id	sid	tid	token	lemma	pos
ejpam-214	1	1	8_214_zhang.dvi	8_214_zhang.dvi	NUM
ejpam-214	1	2	european	european	ADJ
ejpam-214	1	3	journal	journal	NOUN
ejpam-214	1	4	of	of	ADP
ejpam-214	1	5	pure	pure	ADJ
ejpam-214	1	6	and	and	CCONJ
ejpam-214	1	7	applied	apply	VERB
ejpam-214	1	8	mathematics	mathematic	NOUN
ejpam-214	1	9	vol	vol	NOUN
ejpam-214	1	10	.	.	PUNCT
ejpam-214	2	1	3	3	NUM
ejpam-214	2	2	,	,	PUNCT
ejpam-214	2	3	no	no	INTJ
ejpam-214	2	4	.	.	NOUN
ejpam-214	2	5	1	1	NUM
ejpam-214	2	6	,	,	PUNCT
ejpam-214	2	7	2010	2010	NUM
ejpam-214	2	8	,	,	PUNCT
ejpam-214	2	9	98	98	NUM
ejpam-214	2	10	-	-	SYM
ejpam-214	2	11	106	106	NUM
ejpam-214	2	12	issn	issn	PROPN
ejpam-214	2	13	1307	1307	NUM
ejpam-214	2	14	-	-	SYM
ejpam-214	2	15	5543	5543	NUM
ejpam-214	2	16	–	–	PUNCT
ejpam-214	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-214	2	18	on	on	ADP
ejpam-214	2	19	the	the	DET
ejpam-214	2	20	cross	cross	ADJ
ejpam-214	2	21	-	-	ADJ
ejpam-214	2	22	entropic	entropic	ADJ
ejpam-214	2	23	regularization	regularization	NOUN
ejpam-214	2	24	method	method	NOUN
ejpam-214	2	25	for	for	ADP
ejpam-214	2	26	solving	solve	VERB
ejpam-214	2	27	minmax	minmax	PROPN
ejpam-214	2	28	problems	problem	NOUN
ejpam-214	2	29	lili	lili	PROPN
ejpam-214	2	30	zhang1∗	zhang1∗	PROPN
ejpam-214	2	31	,	,	PUNCT
ejpam-214	2	32	jianyu	jianyu	PROPN
ejpam-214	2	33	li2	li2	PROPN
ejpam-214	2	34	and	and	CCONJ
ejpam-214	2	35	xingsi	xingsi	PROPN
ejpam-214	2	36	li3	li3	PROPN
ejpam-214	2	37	1	1	NUM
ejpam-214	2	38	department	department	NOUN
ejpam-214	2	39	of	of	ADP
ejpam-214	2	40	applied	apply	VERB
ejpam-214	2	41	mathematics	mathematic	NOUN
ejpam-214	2	42	,	,	PUNCT
ejpam-214	2	43	dalian	dalian	PROPN
ejpam-214	2	44	university	university	PROPN
ejpam-214	2	45	of	of	ADP
ejpam-214	2	46	technology	technology	PROPN
ejpam-214	2	47	,	,	PUNCT
ejpam-214	2	48	dalian	dalian	PROPN
ejpam-214	2	49	,	,	PUNCT
ejpam-214	2	50	p.	p.	PROPN
ejpam-214	2	51	r.	r.	PROPN
ejpam-214	3	1	china	china	PROPN
ejpam-214	3	2	2	2	NUM
ejpam-214	3	3	school	school	NOUN
ejpam-214	3	4	of	of	ADP
ejpam-214	3	5	mechanical	mechanical	ADJ
ejpam-214	3	6	engineering	engineering	NOUN
ejpam-214	3	7	,	,	PUNCT
ejpam-214	3	8	tianjin	tianjin	PROPN
ejpam-214	3	9	university	university	PROPN
ejpam-214	3	10	of	of	ADP
ejpam-214	3	11	science	science	NOUN
ejpam-214	3	12	and	and	CCONJ
ejpam-214	3	13	technology	technology	NOUN
ejpam-214	3	14	,	,	PUNCT
ejpam-214	3	15	tianjin	tianjin	PROPN
ejpam-214	3	16	,	,	PUNCT
ejpam-214	3	17	p.	p.	PROPN
ejpam-214	3	18	r.	r.	PROPN
ejpam-214	4	1	china	china	PROPN
ejpam-214	4	2	3	3	NUM
ejpam-214	4	3	state	state	NOUN
ejpam-214	4	4	key	key	ADJ
ejpam-214	4	5	laboratory	laboratory	NOUN
ejpam-214	4	6	of	of	ADP
ejpam-214	4	7	structural	structural	ADJ
ejpam-214	4	8	analysis	analysis	NOUN
ejpam-214	4	9	for	for	ADP
ejpam-214	4	10	industrial	industrial	ADJ
ejpam-214	4	11	equipment	equipment	NOUN
ejpam-214	4	12	,	,	PUNCT
ejpam-214	4	13	department	department	NOUN
ejpam-214	4	14	of	of	ADP
ejpam-214	4	15	engineering	engineering	NOUN
ejpam-214	4	16	mechanics	mechanic	NOUN
ejpam-214	4	17	,	,	PUNCT
ejpam-214	4	18	dalian	dalian	PROPN
ejpam-214	4	19	university	university	PROPN
ejpam-214	4	20	of	of	ADP
ejpam-214	4	21	technology	technology	PROPN
ejpam-214	4	22	,	,	PUNCT
ejpam-214	4	23	dalian	dalian	PROPN
ejpam-214	4	24	,	,	PUNCT
ejpam-214	5	1	p.	p.	PROPN
ejpam-214	5	2	r.	r.	PROPN
ejpam-214	5	3	china	china	PROPN
ejpam-214	5	4	abstract	abstract	PROPN
ejpam-214	5	5	.	.	PUNCT
ejpam-214	6	1	a	a	DET
ejpam-214	6	2	smoothing	smoothing	NOUN
ejpam-214	6	3	method	method	NOUN
ejpam-214	6	4	of	of	ADP
ejpam-214	6	5	multipliers	multiplier	NOUN
ejpam-214	6	6	which	which	PRON
ejpam-214	6	7	is	be	AUX
ejpam-214	6	8	a	a	DET
ejpam-214	6	9	natural	natural	ADJ
ejpam-214	6	10	result	result	NOUN
ejpam-214	6	11	of	of	ADP
ejpam-214	6	12	cross	cross	ADJ
ejpam-214	6	13	-	-	ADJ
ejpam-214	6	14	entropic	entropic	ADJ
ejpam-214	6	15	regularization	regularization	NOUN
ejpam-214	6	16	for	for	ADP
ejpam-214	6	17	min	min	NOUN
ejpam-214	6	18	-	-	ADJ
ejpam-214	6	19	max	max	ADJ
