-811	322	22	=	=	PUNCT
ejpam-811	322	23	�	�	PROPN
ejpam-811	322	24	∑k	∑k	PROPN
ejpam-811	322	25	i=1λire	i=1λire	VERB
ejpam-811	323	1	�	�	PROPN
ejpam-811	323	2	f	f	PROPN
ejpam-811	323	3	(	(	PUNCT
ejpam-811	323	4	ζ	ζ	PROPN
ejpam-811	323	5	,	,	PUNCT
ejpam-811	323	6	ηi	ηi	NOUN
ejpam-811	323	7	)	)	PUNCT
ejpam-811	323	8	+	+	NUM
ejpam-811	323	9	zhaw1	zhaw1	PROPN
ejpam-811	323	10	�	�	PROPN
ejpam-811	323	11	�	�	PROPN
ejpam-811	323	12	×	×	PROPN
ejpam-811	323	13	�	�	PROPN
ejpam-811	323	14	∑k	∑k	PROPN
ejpam-811	323	15	i=1λire	i=1λire	NOUN
ejpam-811	323	16	�	�	PROPN
ejpam-811	323	17	g(ξ	g(ξ	PROPN
ejpam-811	323	18	,	,	PUNCT
ejpam-811	323	19	ηi)−α	ηi)−α	PROPN
ejpam-811	323	20	h	h	PROPN
ejpam-811	323	21	bw2	bw2	PROPN
ejpam-811	323	22	�	�	PROPN
ejpam-811	323	23	�	�	PROPN
ejpam-811	323	24	−	−	PROPN
ejpam-811	323	25	�	�	PROPN
ejpam-811	323	26	∑k	∑k	PROPN
ejpam-811	323	27	i=1λire	i=1λire	VERB
ejpam-811	323	28	�	�	PROPN
ejpam-811	323	29	f	f	PROPN
ejpam-811	323	30	(	(	PUNCT
ejpam-811	323	31	ξ	ξ	PROPN
ejpam-811	323	32	,	,	PUNCT
ejpam-811	323	33	ηi	ηi	X
ejpam-811	323	34	)	)	PUNCT
ejpam-811	324	1	+	+	NOUN
ejpam-811	324	2	α	α	PROPN
ejpam-811	324	3	haw1	haw1	PROPN
ejpam-811	324	4	�	�	PROPN
ejpam-811	324	5	�	�	PROPN
ejpam-811	324	6	×	×	PROPN
ejpam-811	324	7	�	�	PROPN
ejpam-811	324	8	∑k	∑k	PROPN
ejpam-811	324	9	i=1λire	i=1λire	NOUN
ejpam-811	324	10	�	�	PROPN
ejpam-811	324	11	g(ζ	g(ζ	PROPN
ejpam-811	324	12	,	,	PUNCT
ejpam-811	324	13	ηi)−	ηi)−	PUNCT
ejpam-811	324	14	zh	zh	PROPN
ejpam-811	324	15	bw2	bw2	PROPN
ejpam-811	324	16	�	�	PROPN
ejpam-811	324	17	�	�	PROPN
ejpam-811	324	18	<	<	X
ejpam-811	324	19	�	�	PROPN
ejpam-811	324	20	∑k	∑k	PROPN
ejpam-811	324	21	i=1λire	i=1λire	NOUN
ejpam-811	324	22	�	�	PROPN
ejpam-811	324	23	f	f	PROPN
ejpam-811	324	24	(	(	PUNCT
ejpam-811	324	25	ζ	ζ	PROPN
ejpam-811	324	26	,	,	PUNCT
ejpam-811	324	27	ηi	ηi	PROPN
ejpam-811	324	28	)	)	PUNCT
ejpam-811	325	1	+	+	CCONJ
ejpam-811	325	2	(	(	PUNCT
ejpam-811	325	3	z	z	NOUN
ejpam-811	325	4	haz)1/2	haz)1/2	PROPN
ejpam-811	325	5	�	�	PROPN
ejpam-811	325	6	�	�	PROPN
ejpam-811	325	7	×	×	PROPN
ejpam-811	325	8	�	�	PROPN
ejpam-811	325	9	∑k	∑k	PROPN
ejpam-811	325	10	i=1λire	i=1λire	NOUN
ejpam-811	325	11	�	�	PROPN
ejpam-811	325	12	g(ξ	g(ξ	PROPN
ejpam-811	325	13	,	,	PUNCT
ejpam-811	325	14	ηi)−α	ηi)−α	PROPN
ejpam-811	325	15	h	h	PROPN
ejpam-811	325	16	bw2	bw2	PROPN
ejpam-811	325	17	�	�	PROPN
ejpam-811	325	18	�	�	PROPN
ejpam-811	325	19	−	−	PROPN
ejpam-811	325	20	�	�	PROPN
ejpam-811	325	21	∑k	∑k	PROPN
ejpam-811	325	22	i=1λire	i=1λire	VERB
ejpam-811	325	23	�	�	PROPN
ejpam-811	325	24	f	f	PROPN
ejpam-811	325	25	(	(	PUNCT
ejpam-811	325	26	ξ	ξ	PROPN
ejpam-811	325	27	,	,	PUNCT
ejpam-811	325	28	ηi	ηi	X
ejpam-811	325	29	)	)	PUNCT
ejpam-811	326	1	+	+	NOUN
ejpam-811	326	2	α	α	PROPN
ejpam-811	326	3	haw1	haw1	PROPN
ejpam-811	326	4	�	�	PROPN
ejpam-811	326	5	�	�	PROPN
ejpam-811	326	6	×	×	PROPN
ejpam-811	326	7	�	�	PROPN
ejpam-811	326	8	∑k	∑k	PROPN
ejpam-811	326	9	i=1λire	i=1λire	NOUN
ejpam-811	326	10	�	�	PROPN
ejpam-811	326	11	g(ζ	g(ζ	PROPN
ejpam-811	326	12	,	,	PUNCT
ejpam-811	326	13	ηi)−	ηi)−	PUNCT
ejpam-811	326	14	(	(	PUNCT
ejpam-811	326	15	z	z	NOUN
ejpam-811	326	16	h	h	PROPN
ejpam-811	326	17	bz)1/2	bz)1/2	PROPN
ejpam-811	326	18	�	�	PROPN
ejpam-811	326	19	�	�	PROPN
ejpam-811	326	20	<	<	X
ejpam-811	326	21	0=	0=	NOUN
ejpam-811	326	22	φ2(ξ	φ2(ξ	NOUN
ejpam-811	326	23	)	)	PUNCT
ejpam-811	326	24	.	.	PUNCT
ejpam-811	327	1	we	we	PRON
ejpam-811	327	2	obtain	obtain	VERB
ejpam-811	327	3	φ2(ζ	φ2(ζ	PRON
ejpam-811	327	4	)	)	PUNCT
ejpam-811	327	5	<	<	X
ejpam-811	327	6	0=	0=	NOUN
ejpam-811	328	1	φ2(ξ	φ2(ξ	NOUN
ejpam-811	328	2	)	)	PUNCT
ejpam-811	328	3	.	.	PUNCT
ejpam-811	329	1	(	(	PUNCT
ejpam-811	329	2	23	23	NUM
ejpam-811	329	3	)	)	PUNCT
ejpam-811	329	4	since	since	SCONJ
ejpam-811	329	5	ζ=	ζ=	X
ejpam-811	329	6	(	(	PUNCT
ejpam-811	329	7	z	z	NOUN
ejpam-811	329	8	,	,	PUNCT
ejpam-811	329	9	z	z	NOUN
ejpam-811	329	10	)	)	PUNCT
ejpam-811	329	11	and	and	CCONJ
ejpam-811	329	12	ξ=	ξ=	NOUN
ejpam-811	329	13	(	(	PUNCT
ejpam-811	329	14	α	α	NOUN
ejpam-811	329	15	,	,	PUNCT
ejpam-811	329	16	α	α	NOUN
ejpam-811	329	17	)	)	PUNCT
ejpam-811	329	18	are	be	AUX
ejpam-811	329	19	feasible	feasible	ADJ