ejpam-214	6	20	problems	problem	NOUN
ejpam-214	6	21	is	be	AUX
ejpam-214	6	22	analyzed	analyze	VERB
ejpam-214	6	23	.	.	PUNCT
ejpam-214	7	1	as	as	ADP
ejpam-214	7	2	a	a	DET
ejpam-214	7	3	smoothing	smooth	VERB
ejpam-214	7	4	technique	technique	NOUN
ejpam-214	7	5	,	,	PUNCT
ejpam-214	7	6	we	we	PRON
ejpam-214	7	7	first	first	ADV
ejpam-214	7	8	show	show	VERB
ejpam-214	7	9	how	how	SCONJ
ejpam-214	7	10	the	the	DET
ejpam-214	7	11	smooth	smooth	ADJ
ejpam-214	7	12	approximation	approximation	NOUN
ejpam-214	7	13	yields	yield	VERB
ejpam-214	7	14	the	the	DET
ejpam-214	7	15	first	first	ADJ
ejpam-214	7	16	order	order	NOUN
ejpam-214	7	17	information	information	NOUN
ejpam-214	7	18	on	on	ADP
ejpam-214	7	19	the	the	DET
ejpam-214	7	20	behavior	behavior	NOUN
ejpam-214	7	21	of	of	ADP
ejpam-214	7	22	max	max	PROPN
ejpam-214	7	23	function	function	NOUN
ejpam-214	7	24	.	.	PUNCT
ejpam-214	8	1	then	then	ADV
ejpam-214	8	2	under	under	ADP
ejpam-214	8	3	suitable	suitable	ADJ
ejpam-214	8	4	assumptions	assumption	NOUN
ejpam-214	8	5	,	,	PUNCT
ejpam-214	8	6	some	some	DET
ejpam-214	8	7	basic	basic	ADJ
ejpam-214	8	8	properties	property	NOUN
ejpam-214	8	9	including	include	VERB
ejpam-214	8	10	the	the	DET
ejpam-214	8	11	hessian	hessian	NOUN
ejpam-214	8	12	are	be	AUX
ejpam-214	8	13	given	give	VERB
ejpam-214	8	14	.	.	PUNCT
ejpam-214	9	1	at	at	ADP
ejpam-214	9	2	last	last	ADJ
ejpam-214	9	3	,	,	PUNCT
ejpam-214	9	4	the	the	DET
ejpam-214	9	5	condition	condition	NOUN
ejpam-214	9	6	number	number	NOUN
ejpam-214	9	7	is	be	AUX
ejpam-214	9	8	analyzed	analyze	VERB
ejpam-214	9	9	,	,	PUNCT
ejpam-214	9	10	and	and	CCONJ
ejpam-214	9	11	the	the	DET
ejpam-214	9	12	results	result	NOUN
ejpam-214	9	13	reveal	reveal	VERB
ejpam-214	9	14	that	that	SCONJ
ejpam-214	9	15	the	the	DET
ejpam-214	9	16	smoothing	smoothing	NOUN
ejpam-214	9	17	method	method	NOUN
ejpam-214	9	18	of	of	ADP
ejpam-214	9	19	multipliers	multiplier	NOUN
ejpam-214	9	20	is	be	AUX
ejpam-214	9	21	stable	stable	ADJ
ejpam-214	9	22	for	for	ADP
ejpam-214	9	23	any	any	DET
ejpam-214	9	24	fixed	fix	VERB
ejpam-214	9	25	smoothing	smoothing	NOUN
ejpam-214	9	26	parameter	parameter	NOUN
ejpam-214	9	27	.	.	PUNCT
ejpam-214	10	1	2000	2000	NUM
ejpam-214	10	2	mathematics	mathematic	NOUN
ejpam-214	10	3	subject	subject	NOUN
ejpam-214	10	4	classifications	classification	NOUN
ejpam-214	10	5	:	:	PUNCT
ejpam-214	10	6	90c47	90c47	NUM
ejpam-214	10	7	;	;	PUNCT
ejpam-214	10	8	41a46	41a46	NUM
ejpam-214	10	9	;	;	PUNCT
ejpam-214	10	10	57r12	57r12	NUM
ejpam-214	10	11	key	key	ADJ
ejpam-214	10	12	words	word	NOUN
ejpam-214	10	13	and	and	CCONJ
ejpam-214	10	14	phrases	phrase	NOUN
ejpam-214	10	15	:	:	PUNCT
ejpam-214	10	16	min	min	ADJ
ejpam-214	10	17	-	-	ADJ
ejpam-214	10	18	max	max	PROPN
ejpam-214	10	19	problem	problem	NOUN
ejpam-214	10	20	;	;	PUNCT
ejpam-214	10	21	cross	cross	ADJ
ejpam-214	10	22	-	-	ADJ
ejpam-214	10	23	entropic	entropic	ADJ
ejpam-214	10	24	regularization	regularization	NOUN
ejpam-214	10	25	;	;	PUNCT
ejpam-214	10	26	smooth	smooth	ADJ
ejpam-214	10	27	approximation	approximation	NOUN
ejpam-214	10	28	;	;	PUNCT
ejpam-214	10	29	subgradient	subgradient	NOUN
ejpam-214	10	30	;	;	PUNCT
ejpam-214	10	31	condition	condition	NOUN
ejpam-214	10	32	number	number	NOUN
ejpam-214	10	33	1	1	NUM
ejpam-214	10	34	.	.	PUNCT
ejpam-214	11	1	introduction	introduction	NOUN
ejpam-214	11	2	a	a	DET
ejpam-214	11	3	variety	variety	NOUN
ejpam-214	11	4	of	of	ADP
ejpam-214	11	5	scientific	scientific	ADJ
ejpam-214	11	6	and	and	CCONJ
ejpam-214	11	7	engineering	engineering	NOUN
ejpam-214	11	8	problems	problem	NOUN
ejpam-214	11	9	(	(	PUNCT
ejpam-214	11	10	such	such	ADJ
ejpam-214	11	11	as	as	ADP
ejpam-214	11	12	the	the	DET
ejpam-214	11	13	problems	problem	NOUN
ejpam-214	11	14	that	that	PRON
ejpam-214	11	15	arise	arise	VERB
ejpam-214	11	16	in	in	ADP
ejpam-214	11	17	structural	structural	ADJ
ejpam-214	11	18	optimization	optimization	NOUN
ejpam-214	11	19	,	,	PUNCT
ejpam-214	11	20	synthesis	synthesis	NOUN
ejpam-214	11	21	of	of	ADP
ejpam-214	11	22	filters	filter	NOUN
ejpam-214	11	23	,	,	PUNCT
ejpam-214	11	24	antenna	antenna	NOUN