ejpam-811	329	20	solutions	solution	NOUN
ejpam-811	329	21	of	of	ADP
ejpam-811	329	22	(	(	PUNCT
ejpam-811	329	23	p	p	NOUN
ejpam-811	329	24	)	)	PUNCT
ejpam-811	329	25	and	and	CCONJ
ejpam-811	329	26	(	(	PUNCT
ejpam-811	329	27	mwd	mwd	PROPN
ejpam-811	329	28	)	)	PUNCT
ejpam-811	329	29	,	,	PUNCT
ejpam-811	329	30	we	we	PRON
ejpam-811	329	31	have	have	VERB
ejpam-811	329	32	re〈h(ζ),µ	re〈h(ζ),µ	NOUN
ejpam-811	329	33	〉	〉	NOUN
ejpam-811	329	34	≤	≤	NOUN
ejpam-811	329	35	0≤	0≤	NUM
ejpam-811	329	36	re〈h(ξ),µ	re〈h(ξ),µ	ADJ
ejpam-811	329	37	〉	〉	X
ejpam-811	329	38	.	.	PUNCT
ejpam-811	330	1	(	(	PUNCT
ejpam-811	330	2	24	24	NUM
ejpam-811	330	3	)	)	PUNCT
ejpam-811	330	4	if	if	SCONJ
ejpam-811	330	5	hypothesis	hypothesis	NOUN
ejpam-811	330	6	(	(	PUNCT
ejpam-811	330	7	i	i	NOUN
ejpam-811	330	8	)	)	PUNCT
ejpam-811	330	9	holds	hold	NOUN
ejpam-811	330	10	,	,	PUNCT
ejpam-811	330	11	φ2(•	φ2(•	ADV
ejpam-811	330	12	)	)	PUNCT
ejpam-811	330	13	is	be	AUX
ejpam-811	330	14	pseudoconvex	pseudoconvex	NOUN
ejpam-811	330	15	at	at	ADP
ejpam-811	330	16	ξ	ξ	PROPN
ejpam-811	330	17	and	and	CCONJ
ejpam-811	330	18	〈	〈	PROPN
ejpam-811	330	19	h(•),µ	h(•),µ	PROPN
ejpam-811	330	20	〉	〉	NOUN
ejpam-811	330	21	is	be	AUX
ejpam-811	330	22	quasiconvex	quasiconvex	NOUN
ejpam-811	330	23	at	at	ADP
ejpam-811	330	24	ξ	ξ	PROPN
ejpam-811	330	25	,	,	PUNCT
ejpam-811	330	26	then	then	ADV
ejpam-811	330	27	by	by	ADP
ejpam-811	330	28	(	(	PUNCT
ejpam-811	330	29	23	23	NUM
ejpam-811	330	30	)	)	PUNCT
ejpam-811	330	31	and	and	CCONJ
ejpam-811	330	32	(	(	PUNCT
ejpam-811	330	33	24	24	NUM
ejpam-811	330	34	)	)	PUNCT
ejpam-811	330	35	,	,	PUNCT
ejpam-811	330	36	we	we	PRON
ejpam-811	330	37	have	have	VERB
ejpam-811	330	38	re[φ′2(ξ)(ζ−	re[φ′2(ξ)(ζ−	NOUN
ejpam-811	330	39	ξ	ξ	PROPN
ejpam-811	330	40	)	)	PUNCT
ejpam-811	331	1	]	]	PUNCT
ejpam-811	331	2	<	<	X
ejpam-811	331	3	0	0	PUNCT
ejpam-811	331	4	and	and	CCONJ
ejpam-811	331	5	re	re	VERB
ejpam-811	331	6	〈	〈	PROPN
ejpam-811	331	7	h′(ξ)(ζ−	h′(ξ)(ζ−	NOUN
ejpam-811	331	8	ξ),µ	ξ),µ	PROPN
ejpam-811	331	9	〉	〉	NOUN
ejpam-811	331	10	≤	≤	NOUN
ejpam-811	331	11	0	0	NUM
ejpam-811	331	12	.	.	PUNCT
ejpam-811	332	1	that	that	PRON
ejpam-811	332	2	is	be	AUX
ejpam-811	332	3	�	�	PROPN
ejpam-811	332	4	k∑	k∑	VERB
ejpam-811	332	5	i=1	i=1	PROPN
ejpam-811	332	6	λi	λi	PROPN
ejpam-811	332	7	�	�	PROPN
ejpam-811	332	8	∇z	∇z	PROPN
ejpam-811	332	9	f	f	PROPN
ejpam-811	332	10	(	(	PUNCT
ejpam-811	332	11	ξ	ξ	PROPN
ejpam-811	332	12	,	,	PUNCT
ejpam-811	332	13	ηi	ηi	X
ejpam-811	332	14	)	)	PUNCT
ejpam-811	332	15	+	+	PROPN
ejpam-811	332	16	∇z	∇z	ADJ
ejpam-811	332	17	f	f	X
ejpam-811	332	18	(	(	PUNCT
ejpam-811	332	19	ξ	ξ	PROPN
ejpam-811	332	20	,	,	PUNCT
ejpam-811	332	21	ηi	ηi	PROPN
ejpam-811	332	22	)	)	PUNCT
ejpam-811	332	23	�	�	PROPN
ejpam-811	333	1	+	+	NOUN
ejpam-811	333	2	aw1	aw1	PROPN
ejpam-811	333	3	�	�	PROPN
ejpam-811	333	4	·	·	PUNCT
ejpam-811	333	5	�	�	PROPN
ejpam-811	333	6	k∑	k∑	VERB
ejpam-811	333	7	i=1	i=1	PROPN
ejpam-811	333	8	λi	λi	X
ejpam-811	333	9	re	re	VERB
ejpam-811	333	10	[	[	X
ejpam-811	333	11	g(ξ	g(ξ	PROPN
ejpam-811	333	12	,	,	PUNCT
ejpam-811	333	13	ηi)−	ηi)−	PUNCT
ejpam-811	333	14	(	(	PUNCT
ejpam-811	333	15	α	α	PROPN
ejpam-811	333	16	h	h	PROPN
ejpam-811	333	17	bα)1/2	bα)1/2	PROPN
ejpam-811	333	18	]	]	PUNCT
ejpam-811	333	19	�	�	PROPN
ejpam-811	334	1	−	−	PROPN
ejpam-811	335	1	�	�	PROPN
ejpam-811	336	1	k∑	k∑	VERB
ejpam-811	337	1	i=1	i=1	PROPN
ejpam-811	338	1	λi	λi	X
ejpam-811	338	2	re	re	VERB
ejpam-811	338	3	[	[	PUNCT
ejpam-811	338	4	f	f	X
ejpam-811	338	5	(	(	PUNCT
ejpam-811	338	6	ξ	ξ	PROPN
ejpam-811	338	7	,	,	PUNCT
ejpam-811	338	8	ηi	ηi	X
ejpam-811	338	9	)	)	PUNCT
ejpam-811	338	10	+	+	CCONJ
ejpam-811	339	1	(	(	PUNCT
ejpam-811	339	2	α	α	PROPN
ejpam-811	339	3	haα)1/2	haα)1/2	PROPN
ejpam-811	339	4	]	]	X
ejpam-811	339	5	�	�	PROPN
ejpam-811	339	6	·	·	PUNCT
ejpam-811	339	7	�	�	PROPN
ejpam-811	339	8	k∑	k∑	PROPN
ejpam-811	339	9	i=1	i=1	PROPN
ejpam-811	339	10	λi	λi	ADP
ejpam-811	339	11	�	�	PROPN
ejpam-811	339	12	∇z	∇z	PROPN
ejpam-811	339	13	g(ξ	g(ξ	PROPN
ejpam-811	339	14	,	,	PUNCT
ejpam-811	339	15	ηi	ηi	X
ejpam-811	339	16	)	)	PUNCT
ejpam-811	339	17	+	+	PROPN
ejpam-811	339	18	∇z	∇z	PROPN
ejpam-811	339	19	g(ξ	g(ξ	PROPN
ejpam-811	339	20	,	,	PUNCT