ejpam-214	11	25	design	design	NOUN
ejpam-214	11	26	etc	etc	X
ejpam-214	11	27	)	)	PUNCT
ejpam-214	11	28	can	can	AUX
ejpam-214	11	29	be	be	AUX
ejpam-214	11	30	formulated	formulate	VERB
ejpam-214	11	31	as	as	ADP
ejpam-214	11	32	the	the	DET
ejpam-214	11	33	following	follow	VERB
ejpam-214	11	34	min	min	ADJ
ejpam-214	11	35	-	-	ADJ
ejpam-214	11	36	max	max	PROPN
ejpam-214	11	37	problem	problem	NOUN
ejpam-214	11	38	(	(	PUNCT
ejpam-214	11	39	see	see	VERB
ejpam-214	11	40	[	[	X
ejpam-214	11	41	1	1	NUM
ejpam-214	11	42	]	]	PUNCT
ejpam-214	11	43	,	,	PUNCT
ejpam-214	12	1	[	[	X
ejpam-214	12	2	2	2	NUM
ejpam-214	12	3	]	]	PUNCT
ejpam-214	12	4	,	,	PUNCT
ejpam-214	12	5	[	[	X
ejpam-214	12	6	3	3	NUM
ejpam-214	12	7	]	]	PUNCT
ejpam-214	12	8	,	,	PUNCT
ejpam-214	12	9	[	[	X
ejpam-214	12	10	4	4	NUM
ejpam-214	12	11	]	]	PUNCT
ejpam-214	12	12	):	):	PUNCT
ejpam-214	12	13	min	min	PROPN
ejpam-214	12	14	x∈x	x∈x	PROPN
ejpam-214	12	15	max	max	PROPN
ejpam-214	12	16	1¶i¶m	1¶i¶m	NUM
ejpam-214	12	17	�	�	PROPN
ejpam-214	12	18	fi	fi	NOUN
ejpam-214	12	19	(	(	PUNCT
ejpam-214	12	20	x	x	X
ejpam-214	12	21	)	)	PUNCT
ejpam-214	12	22	(	(	PUNCT
ejpam-214	12	23	1	1	X
ejpam-214	12	24	)	)	PUNCT
ejpam-214	12	25	where	where	SCONJ
ejpam-214	12	26	x	x	PRON
ejpam-214	12	27	is	be	AUX
ejpam-214	12	28	a	a	DET
ejpam-214	12	29	common	common	ADJ
ejpam-214	12	30	domain	domain	NOUN
ejpam-214	12	31	of	of	ADP
ejpam-214	12	32	the	the	DET
ejpam-214	12	33	component	component	NOUN
ejpam-214	12	34	functions	function	NOUN
ejpam-214	12	35	fi(x	fi(x	NUM
ejpam-214	12	36	)	)	PUNCT
ejpam-214	12	37	,	,	PUNCT
ejpam-214	13	1	i	i	NOUN
ejpam-214	13	2	=	=	NOUN
ejpam-214	13	3	1,2	1,2	NUM
ejpam-214	13	4	,	,	PUNCT
ejpam-214	13	5	...	...	PUNCT
ejpam-214	13	6	m	m	VERB
ejpam-214	13	7	,	,	PUNCT
ejpam-214	13	8	which	which	PRON
ejpam-214	13	9	are	be	AUX
ejpam-214	13	10	usually	usually	ADV
ejpam-214	13	11	assumed	assume	VERB
ejpam-214	13	12	to	to	PART
ejpam-214	13	13	be	be	AUX
ejpam-214	13	14	twice	twice	ADV
ejpam-214	13	15	continuously	continuously	ADV
ejpam-214	13	16	differentiable	differentiable	ADJ
ejpam-214	13	17	.	.	PUNCT
ejpam-214	14	1	for	for	ADP
ejpam-214	14	2	a	a	DET
ejpam-214	14	3	complete	complete	ADJ
ejpam-214	14	4	treatment	treatment	NOUN
ejpam-214	14	5	of	of	ADP
ejpam-214	14	6	the	the	DET
ejpam-214	14	7	min	min	PROPN
ejpam-214	14	8	-	-	ADJ
ejpam-214	14	9	max	max	PROPN
ejpam-214	14	10	problems	problem	NOUN
ejpam-214	14	11	,	,	PUNCT
ejpam-214	14	12	see	see	VERB
ejpam-214	14	13	the	the	DET
ejpam-214	14	14	books	book	NOUN
ejpam-214	14	15	(	(	PUNCT
ejpam-214	14	16	[	[	X
ejpam-214	14	17	5	5	NUM
ejpam-214	14	18	]	]	PUNCT
ejpam-214	14	19	,	,	PUNCT
ejpam-214	14	20	[	[	X
ejpam-214	14	21	6	6	NUM
ejpam-214	14	22	]	]	PUNCT
ejpam-214	14	23	,	,	PUNCT
ejpam-214	14	24	[	[	X
ejpam-214	14	25	7	7	NUM
ejpam-214	14	26	]	]	NUM
ejpam-214	14	27	)	)	PUNCT
ejpam-214	14	28	.	.	PUNCT
ejpam-214	15	1	∗corresponding	∗corresponde	VERB
ejpam-214	15	2	author	author	NOUN
ejpam-214	15	3	.	.	PUNCT
ejpam-214	16	1	email	email	NOUN
ejpam-214	16	2	address	address	PROPN
ejpam-214	16	3	:	:	PUNCT
ejpam-214	16	4	jnlilizhang	jnlilizhang	PROPN
ejpam-214	16	5	�	�	PROPN
ejpam-214	16	6	163	163	NUM
ejpam-214	16	7	.	.	PUNCT
ejpam-214	17	1	om	om	PROPN
ejpam-214	17	2	(	(	PUNCT
ejpam-214	17	3	l.	l.	PROPN
ejpam-214	17	4	zhang	zhang	PROPN
ejpam-214	17	5	)	)	PUNCT
ejpam-214	17	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-214	18	1	98	98	NUM
ejpam-214	19	1	c	c	X
ejpam-214	19	2	©	©	PROPN
ejpam-214	19	3	2009	2009	NUM
ejpam-214	19	4	ejpam	ejpam	NOUN
ejpam-214	19	5	all	all	DET
ejpam-214	19	6	rights	right	NOUN
ejpam-214	19	7	reserved	reserve	VERB
ejpam-214	19	8	.	.	PUNCT
ejpam-214	20	1	l.	l.	PROPN
ejpam-214	20	2	zhang	zhang	PROPN
ejpam-214	20	3	,	,	PUNCT
ejpam-214	20	4	j.	j.	PROPN
ejpam-214	20	5	li	li	PROPN
ejpam-214	20	6	,	,	PUNCT
ejpam-214	20	7	x.	x.	PROPN
ejpam-214	20	8	li	li	PROPN
ejpam-214	20	9	/	/	SYM
ejpam-214	20	10	eur	eur	PROPN
ejpam-214	20	11	.	.	PUNCT
ejpam-214	21	1	j.	j.	PROPN
ejpam-214	21	2	pure	pure	PROPN
ejpam-214	21	3	appl	appl	PROPN