ejpam-811	339	21	ηi	ηi	PROPN
ejpam-811	339	22	)	)	PUNCT
ejpam-811	339	23	�	�	PROPN
ejpam-811	339	24	−	−	PROPN
ejpam-811	339	25	bw2	bw2	PROPN
ejpam-811	339	26	�	�	PROPN
ejpam-811	339	27	+	+	PROPN
ejpam-811	339	28	µt	µt	PROPN
ejpam-811	339	29	∇zh(ξ	∇zh(ξ	PROPN
ejpam-811	339	30	)	)	PUNCT
ejpam-811	339	31	+	+	NOUN
ejpam-811	339	32	µh∇zh(ξ	µh∇zh(ξ	X
ejpam-811	339	33	)	)	PUNCT
ejpam-811	339	34	<	<	X
ejpam-811	339	35	0	0	X
ejpam-811	339	36	.	.	PUNCT
ejpam-811	340	1	this	this	PRON
ejpam-811	340	2	contradicts	contradict	VERB
ejpam-811	340	3	the	the	DET
ejpam-811	340	4	equality	equality	NOUN
ejpam-811	340	5	of	of	ADP
ejpam-811	340	6	(	(	PUNCT
ejpam-811	340	7	16	16	NUM
ejpam-811	340	8	)	)	PUNCT
ejpam-811	340	9	.	.	PUNCT
ejpam-811	341	1	in	in	ADP
ejpam-811	341	2	hypothesis	hypothesis	NOUN
ejpam-811	341	3	(	(	PUNCT
ejpam-811	341	4	ii	ii	NOUN
ejpam-811	341	5	)	)	PUNCT
ejpam-811	341	6	,	,	PUNCT
ejpam-811	341	7	it	it	PRON
ejpam-811	341	8	follows	follow	VERB
ejpam-811	341	9	by	by	ADP
ejpam-811	341	10	the	the	DET
ejpam-811	341	11	same	same	ADJ
ejpam-811	341	12	lines	line	NOUN
ejpam-811	341	13	as	as	ADP
ejpam-811	341	14	the	the	DET
ejpam-811	341	15	proof	proof	NOUN
ejpam-811	341	16	given	give	VERB
ejpam-811	341	17	for	for	ADP
ejpam-811	341	18	(	(	PUNCT
ejpam-811	341	19	i	i	NOUN
ejpam-811	341	20	)	)	PUNCT
ejpam-811	341	21	.	.	PUNCT
ejpam-811	342	1	hence	hence	ADV
ejpam-811	342	2	the	the	DET
ejpam-811	342	3	proof	proof	NOUN
ejpam-811	342	4	is	be	AUX
ejpam-811	342	5	complete	complete	ADJ
ejpam-811	342	6	.	.	PUNCT
ejpam-811	343	1	�	�	PROPN
ejpam-811	343	2	as	as	ADP
ejpam-811	343	3	for	for	ADP
ejpam-811	343	4	the	the	DET
ejpam-811	343	5	strong	strong	ADJ
ejpam-811	343	6	and	and	CCONJ
ejpam-811	343	7	strict	strict	ADJ
ejpam-811	343	8	converse	converse	NOUN
ejpam-811	343	9	duality	duality	NOUN
ejpam-811	343	10	theorems	theorem	NOUN
ejpam-811	343	11	of	of	ADP
ejpam-811	343	12	(	(	PUNCT
ejpam-811	343	13	mwd	mwd	PROPN
ejpam-811	343	14	)	)	PUNCT
ejpam-811	343	15	,	,	PUNCT
ejpam-811	343	16	mutatis	mutatis	NOUN
ejpam-811	343	17	mutandis	mutandis	PROPN
ejpam-811	343	18	,	,	PUNCT
ejpam-811	343	19	the	the	DET
ejpam-811	343	20	same	same	ADJ
ejpam-811	343	21	as	as	ADP
ejpam-811	343	22	the	the	DET
ejpam-811	343	23	proof	proof	NOUN
ejpam-811	343	24	of	of	ADP
ejpam-811	343	25	duality	duality	NOUN
ejpam-811	343	26	theorems	theorem	VERB
ejpam-811	343	27	for	for	ADP
ejpam-811	343	28	(	(	PUNCT
ejpam-811	343	29	wd	wd	PROPN
ejpam-811	343	30	)	)	PUNCT
ejpam-811	343	31	.	.	PUNCT
ejpam-811	344	1	hence	hence	ADV
ejpam-811	344	2	,	,	PUNCT
ejpam-811	344	3	we	we	PRON
ejpam-811	344	4	state	state	VERB
ejpam-811	344	5	directly	directly	ADV
ejpam-811	344	6	the	the	DET
ejpam-811	344	7	strong	strong	ADJ
ejpam-811	344	8	and	and	CCONJ
ejpam-811	344	9	strict	strict	ADJ
ejpam-811	344	10	converse	converse	NOUN
ejpam-811	344	11	duality	duality	NOUN
ejpam-811	344	12	theorems	theorem	VERB
ejpam-811	344	13	as	as	ADP
ejpam-811	344	14	in	in	ADP
ejpam-811	344	15	the	the	DET
ejpam-811	344	16	following	following	NOUN
ejpam-811	344	17	:	:	PUNCT
ejpam-811	344	18	references	reference	NOUN
ejpam-811	344	19	1004	1004	NUM
ejpam-811	344	20	theorem	theorem	VERB
ejpam-811	344	21	8	8	NUM
ejpam-811	344	22	(	(	PUNCT
ejpam-811	344	23	strong	strong	ADJ
ejpam-811	344	24	duality	duality	NOUN
ejpam-811	344	25	)	)	PUNCT
ejpam-811	344	26	.	.	PUNCT
ejpam-811	345	1	let	let	VERB
ejpam-811	345	2	ζ0	ζ0	NOUN
ejpam-811	345	3	=	=	SYM
ejpam-811	345	4	(	(	PUNCT
ejpam-811	345	5	z0	z0	PROPN
ejpam-811	345	6	,	,	PUNCT
ejpam-811	345	7	z0	z0	PROPN
ejpam-811	345	8	)	)	PUNCT
ejpam-811	345	9	be	be	VERB
ejpam-811	345	10	an	an	DET
ejpam-811	345	11	optimal	optimal	ADJ
ejpam-811	345	12	solution	solution	NOUN
ejpam-811	345	13	of	of	ADP
ejpam-811	345	14	problem	problem	NOUN
ejpam-811	345	15	(	(	PUNCT
ejpam-811	345	16	p	p	X
ejpam-811	345	17	)	)	PUNCT
ejpam-811	345	18	satisfying	satisfy	VERB
ejpam-811	345	19	the	the	DET
ejpam-811	345	20	hypothesis	hypothesis	NOUN
ejpam-811	345	21	of	of	ADP
ejpam-811	345	22	theorem	theorem	NOUN
ejpam-811	345	23	1	1	NUM
ejpam-811	345	24	.	.	PUNCT
ejpam-811	346	1	then	then	ADV
ejpam-811	346	2	there	there	PRON
ejpam-811	346	3	exist	exist	VERB