ejpam-214	21	4	.	.	PROPN
ejpam-214	21	5	math	math	PROPN
ejpam-214	21	6	,	,	PUNCT
ejpam-214	21	7	3	3	NUM
ejpam-214	21	8	(	(	PUNCT
ejpam-214	21	9	2010	2010	NUM
ejpam-214	21	10	)	)	PUNCT
ejpam-214	21	11	,	,	PUNCT
ejpam-214	21	12	98	98	NUM
ejpam-214	21	13	-	-	SYM
ejpam-214	21	14	106	106	NUM
ejpam-214	21	15	99	99	NUM
ejpam-214	21	16	one	one	NUM
ejpam-214	21	17	major	major	ADJ
ejpam-214	21	18	difficulty	difficulty	NOUN
ejpam-214	21	19	encountered	encounter	VERB
ejpam-214	21	20	in	in	ADP
ejpam-214	21	21	developing	develop	VERB
ejpam-214	21	22	solution	solution	NOUN
ejpam-214	21	23	methods	method	NOUN
ejpam-214	21	24	is	be	AUX
ejpam-214	21	25	the	the	DET
ejpam-214	21	26	non	non	ADJ
ejpam-214	21	27	-	-	NOUN
ejpam-214	21	28	differentiability	differentiability	NOUN
ejpam-214	21	29	of	of	ADP
ejpam-214	21	30	the	the	DET
ejpam-214	21	31	max	max	PROPN
ejpam-214	21	32	function	function	NOUN
ejpam-214	21	33	:	:	PUNCT
ejpam-214	21	34	f	f	PROPN
ejpam-214	21	35	(	(	PUNCT
ejpam-214	21	36	x	x	X
ejpam-214	21	37	)	)	PUNCT
ejpam-214	21	38	:	:	PUNCT
ejpam-214	21	39	=	=	SYM
ejpam-214	21	40	max	max	PROPN
ejpam-214	21	41	1¶i¶m	1¶i¶m	NUM
ejpam-214	21	42	�	�	PROPN
ejpam-214	21	43	fi	fi	NOUN
ejpam-214	21	44	(	(	PUNCT
ejpam-214	21	45	x	x	X
ejpam-214	21	46	)	)	PUNCT
ejpam-214	21	47	(	(	PUNCT
ejpam-214	21	48	2	2	NUM
ejpam-214	21	49	)	)	PUNCT
ejpam-214	21	50	and	and	CCONJ
ejpam-214	21	51	along	along	ADP
ejpam-214	21	52	with	with	ADP
ejpam-214	21	53	non	non	ADJ
ejpam-214	21	54	-	-	ADJ
ejpam-214	21	55	smooth	smooth	ADJ
ejpam-214	21	56	optimization	optimization	NOUN
ejpam-214	21	57	methods	method	NOUN
ejpam-214	21	58	,	,	PUNCT
ejpam-214	21	59	the	the	DET
ejpam-214	21	60	smoothing	smoothing	NOUN
ejpam-214	21	61	technique	technique	NOUN
ejpam-214	21	62	has	have	AUX
ejpam-214	21	63	been	be	AUX
ejpam-214	21	64	used	use	VERB
ejpam-214	21	65	for	for	ADP
ejpam-214	21	66	the	the	DET
ejpam-214	21	67	min	min	NOUN
ejpam-214	21	68	-	-	NOUN
ejpam-214	21	69	max	max	NOUN
ejpam-214	21	70	since	since	SCONJ
ejpam-214	21	71	the	the	DET
ejpam-214	21	72	early	early	ADJ
ejpam-214	21	73	70s([8	70s([8	NOUN
ejpam-214	21	74	]	]	PUNCT
ejpam-214	21	75	)	)	PUNCT
ejpam-214	21	76	,	,	PUNCT
ejpam-214	21	77	(	(	PUNCT
ejpam-214	21	78	see	see	VERB
ejpam-214	21	79	also	also	ADV
ejpam-214	21	80	[	[	X
ejpam-214	21	81	3	3	NUM
ejpam-214	21	82	]	]	PUNCT
ejpam-214	21	83	,	,	PUNCT
ejpam-214	21	84	[	[	X
ejpam-214	21	85	9	9	NUM
ejpam-214	21	86	]	]	PUNCT
ejpam-214	21	87	,	,	PUNCT
ejpam-214	21	88	[	[	X
ejpam-214	21	89	10	10	NUM
ejpam-214	21	90	]	]	PUNCT
ejpam-214	21	91	,	,	PUNCT
ejpam-214	21	92	[	[	X
ejpam-214	21	93	11	11	NUM
ejpam-214	21	94	]	]	PUNCT
ejpam-214	21	95	,	,	PUNCT
ejpam-214	21	96	[	[	X
ejpam-214	21	97	12	12	NUM
ejpam-214	21	98	]	]	PUNCT
ejpam-214	21	99	,	,	PUNCT
ejpam-214	21	100	[	[	X
ejpam-214	21	101	13	13	NUM
ejpam-214	21	102	]	]	NUM
ejpam-214	21	103	)	)	PUNCT
ejpam-214	21	104	.	.	PUNCT
ejpam-214	22	1	among	among	ADP
ejpam-214	22	2	them	they	PRON
ejpam-214	22	3	,	,	PUNCT
ejpam-214	22	4	a	a	DET
ejpam-214	22	5	class	class	NOUN
ejpam-214	22	6	called	call	VERB
ejpam-214	22	7	regularization	regularization	NOUN
ejpam-214	22	8	methods	method	NOUN
ejpam-214	22	9	has	have	AUX
ejpam-214	22	10	been	be	AUX
ejpam-214	22	11	developed	develop	VERB
ejpam-214	22	12	base	base	NOUN
ejpam-214	22	13	on	on	ADP
ejpam-214	22	14	approximating	approximate	VERB
ejpam-214	22	15	the	the	DET
ejpam-214	22	16	max	max	PROPN
ejpam-214	22	17	function	function	NOUN
ejpam-214	22	18	by	by	ADP
ejpam-214	22	19	certain	certain	ADJ
ejpam-214	22	20	smooth	smooth	ADJ
ejpam-214	22	21	functions([1	functions([1	PROPN
ejpam-214	22	22	]	]	PUNCT
ejpam-214	22	23	,	,	PUNCT
ejpam-214	22	24	[	[	X
ejpam-214	22	25	2	2	NUM
ejpam-214	22	26	]	]	PUNCT
ejpam-214	22	27	,	,	PUNCT
ejpam-214	22	28	[	[	X
ejpam-214	22	29	10	10	NUM
ejpam-214	22	30	]	]	PUNCT
ejpam-214	22	31	,	,	PUNCT
ejpam-214	22	32	[	[	X
ejpam-214	22	33	15	15	NUM
ejpam-214	22	34	]	]	PUNCT
ejpam-214	22	35	,	,	PUNCT
ejpam-214	22	36	[	[	X
ejpam-214	22	37	11	11	NUM
ejpam-214	22	38	]	]	PUNCT
ejpam-214	22	39	,	,	PUNCT