ejpam-811	346	4	(	(	PUNCT
ejpam-811	346	5	k	k	X
ejpam-811	346	6	,	,	PUNCT
ejpam-811	346	7	eλ	eλ	INTJ
ejpam-811	346	8	,	,	PUNCT
ejpam-811	346	9	eη	eη	NOUN
ejpam-811	346	10	)	)	PUNCT
ejpam-811	346	11	∈	∈	PROPN
ejpam-811	346	12	k(ζ0	k(ζ0	NOUN
ejpam-811	346	13	)	)	PUNCT
ejpam-811	346	14	and	and	CCONJ
ejpam-811	346	15	(	(	PUNCT
ejpam-811	346	16	ζ0,µ	ζ0,µ	PROPN
ejpam-811	346	17	,	,	PUNCT
ejpam-811	346	18	w1	w1	NOUN
ejpam-811	346	19	,	,	PUNCT
ejpam-811	346	20	w2	w2	NOUN
ejpam-811	346	21	)	)	PUNCT
ejpam-811	346	22	∈	∈	PROPN
ejpam-811	346	23	x	x	X
ejpam-811	346	24	(	(	PUNCT
ejpam-811	346	25	k	k	X
ejpam-811	346	26	,	,	PUNCT
ejpam-811	346	27	eλ	eλ	INTJ
ejpam-811	346	28	,	,	PUNCT
ejpam-811	346	29	eη	eη	NOUN
ejpam-811	346	30	)	)	PUNCT
ejpam-811	346	31	such	such	ADJ
ejpam-811	346	32	that	that	SCONJ
ejpam-811	346	33	(	(	PUNCT
ejpam-811	346	34	k	k	X
ejpam-811	346	35	,	,	PUNCT
ejpam-811	346	36	eλ	eλ	INTJ
ejpam-811	346	37	,	,	PUNCT
ejpam-811	346	38	eη	eη	NOUN
ejpam-811	346	39	,	,	PUNCT
ejpam-811	346	40	ζ0,µ	ζ0,µ	PROPN
ejpam-811	346	41	,	,	PUNCT
ejpam-811	346	42	w1	w1	NOUN
ejpam-811	346	43	,	,	PUNCT
ejpam-811	346	44	w2	w2	NOUN
ejpam-811	346	45	)	)	PUNCT
ejpam-811	346	46	is	be	AUX
ejpam-811	346	47	a	a	DET
ejpam-811	346	48	feasible	feasible	ADJ
ejpam-811	346	49	solution	solution	NOUN
ejpam-811	346	50	of	of	ADP
ejpam-811	346	51	the	the	DET
ejpam-811	346	52	dual	dual	ADJ
ejpam-811	346	53	problem	problem	NOUN
ejpam-811	346	54	(	(	PUNCT
ejpam-811	346	55	mwd	mwd	PROPN
ejpam-811	346	56	)	)	PUNCT
ejpam-811	346	57	.	.	PUNCT
ejpam-811	347	1	if	if	SCONJ
ejpam-811	347	2	the	the	DET
ejpam-811	347	3	hypotheses	hypothesis	NOUN
ejpam-811	347	4	of	of	ADP
ejpam-811	347	5	theorem	theorem	NOUN
ejpam-811	347	6	7	7	NUM
ejpam-811	347	7	are	be	AUX
ejpam-811	347	8	fulfilled	fulfil	VERB
ejpam-811	347	9	,	,	PUNCT
ejpam-811	347	10	then	then	ADV
ejpam-811	347	11	(	(	PUNCT
ejpam-811	347	12	k	k	X
ejpam-811	347	13	,	,	PUNCT
ejpam-811	347	14	eλ	eλ	INTJ
ejpam-811	347	15	,	,	PUNCT
ejpam-811	347	16	eη	eη	NOUN
ejpam-811	347	17	,	,	PUNCT
ejpam-811	347	18	ζ0,µ	ζ0,µ	PROPN
ejpam-811	347	19	,	,	PUNCT
ejpam-811	347	20	w1	w1	NOUN
ejpam-811	347	21	,	,	PUNCT
ejpam-811	347	22	w2	w2	NOUN
ejpam-811	347	23	)	)	PUNCT
ejpam-811	347	24	is	be	AUX
ejpam-811	347	25	an	an	DET
ejpam-811	347	26	optimal	optimal	ADJ
ejpam-811	347	27	solution	solution	NOUN
ejpam-811	347	28	of	of	ADP
ejpam-811	347	29	(	(	PUNCT
ejpam-811	347	30	mwd	mwd	PROPN
ejpam-811	347	31	)	)	PUNCT
ejpam-811	347	32	,	,	PUNCT
ejpam-811	347	33	and	and	CCONJ
ejpam-811	347	34	the	the	DET
ejpam-811	347	35	two	two	NUM
ejpam-811	347	36	problems	problem	NOUN
ejpam-811	347	37	(	(	PUNCT
ejpam-811	347	38	p	p	NOUN
ejpam-811	347	39	)	)	PUNCT
ejpam-811	347	40	and	and	CCONJ
ejpam-811	347	41	(	(	PUNCT
ejpam-811	347	42	mwd	mwd	PROPN
ejpam-811	347	43	)	)	PUNCT
ejpam-811	347	44	have	have	VERB
ejpam-811	347	45	the	the	DET
ejpam-811	347	46	same	same	ADJ
ejpam-811	347	47	optimal	optimal	ADJ
ejpam-811	347	48	values	value	NOUN
ejpam-811	347	49	.	.	PUNCT
ejpam-811	348	1	theorem	theorem	NOUN
ejpam-811	348	2	9	9	NUM
ejpam-811	348	3	(	(	PUNCT
ejpam-811	348	4	strict	strict	ADJ
ejpam-811	348	5	converse	converse	NOUN
ejpam-811	348	6	duality	duality	NOUN
ejpam-811	348	7	)	)	PUNCT
ejpam-811	348	8	.	.	PUNCT
ejpam-811	349	1	let	let	VERB
ejpam-811	349	2	bζ	bζ	PROPN
ejpam-811	349	3	and	and	CCONJ
ejpam-811	349	4	(	(	PUNCT
ejpam-811	349	5	bk	bk	INTJ
ejpam-811	349	6	,	,	PUNCT
ejpam-811	349	7	bλ	bλ	PROPN
ejpam-811	349	8	,	,	PUNCT
ejpam-811	349	9	bη	bη	VERB
ejpam-811	349	10	,	,	PUNCT
ejpam-811	349	11	bξ	bξ	PROPN
ejpam-811	349	12	,	,	PUNCT
ejpam-811	349	13	bµ,cw1	bµ,cw1	NOUN
ejpam-811	349	14	,	,	PUNCT
ejpam-811	349	15	,	,	PUNCT
ejpam-811	349	16	cw1	cw1	PROPN
ejpam-811	349	17	)	)	PUNCT
ejpam-811	349	18	be	be	VERB
ejpam-811	349	19	the	the	DET
ejpam-811	349	20	optimal	optimal	ADJ
ejpam-811	349	21	solutions	solution	NOUN
ejpam-811	349	22	of	of	ADP
ejpam-811	349	23	(	(	PUNCT
ejpam-811	349	24	p	p	NOUN
ejpam-811	349	25	)	)	PUNCT
ejpam-811	349	26	and	and	CCONJ
ejpam-811	349	27	(	(	PUNCT
ejpam-811	349	28	wd	wd	PROPN
ejpam-811	349	29	)	)	PUNCT
ejpam-811	349	30	,	,	PUNCT
ejpam-811	349	31	respectively	respectively	ADV
ejpam-811	349	32	,	,	PUNCT