ejpam-214	22	40	[	[	X
ejpam-214	22	41	13	13	NUM
ejpam-214	22	42	]	]	NUM
ejpam-214	22	43	)	)	PUNCT
ejpam-214	22	44	.	.	PUNCT
ejpam-214	23	1	gigola	gigola	PROPN
ejpam-214	23	2	and	and	CCONJ
ejpam-214	23	3	gomez	gomez	PROPN
ejpam-214	23	4	(	(	PUNCT
ejpam-214	23	5	[	[	X
ejpam-214	23	6	10	10	NUM
ejpam-214	23	7	]	]	NUM
ejpam-214	23	8	)	)	PUNCT
ejpam-214	23	9	,	,	PUNCT
ejpam-214	23	10	hiriart	hiriart	NOUN
ejpam-214	23	11	-	-	PUNCT
ejpam-214	23	12	urruty	urruty	NOUN
ejpam-214	23	13	and	and	CCONJ
ejpam-214	23	14	lemarechal	lemarechal	ADJ
ejpam-214	23	15	(	(	PUNCT
ejpam-214	23	16	[	[	X
ejpam-214	23	17	14	14	NUM
ejpam-214	23	18	]	]	PUNCT
ejpam-214	23	19	)	)	PUNCT
ejpam-214	23	20	had	have	AUX
ejpam-214	23	21	given	give	VERB
ejpam-214	23	22	some	some	DET
ejpam-214	23	23	regularization	regularization	NOUN
ejpam-214	23	24	functions	function	NOUN
ejpam-214	23	25	,	,	PUNCT
ejpam-214	23	26	but	but	CCONJ
ejpam-214	23	27	no	no	DET
ejpam-214	23	28	explicit	explicit	ADJ
ejpam-214	23	29	expressions	expression	NOUN
ejpam-214	23	30	of	of	ADP
ejpam-214	23	31	the	the	DET
ejpam-214	23	32	smooth	smooth	ADJ
ejpam-214	23	33	approximation	approximation	NOUN
ejpam-214	23	34	functions	function	NOUN
ejpam-214	23	35	were	be	AUX
ejpam-214	23	36	given	give	VERB
ejpam-214	23	37	in	in	ADP
ejpam-214	23	38	their	their	PRON
ejpam-214	23	39	work	work	NOUN
ejpam-214	23	40	.	.	PUNCT
ejpam-214	24	1	li	li	PROPN
ejpam-214	25	1	(	(	PUNCT
ejpam-214	25	2	[	[	X
ejpam-214	25	3	15	15	NUM
ejpam-214	25	4	]	]	PUNCT
ejpam-214	25	5	,	,	PUNCT
ejpam-214	25	6	[	[	X
ejpam-214	25	7	16	16	NUM
ejpam-214	25	8	]	]	PUNCT
ejpam-214	25	9	)	)	PUNCT
ejpam-214	25	10	used	use	VERB
ejpam-214	25	11	entropy	entropy	NOUN
ejpam-214	25	12	function	function	NOUN
ejpam-214	25	13	as	as	ADP
ejpam-214	25	14	the	the	DET
ejpam-214	25	15	regularization	regularization	NOUN
ejpam-214	25	16	function	function	NOUN
ejpam-214	25	17	and	and	CCONJ
ejpam-214	25	18	derived	derive	VERB
ejpam-214	25	19	a	a	DET
ejpam-214	25	20	smooth	smooth	ADJ
ejpam-214	25	21	and	and	CCONJ
ejpam-214	25	22	good	good	ADJ
ejpam-214	25	23	approximation	approximation	NOUN
ejpam-214	25	24	function	function	NOUN
ejpam-214	25	25	in	in	ADP
ejpam-214	25	26	explicit	explicit	ADJ
ejpam-214	25	27	expression	expression	NOUN
ejpam-214	25	28	for	for	ADP
ejpam-214	25	29	the	the	DET
ejpam-214	25	30	max	max	PROPN
ejpam-214	25	31	function	function	PROPN
ejpam-214	25	32	f	f	PROPN
ejpam-214	26	1	(	(	PUNCT
ejpam-214	26	2	x)≈	x)≈	PROPN
ejpam-214	26	3	1	1	NUM
ejpam-214	26	4	p	p	X
ejpam-214	26	5	ln	ln	NOUN
ejpam-214	26	6	m	m	PROPN
ejpam-214	26	7	∑	∑	PROPN
ejpam-214	26	8	i=1	i=1	PROPN
ejpam-214	26	9	exp	exp	NOUN
ejpam-214	26	10	�	�	PROPN
ejpam-214	26	11	p	p	PROPN
ejpam-214	26	12	fi	fi	NOUN
ejpam-214	26	13	(	(	PUNCT
ejpam-214	26	14	x	x	NOUN
ejpam-214	26	15	)	)	PUNCT
ejpam-214	26	16	�	�	PROPN
ejpam-214	26	17	.	.	PUNCT
ejpam-214	27	1	this	this	DET
ejpam-214	27	2	smooth	smooth	ADJ
ejpam-214	27	3	approximation	approximation	NOUN
ejpam-214	27	4	function	function	NOUN
ejpam-214	27	5	is	be	AUX
ejpam-214	27	6	called	call	VERB
ejpam-214	27	7	aggregate	aggregate	ADJ
ejpam-214	27	8	function	function	NOUN
ejpam-214	27	9	and	and	CCONJ
ejpam-214	27	10	instead	instead	ADV
ejpam-214	27	11	of	of	ADP
ejpam-214	27	12	using	use	VERB
ejpam-214	27	13	the	the	DET
ejpam-214	27	14	entropy	entropy	NOUN
ejpam-214	27	15	regularization	regularization	NOUN
ejpam-214	27	16	function	function	NOUN
ejpam-214	27	17	,	,	PUNCT
ejpam-214	27	18	the	the	DET
ejpam-214	27	19	cross	cross	ADJ
ejpam-214	27	20	-	-	ADJ
ejpam-214	27	21	entropy	entropy	ADJ
ejpam-214	27	22	regularization	regularization	NOUN
ejpam-214	27	23	function	function	NOUN
ejpam-214	27	24	can	can	AUX
ejpam-214	27	25	lead	lead	VERB
ejpam-214	27	26	to	to	ADP
ejpam-214	27	27	another	another	DET
ejpam-214	27	28	smooth	smooth	ADJ
ejpam-214	27	29	and	and	CCONJ
ejpam-214	27	30	good	good	ADJ
ejpam-214	27	31	approximation	approximation	NOUN
ejpam-214	27	32	function	function	NOUN
ejpam-214	27	33	which	which	PRON
ejpam-214	27	34	is	be	AUX
ejpam-214	27	35	a	a	DET
ejpam-214	27	36	smooth	smooth	ADJ
ejpam-214	27	37	approximation	approximation	NOUN
ejpam-214	27	38	function	function	NOUN
ejpam-214	27	39	of	of	ADP
ejpam-214	27	40	multipliers	multiplier	NOUN
ejpam-214	27	41	and	and	CCONJ
ejpam-214	27	42	is	be	AUX
ejpam-214	27	43	called	call	VERB
ejpam-214	27	44	cross	cross	ADJ
ejpam-214	27	45	-	-	ADJ
ejpam-214	27	46	entropy	entropy	ADJ
ejpam-214	27	47	aggregate	aggregate	ADJ
ejpam-214	27	48	function	function	NOUN
ejpam-214	27	49	:	:	PUNCT
ejpam-214	28	1	fp	fp	X
ejpam-214	28	2	(	(	PUNCT
ejpam-214	28	3	x	x	INTJ
ejpam-214	28	4	,	,	PUNCT
ejpam-214	28	5	λ	λ	NOUN
ejpam-214	28	6	)	)	PUNCT
ejpam-214	28	7	=	=	SYM
ejpam-214	29	1	1	1	NUM
ejpam-214	29	2	p	p	NOUN
ejpam-214	29	3	ln	ln	NOUN
ejpam-214	29	4	m	m	VERB
ejpam-214	29	5	∑	∑	PROPN
ejpam-214	29	6	i=1	i=1	PROPN
ejpam-214	29	7	λi	λi	INTJ
ejpam-214	29	8	exp	exp	PRON
ejpam-214	29	9	�	�	PROPN
ejpam-214	29	10	p	p	PROPN
ejpam-214	29	11	fi	fi	NOUN
ejpam-214	29	12	(	(	PUNCT
ejpam-214	29	13	x	x	NOUN
ejpam-214	29	14	)	)	PUNCT
ejpam-214	29	15	�	�	PROPN
ejpam-214	29	16	(	(	PUNCT
ejpam-214	29	17	3	3	NUM
ejpam-214	29	18	)	)	PUNCT
ejpam-214	29	19	both	both	CCONJ
ejpam-214	29	20	the	the	DET
ejpam-214	29	21	two	two	NUM
ejpam-214	29	22	smoothing	smooth	VERB
ejpam-214	29	23	approximation	approximation	NOUN
ejpam-214	29	24	functions	function	NOUN
ejpam-214	29	25	have	have	VERB
ejpam-214	29	26	a	a	DET
ejpam-214	29	27	natural	natural	ADJ
ejpam-214	29	28	interpretation	interpretation	NOUN
ejpam-214	29	29	which	which	PRON
ejpam-214	29	30	fits	fit	VERB
ejpam-214	29	31	the	the	DET
ejpam-214	29	32	special	special	ADJ
ejpam-214	29	33	structure	structure	NOUN
ejpam-214	29	34	of	of	ADP
ejpam-214	29	35	the	the	DET
ejpam-214	29	36	min	min	PROPN
ejpam-214	29	37	-	-	ADJ
ejpam-214	29	38	max	max	PROPN
ejpam-214	29	39	problem	problem	NOUN
ejpam-214	29	40	and	and	CCONJ
ejpam-214	29	41	apply	apply	VERB
ejpam-214	29	42	to	to	ADP
ejpam-214	29	43	related	relate	VERB
ejpam-214	29	44	problems	problem	NOUN
ejpam-214	29	45	.	.	PUNCT
ejpam-214	30	1	the	the	DET
ejpam-214	30	2	function	function	NOUN
ejpam-214	30	3	(	(	PUNCT
ejpam-214	30	4	3	3	X
ejpam-214	30	5	)	)	PUNCT
ejpam-214	30	6	is	be	AUX
ejpam-214	30	7	also	also	ADV
ejpam-214	30	8	proposed	propose	VERB
ejpam-214	30	9	by	by	ADP
ejpam-214	30	10	bertsekas	bertsekas	PROPN
ejpam-214	30	11	(	(	PUNCT
ejpam-214	30	12	[	[	X
ejpam-214	30	13	1	1	NUM
ejpam-214	30	14	]	]	PUNCT
ejpam-214	30	15	)	)	PUNCT
ejpam-214	30	16	by	by	ADP
ejpam-214	30	17	means	mean	NOUN
ejpam-214	30	18	of	of	ADP
ejpam-214	30	19	a	a	DET
ejpam-214	30	20	tedious	tedious	ADJ
ejpam-214	30	21	derivation	derivation	NOUN
ejpam-214	30	22	using	use	VERB
ejpam-214	30	23	the	the	DET
ejpam-214	30	24	multiplier	multipli	ADJ
ejpam-214	30	25	methods	method	NOUN
ejpam-214	30	26	with	with	ADP
ejpam-214	30	27	an	an	DET
ejpam-214	30	28	exponential	exponential	ADJ
ejpam-214	30	29	penalty	penalty	NOUN
ejpam-214	30	30	function	function	NOUN
ejpam-214	30	31	.	.	PUNCT
ejpam-214	31	1	in	in	ADP
ejpam-214	31	2	this	this	DET
ejpam-214	31	3	paper	paper	NOUN
ejpam-214	31	4	,	,	PUNCT
ejpam-214	31	5	we	we	PRON
ejpam-214	31	6	mainly	mainly	ADV
ejpam-214	31	7	investigate	investigate	VERB
ejpam-214	31	8	the	the	DET
ejpam-214	31	9	approximation	approximation	NOUN
ejpam-214	31	10	function	function	NOUN
ejpam-214	31	11	(	(	PUNCT
ejpam-214	31	12	3	3	NUM
ejpam-214	31	13	)	)	PUNCT
ejpam-214	31	14	,	,	PUNCT
ejpam-214	31	15	although	although	SCONJ
ejpam-214	31	16	the	the	DET
ejpam-214	31	17	uniform	uniform	ADJ
ejpam-214	31	18	convergence	convergence	NOUN
ejpam-214	31	19	and	and	CCONJ
ejpam-214	31	20	the	the	DET
ejpam-214	31	21	algorithmic	algorithmic	ADJ
ejpam-214	31	22	convergence	convergence	NOUN
ejpam-214	31	23	based	base	VERB
ejpam-214	31	24	on	on	ADP
ejpam-214	31	25	this	this	DET
ejpam-214	31	26	function	function	NOUN
ejpam-214	31	27	had	have	AUX
ejpam-214	31	28	been	be	AUX
ejpam-214	31	29	already	already	ADV
ejpam-214	31	30	given	give	VERB
ejpam-214	31	31	(	(	PUNCT
ejpam-214	31	32	[	[	X
ejpam-214	31	33	16	16	NUM