ejpam-811	349	33	and	and	CCONJ
ejpam-811	349	34	assume	assume	VERB
ejpam-811	349	35	that	that	SCONJ
ejpam-811	349	36	the	the	DET
ejpam-811	349	37	assumptions	assumption	NOUN
ejpam-811	349	38	of	of	ADP
ejpam-811	349	39	theorem	theorem	ADJ
ejpam-811	349	40	8	8	NUM
ejpam-811	349	41	are	be	AUX
ejpam-811	349	42	fulfilled	fulfil	VERB
ejpam-811	349	43	.	.	PUNCT
ejpam-811	350	1	if	if	SCONJ
ejpam-811	350	2	φ2(•	φ2(•	ADV
ejpam-811	350	3	)	)	PUNCT
ejpam-811	350	4	is	be	AUX
ejpam-811	350	5	strictly	strictly	ADV
ejpam-811	350	6	pseudoconvex	pseudoconvex	ADJ
ejpam-811	350	7	on	on	ADP
ejpam-811	350	8	q	q	PROPN
ejpam-811	350	9	and	and	CCONJ
ejpam-811	350	10	〈	〈	PROPN
ejpam-811	350	11	h(•),µ	h(•),µ	PROPN
ejpam-811	350	12	〉	〉	NOUN
ejpam-811	350	13	is	be	AUX
ejpam-811	350	14	quasiconvex	quasiconvex	NOUN
ejpam-811	350	15	on	on	ADP
ejpam-811	350	16	q	q	NOUN
ejpam-811	350	17	,	,	PUNCT
ejpam-811	350	18	then	then	ADV
ejpam-811	350	19	bζ	bζ	PROPN
ejpam-811	350	20	=	=	PUNCT
ejpam-811	350	21	bξ	bξ	PROPN
ejpam-811	350	22	;	;	PUNCT
ejpam-811	350	23	and	and	CCONJ
ejpam-811	350	24	the	the	DET
ejpam-811	350	25	optimal	optimal	ADJ
ejpam-811	350	26	values	value	NOUN
ejpam-811	350	27	of	of	ADP
ejpam-811	350	28	(	(	PUNCT
ejpam-811	350	29	p	p	NOUN
ejpam-811	350	30	)	)	PUNCT
ejpam-811	350	31	and	and	CCONJ
ejpam-811	350	32	(	(	PUNCT
ejpam-811	350	33	wd	wd	X
ejpam-811	350	34	)	)	PUNCT
ejpam-811	350	35	are	be	AUX
ejpam-811	350	36	equal	equal	ADJ
ejpam-811	350	37	.	.	PUNCT
ejpam-811	351	1	references	reference	NOUN
ejpam-811	351	2	[	[	X
ejpam-811	351	3	1	1	NUM
ejpam-811	351	4	]	]	X
ejpam-811	351	5	o.	o.	PROPN
ejpam-811	351	6	ferrero	ferrero	PROPN
ejpam-811	351	7	.	.	PUNCT
ejpam-811	352	1	on	on	ADP
ejpam-811	352	2	nonlinear	nonlinear	ADJ
ejpam-811	352	3	programming	programming	NOUN
ejpam-811	352	4	in	in	ADP
ejpam-811	352	5	complex	complex	ADJ
ejpam-811	352	6	space	space	NOUN
ejpam-811	352	7	.	.	PUNCT
ejpam-811	353	1	journal	journal	PROPN
ejpam-811	353	2	of	of	ADP
ejpam-811	353	3	mathematical	mathematical	ADJ
ejpam-811	353	4	analysis	analysis	NOUN
ejpam-811	353	5	and	and	CCONJ
ejpam-811	353	6	applications	application	NOUN
ejpam-811	353	7	,	,	PUNCT
ejpam-811	353	8	164:399	164:399	PROPN
ejpam-811	353	9	-	-	SYM
ejpam-811	353	10	416	416	NUM
ejpam-811	353	11	,	,	PUNCT
ejpam-811	353	12	1992	1992	NUM
ejpam-811	353	13	.	.	PUNCT
ejpam-811	354	1	[	[	X
ejpam-811	354	2	2	2	X
ejpam-811	354	3	]	]	PUNCT
ejpam-811	354	4	s.	s.	PROPN
ejpam-811	354	5	haykin	haykin	PROPN
ejpam-811	354	6	.	.	PUNCT
ejpam-811	355	1	adaptive	adaptive	ADJ
ejpam-811	355	2	filter	filter	NOUN
ejpam-811	355	3	theory	theory	NOUN
ejpam-811	355	4	,	,	PUNCT
ejpam-811	355	5	3	3	NUM
ejpam-811	355	6	rd	rd	NOUN
ejpam-811	355	7	edition	edition	NOUN
ejpam-811	355	8	.	.	PUNCT
ejpam-811	356	1	prentice	prentice	PROPN
ejpam-811	356	2	-	-	PUNCT
ejpam-811	356	3	hill	hill	PROPN
ejpam-811	356	4	,	,	PUNCT
ejpam-811	356	5	englewood	englewood	PROPN
ejpam-811	356	6	cliffs	cliffs	PROPN
ejpam-811	356	7	,	,	PUNCT
ejpam-811	356	8	new	new	PROPN
ejpam-811	356	9	jersey	jersey	PROPN
ejpam-811	356	10	,	,	PUNCT
ejpam-811	356	11	1996	1996	NUM
ejpam-811	356	12	.	.	PUNCT
ejpam-811	357	1	[	[	X
ejpam-811	357	2	3	3	X
ejpam-811	357	3	]	]	X
ejpam-811	357	4	h.c	h.c	PROPN
ejpam-811	357	5	.	.	PROPN
ejpam-811	357	6	lai	lai	PROPN
ejpam-811	357	7	and	and	CCONJ
ejpam-811	357	8	t.y	t.y	PROPN
ejpam-811	357	9	.	.	PROPN
ejpam-811	358	1	huang	huang	PROPN
ejpam-811	358	2	.	.	PUNCT
ejpam-811	358	3	optimality	optimality	NOUN
ejpam-811	358	4	conditions	condition	NOUN
ejpam-811	358	5	for	for	ADP
ejpam-811	358	6	nondifferentiable	nondifferentiable	ADJ
ejpam-811	358	7	minimax	minimax	NOUN
ejpam-811	358	8	fractional	fractional	ADJ
ejpam-811	358	9	programming	programming	NOUN
ejpam-811	358	10	with	with	ADP
ejpam-811	358	11	complex	complex	ADJ
ejpam-811	358	12	variables	variable	NOUN
ejpam-811	358	13	.	.	PUNCT
ejpam-811	359	1	journal	journal	NOUN
ejpam-811	359	2	of	of	ADP
ejpam-811	359	3	mathematical	mathematical	ADJ
ejpam-811	359	4	analysis	analysis	NOUN
ejpam-811	359	5	and	and	CCONJ
ejpam-811	359	6	applications	application	NOUN
ejpam-811	359	7	,	,	PUNCT
ejpam-811	359	8	359:229	359:229	NUM
ejpam-811	359	9	-	-	SYM
ejpam-811	359	10	239	239	NUM
ejpam-811	359	11	,	,	PUNCT
ejpam-811	359	12	2009	2009	NUM
ejpam-811	359	13	.	.	PUNCT
ejpam-811	360	1	[	[	X
ejpam-811	360	2	4	4	X
ejpam-811	360	3	]	]	X
ejpam-811	360	4	h.c	h.c	PROPN
ejpam-811	360	5	.	.	PROPN
ejpam-811	360	6	lai	lai	PROPN
ejpam-811	360	7	and	and	CCONJ
ejpam-811	360	8	t.y	t.y	PROPN
ejpam-811	360	9	.	.	PROPN
ejpam-811	361	1	huang	huang	PROPN
ejpam-811	361	2	.	.	PUNCT
ejpam-811	361	3	optimality	optimality	NOUN
ejpam-811	361	4	conditions	condition	NOUN
ejpam-811	361	5	for	for	ADP
ejpam-811	361	6	a	a	DET
ejpam-811	361	7	nondifferentiable	nondifferentiable	ADJ
ejpam-811	361	8	minimax	minimax	NOUN
ejpam-811	361	9	programming	programming	NOUN
ejpam-811	361	10	in	in	ADP
ejpam-811	361	11	complex	complex	ADJ
ejpam-811	361	12	spaces	space	NOUN
ejpam-811	361	13	.	.	PUNCT
ejpam-811	362	1	nonlinear	nonlinear	ADJ
ejpam-811	362	2	analysis	analysis	NOUN
ejpam-811	362	3	,	,	PUNCT
ejpam-811	362	4	71:1205	71:1205	NOUN
ejpam-811	362	5	-	-	SYM
ejpam-811	362	6	1212	1212	NUM
ejpam-811	362	7	,	,	PUNCT
ejpam-811	362	8	2009	2009	NUM
ejpam-811	362	9	.	.	PUNCT
ejpam-811	363	1	[	[	X
ejpam-811	363	2	5	5	X
ejpam-811	363	3	]	]	X
ejpam-811	363	4	h.c	h.c	PROPN
ejpam-811	363	5	.	.	PROPN
ejpam-811	363	6	lai	lai	PROPN
ejpam-811	363	7	and	and	CCONJ
ejpam-811	363	8	j.c	j.c	PROPN
ejpam-811	363	9	.	.	PROPN
ejpam-811	363	10	lee	lee	PROPN
ejpam-811	363	11	.	.	PUNCT
ejpam-811	364	1	on	on	ADP
ejpam-811	364	2	duality	duality	NOUN
ejpam-811	364	3	theorems	theorem	NOUN
ejpam-811	364	4	for	for	ADP
ejpam-811	364	5	a	a	DET
ejpam-811	364	6	nondifferentiable	nondifferentiable	ADJ
ejpam-811	364	7	minimax	minimax	NOUN
ejpam-811	364	8	fractional	fractional	ADJ
ejpam-811	364	9	programming	programming	NOUN
ejpam-811	364	10	.	.	PUNCT
ejpam-811	365	1	journal	journal	PROPN
ejpam-811	365	2	computational	computational	ADJ
ejpam-811	365	3	and	and	CCONJ
ejpam-811	365	4	applied	applied	ADJ
ejpam-811	365	5	mathematics	mathematic	NOUN
ejpam-811	365	6	,	,	PUNCT
ejpam-811	365	7	146:115	146:115	PROPN
ejpam-811	365	8	-	-	SYM
ejpam-811	365	9	126	126	NUM
ejpam-811	365	10	,	,	PUNCT
ejpam-811	365	11	2002	2002	NUM
ejpam-811	365	12	.	.	PUNCT
ejpam-811	366	1	[	[	X
ejpam-811	366	2	6	6	NUM
ejpam-811	366	3	]	]	X
ejpam-811	366	4	h.c	h.c	PROPN
ejpam-811	366	5	.	.	PUNCT
ejpam-811	366	6	lai	lai	PROPN
ejpam-811	366	7	,	,	PUNCT
ejpam-811	366	8	j.c	j.c	PROPN
ejpam-811	366	9	.	.	PROPN
ejpam-811	366	10	lee	lee	PROPN
ejpam-811	366	11	and	and	CCONJ
ejpam-811	366	12	s.c	s.c	PROPN
ejpam-811	366	13	.	.	PROPN
ejpam-811	366	14	ho	ho	PROPN
ejpam-811	366	15	.	.	PROPN
ejpam-811	366	16	parametric	parametric	ADJ
ejpam-811	366	17	duality	duality	NOUN
ejpam-811	366	18	on	on	ADP
ejpam-811	366	19	minimax	minimax	NOUN
ejpam-811	366	20	programming	programming	NOUN
ejpam-811	366	21	involving	involve	VERB
ejpam-811	366	22	generalized	generalized	ADJ
ejpam-811	366	23	convexity	convexity	NOUN
ejpam-811	366	24	in	in	ADP
ejpam-811	366	25	complex	complex	ADJ
ejpam-811	366	26	space	space	NOUN
ejpam-811	366	27	.	.	PUNCT
ejpam-811	367	1	journal	journal	PROPN
ejpam-811	367	2	of	of	ADP
ejpam-811	367	3	mathematical	mathematical	ADJ
ejpam-811	367	4	analysis	analysis	NOUN
ejpam-811	367	5	and	and	CCONJ
ejpam-811	367	6	applications	application	NOUN
ejpam-811	367	7	,	,	PUNCT
ejpam-811	367	8	323:1104	323:1104	PROPN
ejpam-811	367	9	-	-	SYM
ejpam-811	367	10	1115	1115	NUM
ejpam-811	367	11	,	,	PUNCT
ejpam-811	367	12	2006	2006	NUM
ejpam-811	367	13	.	.	PUNCT
ejpam-811	368	1	[	[	X
ejpam-811	368	2	7	7	X
ejpam-811	368	3	]	]	X
ejpam-811	368	4	h.c	h.c	PROPN
ejpam-811	368	5	.	.	PROPN
ejpam-811	368	6	lai	lai	PROPN
ejpam-811	368	7	and	and	CCONJ
ejpam-811	368	8	j.c	j.c	PROPN
ejpam-811	368	9	.	.	PROPN
ejpam-811	368	10	liu	liu	PROPN
ejpam-811	368	11	.	.	PUNCT
ejpam-811	369	1	complex	complex	ADJ
ejpam-811	369	2	fractional	fractional	ADJ
ejpam-811	369	3	programming	programming	NOUN
ejpam-811	369	4	involving	involve	VERB
ejpam-811	369	5	generalized	generalized	ADJ
ejpam-811	369	6	quasi	quasi	ADJ
ejpam-811	369	7	/	/	SYM
ejpam-811	369	8	pseudo	pseudo	ADJ
ejpam-811	369	9	convex	convex	NOUN
ejpam-811	369	10	functions	function	NOUN
ejpam-811	369	11	.	.	PUNCT