ejpam-214	31	34	]	]	PUNCT
ejpam-214	31	35	,	,	PUNCT
ejpam-214	32	1	[	[	X
ejpam-214	32	2	1	1	NUM
ejpam-214	32	3	]	]	NUM
ejpam-214	32	4	)	)	PUNCT
ejpam-214	32	5	,	,	PUNCT
ejpam-214	32	6	the	the	DET
ejpam-214	32	7	main	main	ADJ
ejpam-214	32	8	results	result	NOUN
ejpam-214	32	9	in	in	ADP
ejpam-214	32	10	this	this	DET
ejpam-214	32	11	paper	paper	NOUN
ejpam-214	32	12	have	have	AUX
ejpam-214	32	13	not	not	PART
ejpam-214	32	14	appeared	appear	VERB
ejpam-214	32	15	in	in	ADP
ejpam-214	32	16	either	either	CCONJ
ejpam-214	32	17	[	[	X
ejpam-214	32	18	16	16	NUM
ejpam-214	32	19	]	]	PUNCT
ejpam-214	32	20	or	or	CCONJ
ejpam-214	32	21	[	[	X
ejpam-214	32	22	1	1	NUM
ejpam-214	32	23	]	]	PUNCT
ejpam-214	32	24	.	.	PUNCT
ejpam-214	33	1	we	we	PRON
ejpam-214	33	2	first	first	ADV
ejpam-214	33	3	show	show	VERB
ejpam-214	33	4	how	how	SCONJ
ejpam-214	33	5	the	the	DET
ejpam-214	33	6	smooth	smooth	ADJ
ejpam-214	33	7	approximation	approximation	NOUN
ejpam-214	33	8	yields	yield	VERB
ejpam-214	33	9	the	the	DET
ejpam-214	33	10	first	first	ADJ
ejpam-214	33	11	order	order	NOUN
ejpam-214	33	12	information	information	NOUN
ejpam-214	33	13	on	on	ADP
ejpam-214	33	14	the	the	DET
ejpam-214	33	15	behavior	behavior	NOUN
ejpam-214	33	16	of	of	ADP
ejpam-214	33	17	max	max	PROPN
ejpam-214	33	18	function	function	NOUN
ejpam-214	33	19	.	.	PUNCT
ejpam-214	34	1	then	then	ADV
ejpam-214	34	2	under	under	ADP
ejpam-214	34	3	suitable	suitable	ADJ
ejpam-214	34	4	assumptions	assumption	NOUN
ejpam-214	34	5	,	,	PUNCT
ejpam-214	34	6	some	some	DET
ejpam-214	34	7	basic	basic	ADJ
ejpam-214	34	8	properties	property	NOUN
ejpam-214	34	9	including	include	VERB
ejpam-214	34	10	the	the	DET
ejpam-214	34	11	hessian	hessian	NOUN
ejpam-214	34	12	are	be	AUX
ejpam-214	34	13	given	give	VERB
ejpam-214	34	14	.	.	PUNCT
ejpam-214	35	1	as	as	SCONJ
ejpam-214	35	2	this	this	DET
ejpam-214	35	3	smooth	smooth	ADJ
ejpam-214	35	4	approximation	approximation	NOUN
ejpam-214	35	5	function	function	NOUN
ejpam-214	35	6	of	of	ADP
ejpam-214	35	7	multipliers	multiplier	NOUN
ejpam-214	35	8	is	be	AUX
ejpam-214	35	9	obtained	obtain	VERB
ejpam-214	35	10	by	by	ADP
ejpam-214	35	11	the	the	DET
ejpam-214	35	12	cross	cross	ADJ
ejpam-214	35	13	-	-	ADJ
ejpam-214	35	14	entropic	entropic	ADJ
ejpam-214	35	15	regularization	regularization	NOUN
ejpam-214	35	16	of	of	ADP
ejpam-214	35	17	the	the	DET
ejpam-214	35	18	classical	classical	ADJ
ejpam-214	35	19	lagrangian	lagrangian	NOUN
ejpam-214	35	20	,	,	PUNCT
ejpam-214	35	21	if	if	SCONJ
ejpam-214	35	22	we	we	PRON
ejpam-214	35	23	treat	treat	VERB
ejpam-214	35	24	this	this	DET
ejpam-214	35	25	smooth	smooth	ADJ
ejpam-214	35	26	approximation	approximation	NOUN
ejpam-214	35	27	as	as	ADP
ejpam-214	35	28	a	a	DET
ejpam-214	35	29	nonlinear	nonlinear	ADJ
ejpam-214	35	30	lagrangian	lagrangian	ADJ
ejpam-214	35	31	function	function	NOUN
ejpam-214	35	32	for	for	ADP
ejpam-214	35	33	the	the	DET
ejpam-214	35	34	min	min	PROPN
ejpam-214	35	35	-	-	ADJ
ejpam-214	35	36	max	max	PROPN
ejpam-214	35	37	problem	problem	NOUN
ejpam-214	35	38	,	,	PUNCT
ejpam-214	35	39	then	then	ADV
ejpam-214	35	40	based	base	VERB
ejpam-214	35	41	on	on	ADP
ejpam-214	35	42	the	the	DET
ejpam-214	35	43	basic	basic	ADJ
ejpam-214	35	44	properties	property	NOUN
ejpam-214	35	45	,	,	PUNCT
ejpam-214	35	46	a	a	DET
ejpam-214	35	47	similar	similar	ADJ
ejpam-214	35	48	saddle	saddle	NOUN
ejpam-214	35	49	point	point	NOUN
ejpam-214	35	50	result	result	NOUN
ejpam-214	35	51	can	can	AUX
ejpam-214	35	52	be	be	AUX
ejpam-214	35	53	obtained	obtain	VERB
ejpam-214	35	54	.	.	PUNCT
ejpam-214	36	1	at	at	ADP
ejpam-214	36	2	last	last	ADJ
ejpam-214	36	3	,	,	PUNCT
ejpam-214	36	4	the	the	DET
ejpam-214	36	5	condition	condition	NOUN
ejpam-214	36	6	number	number	NOUN
ejpam-214	36	7	is	be	AUX
ejpam-214	36	8	analyzed	analyze	VERB
ejpam-214	36	9	,	,	PUNCT
ejpam-214	36	10	and	and	CCONJ
ejpam-214	36	11	the	the	DET
ejpam-214	36	12	results	result	NOUN
ejpam-214	36	13	reveal	reveal	VERB
ejpam-214	36	14	that	that	SCONJ
ejpam-214	36	15	the	the	DET
ejpam-214	36	16	smoothing	smoothing	NOUN