ejpam-811	370	1	zeitschrift	zeitschrift	NOUN
ejpam-811	370	2	fur	fur	PROPN
ejpam-811	370	3	angewandte	angewandte	PROPN
ejpam-811	370	4	mathematik	mathematik	PROPN
ejpam-811	370	5	und	und	PROPN
ejpam-811	370	6	mechanik	mechanik	PROPN
ejpam-811	370	7	,	,	PUNCT
ejpam-811	370	8	82(3):159	82(3):159	NUM
ejpam-811	370	9	-	-	SYM
ejpam-811	370	10	166	166	NUM
ejpam-811	370	11	,	,	PUNCT
ejpam-811	370	12	2002	2002	NUM
ejpam-811	370	13	.	.	PUNCT
ejpam-811	371	1	[	[	X
ejpam-811	371	2	8	8	NUM
ejpam-811	371	3	]	]	X
ejpam-811	371	4	h.c	h.c	PROPN
ejpam-811	371	5	.	.	PUNCT
ejpam-811	371	6	lai	lai	PROPN
ejpam-811	371	7	,	,	PUNCT
ejpam-811	371	8	j.c	j.c	PROPN
ejpam-811	371	9	.	.	PROPN
ejpam-811	371	10	liu	liu	PROPN
ejpam-811	371	11	and	and	CCONJ
ejpam-811	371	12	s.	s.	PROPN
ejpam-811	371	13	schaible	schaible	PROPN
ejpam-811	371	14	.	.	PUNCT
ejpam-811	372	1	complex	complex	ADJ
ejpam-811	372	2	minimax	minimax	NOUN
ejpam-811	372	3	fractional	fractional	ADJ
ejpam-811	372	4	programming	programming	NOUN
ejpam-811	372	5	of	of	ADP
ejpam-811	372	6	analytic	analytic	ADJ
ejpam-811	372	7	functions	function	NOUN
ejpam-811	372	8	.	.	PUNCT
ejpam-811	373	1	journal	journal	NOUN
ejpam-811	373	2	of	of	ADP
ejpam-811	373	3	optimization	optimization	NOUN
ejpam-811	373	4	theory	theory	NOUN
ejpam-811	373	5	and	and	CCONJ
ejpam-811	373	6	applications	application	NOUN
ejpam-811	373	7	,	,	PUNCT
ejpam-811	373	8	137(1):171	137(1):171	NOUN
ejpam-811	373	9	-	-	SYM
ejpam-811	373	10	184	184	NUM
ejpam-811	373	11	,	,	PUNCT
ejpam-811	373	12	2008	2008	NUM
ejpam-811	373	13	.	.	PUNCT
ejpam-811	374	1	[	[	X
ejpam-811	374	2	9	9	NUM
ejpam-811	374	3	]	]	X
ejpam-811	374	4	h.c	h.c	PROPN
ejpam-811	374	5	.	.	PROPN
ejpam-811	374	6	lai	lai	PROPN
ejpam-811	374	7	and	and	CCONJ
ejpam-811	374	8	j.c	j.c	PROPN
ejpam-811	374	9	.	.	PROPN
ejpam-811	374	10	liu	liu	PROPN
ejpam-811	374	11	.	.	PUNCT
ejpam-811	375	1	duality	duality	NOUN
ejpam-811	375	2	for	for	ADP
ejpam-811	375	3	nondifferentiable	nondifferentiable	ADJ
ejpam-811	375	4	minimax	minimax	NOUN
ejpam-811	375	5	programming	programming	NOUN
ejpam-811	375	6	in	in	ADP
ejpam-811	375	7	complex	complex	ADJ
ejpam-811	375	8	spaces	space	NOUN
ejpam-811	375	9	.	.	PUNCT
ejpam-811	376	1	nonlinear	nonlinear	ADJ
ejpam-811	376	2	analysis	analysis	NOUN
ejpam-811	376	3	,	,	PUNCT
ejpam-811	376	4	71	71	NUM
ejpam-811	376	5	:	:	PUNCT
ejpam-811	376	6	e224	e224	PROPN
ejpam-811	376	7	-	-	PUNCT
ejpam-811	376	8	e233	e233	PROPN
ejpam-811	376	9	,	,	PUNCT
ejpam-811	376	10	2009	2009	NUM
ejpam-811	376	11	.	.	PUNCT
ejpam-811	377	1	[	[	X
ejpam-811	377	2	10	10	NUM
ejpam-811	377	3	]	]	X
ejpam-811	377	4	n.	n.	PROPN
ejpam-811	377	5	levinson	levinson	PROPN
ejpam-811	377	6	.	.	PUNCT
ejpam-811	378	1	linear	linear	PROPN
ejpam-811	378	2	programming	programming	NOUN
ejpam-811	378	3	in	in	ADP
ejpam-811	378	4	complex	complex	ADJ
ejpam-811	378	5	space	space	NOUN
ejpam-811	378	6	.	.	PUNCT
ejpam-811	379	1	journal	journal	PROPN
ejpam-811	379	2	of	of	ADP
ejpam-811	379	3	mathematical	mathematical	ADJ
ejpam-811	379	4	analysis	analysis	NOUN
ejpam-811	379	5	and	and	CCONJ
ejpam-811	379	6	applications	application	NOUN
ejpam-811	379	7	,	,	PUNCT
ejpam-811	379	8	14:44	14:44	NUM
ejpam-811	379	9	-	-	SYM
ejpam-811	379	10	62	62	NUM
ejpam-811	379	11	,	,	PUNCT
ejpam-811	379	12	1966	1966	NUM
ejpam-811	379	13	.	.	PUNCT
ejpam-811	380	1	references	reference	NOUN
ejpam-811	380	2	1005	1005	NUM
ejpam-811	380	3	[	[	X
ejpam-811	380	4	11	11	NUM
ejpam-811	380	5	]	]	X
ejpam-811	380	6	b.	b.	PROPN
ejpam-811	380	7	mond	mond	PROPN
ejpam-811	380	8	.	.	PUNCT
ejpam-811	381	1	nonlinear	nonlinear	ADJ
ejpam-811	381	2	complex	complex	ADJ
ejpam-811	381	3	programming	programming	NOUN
ejpam-811	381	4	.	.	PUNCT
ejpam-811	382	1	journal	journal	PROPN
ejpam-811	382	2	of	of	ADP
ejpam-811	382	3	mathematical	mathematical	ADJ
ejpam-811	382	4	analysis	analysis	NOUN
ejpam-811	382	5	and	and	CCONJ
ejpam-811	382	6	applications	application	NOUN
ejpam-811	382	7	,	,	PUNCT
ejpam-811	382	8	43:633	43:633	NUM
ejpam-811	382	9	-	-	SYM
ejpam-811	382	10	641	641	NUM
ejpam-811	382	11	,	,	PUNCT
ejpam-811	382	12	1973	1973	NUM
ejpam-811	382	13	.	.	PUNCT
ejpam-811	383	1	[	[	X
ejpam-811	383	2	12	12	NUM
ejpam-811	383	3	]	]	X
ejpam-811	383	4	b.	b.	PROPN
ejpam-811	383	5	mond	mond	PROPN
ejpam-811	383	6	and	and	CCONJ
ejpam-811	383	7	t.	t.	PROPN
ejpam-811	383	8	weir	weir	PROPN
ejpam-811	383	9	.	.	PUNCT
ejpam-811	384	1	generalized	generalize	VERB
ejpam-811	384	2	convexity	convexity	NOUN
ejpam-811	384	3	and	and	CCONJ
ejpam-811	384	4	duality	duality	NOUN
ejpam-811	384	5	.	.	PUNCT
ejpam-811	385	1	in	in	ADP
ejpam-811	385	2	s.	s.	PROPN
ejpam-811	385	3	schaible	schaible	PROPN
ejpam-811	385	4	and	and	CCONJ
ejpam-811	385	5	w.t	w.t	PROPN
ejpam-811	386	1	.	.	PROPN
ejpam-811	386	2	zieinba	zieinba	PROPN
ejpam-811	386	3	,	,	PUNCT
ejpam-811	386	4	editors	editor	NOUN
ejpam-811	386	5	,	,	PUNCT
ejpam-811	386	6	generalized	generalized	ADJ
ejpam-811	386	7	concavity	concavity	NOUN
ejpam-811	386	8	in	in	ADP
ejpam-811	386	9	optimization	optimization	NOUN
ejpam-811	386	10	and	and	CCONJ
ejpam-811	386	11	economics	economic	NOUN
ejpam-811	386	12	,	,	PUNCT
ejpam-811	386	13	263	263	NUM
ejpam-811	386	14	-	-	SYM
ejpam-811	386	15	2793	2793	NUM
ejpam-811	386	16	,	,	PUNCT
ejpam-811	386	17	academic	academic	ADJ
ejpam-811	386	18	press	press	NOUN
ejpam-811	386	19	,	,	PUNCT
ejpam-811	386	20	newyork	newyork	NOUN
ejpam-811	386	21	,	,	PUNCT
ejpam-811	386	22	1981	1981	NUM
ejpam-811	386	23	.	.	PUNCT
ejpam-811	387	1	[	[	X
ejpam-811	387	2	13	13	NUM
ejpam-811	387	3	]	]	X
ejpam-811	387	4	o.	o.	PROPN
ejpam-811	387	5	parkash	parkash	PROPN
ejpam-811	387	6	,	,	PUNCT
ejpam-811	387	7	p.c	p.c	PROPN
ejpam-811	387	8	.	.	PROPN
ejpam-811	387	9	saxena	saxena	PROPN
ejpam-811	387	10	and	and	CCONJ
ejpam-811	387	11	v.	v.	ADP
ejpam-811	387	12	patkar	patkar	NOUN
ejpam-811	387	13	.	.	PUNCT
ejpam-811	388	1	nondifferentiable	nondifferentiable	ADJ
ejpam-811	388	2	fractional	fractional	ADJ
ejpam-811	388	3	programming	programming	NOUN
ejpam-811	388	4	in	in	ADP
ejpam-811	388	5	complex	complex	ADJ
ejpam-811	388	6	space	space	NOUN
ejpam-811	388	7	.	.	PUNCT
ejpam-811	389	1	zeitschrift	zeitschrift	NOUN
ejpam-811	389	2	fur	fur	PROPN
ejpam-811	389	3	angewandte	angewandte	PROPN
ejpam-811	389	4	mathematik	mathematik	PROPN
ejpam-811	389	5	und	und	PROPN
ejpam-811	389	6	mechanik	mechanik	PROPN
ejpam-811	389	7	,	,	PUNCT
ejpam-811	389	8	64(1):59	64(1):59	PROPN
ejpam-811	389	9	-	-	PUNCT
ejpam-811	389	10	62	62	NUM
ejpam-811	389	11	,	,	PUNCT
ejpam-811	389	12	1984	1984	NUM
ejpam-811	389	13	.	.	PUNCT
ejpam-811	390	1	[	[	X
ejpam-811	390	2	14	14	NUM
ejpam-811	390	3	]	]	PUNCT
ejpam-811	390	4	k.	k.	PROPN
ejpam-811	390	5	swarup	swarup	PROPN
ejpam-811	390	6	and	and	CCONJ
ejpam-811	390	7	j.c	j.c	PROPN
ejpam-811	390	8	.	.	PROPN
ejpam-811	390	9	sharma	sharma	PROPN
ejpam-811	390	10	.	.	PUNCT
ejpam-811	391	1	programming	programming	NOUN
ejpam-811	391	2	with	with	ADP
ejpam-811	391	3	linear	linear	ADJ
ejpam-811	391	4	fractional	fractional	ADJ
ejpam-811	391	5	functionals	functional	NOUN
ejpam-811	391	6	in	in	ADP
ejpam-811	391	7	complex	complex	ADJ
ejpam-811	391	8	spaces	space	NOUN
ejpam-811	391	9	.	.	PUNCT
ejpam-811	392	1	cahiers	cahier	NOUN
ejpam-811	392	2	du	du	PROPN
ejpam-811	392	3	centre	centre	PROPN
ejpam-811	392	4	d’etudes	d’etude	VERB
ejpam-811	392	5	et	et	PROPN
ejpam-811	392	6	de	de	X
ejpam-811	392	7	recherche	recherche	X
ejpam-811	392	8	operationelle	operationelle	PROPN
ejpam-811	392	9	,	,	PUNCT
ejpam-811	392	10	12:103	12:103	NUM
ejpam-811	392	11	-	-	SYM
ejpam-811	392	12	109	109	NUM
ejpam-811	392	13	,	,	PUNCT
ejpam-811	392	14	1970	1970	NUM
ejpam-811	392	15	.	.	PUNCT
ejpam-811	393	1	[	[	X
ejpam-811	393	2	15	15	NUM
ejpam-811	393	3	]	]	X
ejpam-811	393	4	p.	p.	PROPN
ejpam-811	393	5	wolfe	wolfe	PROPN
ejpam-811	393	6	.	.	PUNCT
ejpam-811	394	1	a	a	DET
ejpam-811	394	2	duality	duality	NOUN
ejpam-811	394	3	theorem	theorem	VERB
ejpam-811	394	4	for	for	ADP
ejpam-811	394	5	nonlinear	nonlinear	ADJ
ejpam-811	394	6	programming	programming	NOUN
ejpam-811	394	7	.	.	PUNCT
ejpam-811	395	1	quarterly	quarterly	ADV
ejpam-811	395	2	of	of	ADP
ejpam-811	395	3	applied	applied	ADJ
ejpam-811	395	4	mathematics	mathematic	NOUN
ejpam-811	395	5	,	,	PUNCT
ejpam-811	395	6	19:239	19:239	NUM
ejpam-811	395	7	-	-	SYM
ejpam-811	395	8	244	244	NUM
ejpam-811	395	9	,	,	PUNCT
ejpam-811	395	10	1961	1961	NUM
ejpam-811	395	11	.	.	PUNCT