ejpam-214	36	17	method	method	NOUN
ejpam-214	36	18	of	of	ADP
ejpam-214	36	19	multipliers	multiplier	NOUN
ejpam-214	36	20	is	be	AUX
ejpam-214	36	21	stable	stable	ADJ
ejpam-214	36	22	for	for	ADP
ejpam-214	36	23	any	any	DET
ejpam-214	36	24	fixed	fix	VERB
ejpam-214	36	25	smoothing	smoothing	NOUN
ejpam-214	36	26	parameter	parameter	NOUN
ejpam-214	36	27	.	.	PUNCT
ejpam-214	37	1	the	the	DET
ejpam-214	37	2	rest	rest	NOUN
ejpam-214	37	3	of	of	ADP
ejpam-214	37	4	this	this	DET
ejpam-214	37	5	paper	paper	NOUN
ejpam-214	37	6	is	be	AUX
ejpam-214	37	7	arranged	arrange	VERB
ejpam-214	37	8	as	as	SCONJ
ejpam-214	37	9	follows	follow	VERB
ejpam-214	37	10	:	:	PUNCT
ejpam-214	37	11	section	section	NOUN
ejpam-214	37	12	2	2	NUM
ejpam-214	37	13	gives	give	VERB
ejpam-214	37	14	the	the	DET
ejpam-214	37	15	problem	problem	NOUN
ejpam-214	37	16	formulation	formulation	NOUN
ejpam-214	37	17	and	and	CCONJ
ejpam-214	37	18	some	some	DET
ejpam-214	37	19	basic	basic	ADJ
ejpam-214	37	20	assumptions	assumption	NOUN
ejpam-214	37	21	.	.	PUNCT
ejpam-214	38	1	some	some	DET
ejpam-214	38	2	basic	basic	ADJ
ejpam-214	38	3	results	result	NOUN
ejpam-214	38	4	including	include	VERB
ejpam-214	38	5	the	the	DET
ejpam-214	38	6	first	first	ADJ
ejpam-214	38	7	order	order	NOUN
ejpam-214	38	8	information	information	NOUN
ejpam-214	38	9	,	,	PUNCT
ejpam-214	38	10	basic	basic	ADJ
ejpam-214	38	11	properties	property	NOUN
ejpam-214	38	12	and	and	CCONJ
ejpam-214	38	13	the	the	DET
ejpam-214	38	14	condition	condition	NOUN
ejpam-214	38	15	number	number	NOUN
ejpam-214	38	16	are	be	AUX
ejpam-214	38	17	given	give	VERB
ejpam-214	38	18	in	in	ADP
ejpam-214	38	19	section	section	NOUN
ejpam-214	38	20	3	3	NUM
ejpam-214	38	21	.	.	PUNCT
ejpam-214	38	22	section	section	NOUN
ejpam-214	38	23	4	4	NUM
ejpam-214	38	24	is	be	AUX
ejpam-214	38	25	the	the	DET
ejpam-214	38	26	conclusion	conclusion	NOUN
ejpam-214	38	27	.	.	PUNCT
ejpam-214	39	1	2	2	X
ejpam-214	39	2	.	.	X
ejpam-214	39	3	problem	problem	NOUN
ejpam-214	39	4	formulation	formulation	NOUN
ejpam-214	39	5	and	and	CCONJ
ejpam-214	39	6	basic	basic	ADJ
ejpam-214	39	7	assumptions	assumption	NOUN
ejpam-214	39	8	consider	consider	VERB
ejpam-214	39	9	the	the	DET
ejpam-214	39	10	min	min	ADJ
ejpam-214	39	11	-	-	ADJ
ejpam-214	39	12	max	max	PROPN
ejpam-214	39	13	problem	problem	NOUN
ejpam-214	39	14	(	(	PUNCT
ejpam-214	39	15	1	1	NUM
ejpam-214	39	16	)	)	PUNCT
ejpam-214	39	17	.	.	PUNCT
ejpam-214	40	1	the	the	DET
ejpam-214	40	2	following	follow	VERB
ejpam-214	40	3	are	be	AUX
ejpam-214	40	4	assumptions	assumption	NOUN
ejpam-214	40	5	:	:	PUNCT
ejpam-214	40	6	assumption	assumption	NOUN
ejpam-214	40	7	1	1	NUM
ejpam-214	40	8	.	.	PUNCT
ejpam-214	41	1	the	the	DET
ejpam-214	41	2	optimal	optimal	ADJ
ejpam-214	41	3	set	set	NOUN
ejpam-214	41	4	x	x	VERB
ejpam-214	41	5	∗	∗	NOUN
ejpam-214	41	6	is	be	AUX
ejpam-214	41	7	not	not	PART
ejpam-214	41	8	empty	empty	ADJ
ejpam-214	41	9	and	and	CCONJ
ejpam-214	41	10	bounded	bound	VERB
ejpam-214	41	11	;	;	PUNCT
ejpam-214	41	12	l.	l.	PROPN
ejpam-214	41	13	zhang	zhang	PROPN
ejpam-214	41	14	,	,	PUNCT
ejpam-214	41	15	j.	j.	PROPN
ejpam-214	41	16	li	li	PROPN
ejpam-214	41	17	,	,	PUNCT
ejpam-214	41	18	x.	x.	PROPN
ejpam-214	41	19	li	li	PROPN
ejpam-214	41	20	/	/	SYM
ejpam-214	41	21	eur	eur	PROPN
ejpam-214	41	22	.	.	PUNCT
ejpam-214	42	1	j.	j.	PROPN
ejpam-214	42	2	pure	pure	PROPN
ejpam-214	42	3	appl	appl	PROPN
ejpam-214	42	4	.	.	PROPN
ejpam-214	42	5	math	math	PROPN
ejpam-214	42	6	,	,	PUNCT
ejpam-214	42	7	3	3	NUM
ejpam-214	42	8	(	(	PUNCT
ejpam-214	42	9	2010	2010	NUM
ejpam-214	42	10	)	)	PUNCT
ejpam-214	42	11	,	,	PUNCT
ejpam-214	42	12	98	98	NUM
ejpam-214	42	13	-	-	SYM
ejpam-214	42	14	106	106	NUM
ejpam-214	42	15	100	100	NUM
ejpam-214	42	16	without	without	ADP
ejpam-214	42	17	loss	loss	NOUN
ejpam-214	42	18	of	of	ADP
ejpam-214	42	19	generality	generality	NOUN
ejpam-214	42	20	we	we	PRON
ejpam-214	42	21	can	can	AUX
ejpam-214	42	22	assume	assume	VERB
ejpam-214	42	23	that	that	SCONJ
ejpam-214	42	24	f(x∗	f(x∗	NOUN
ejpam-214	42	25	)	)	PUNCT
ejpam-214	42	26	=	=	SYM
ejpam-214	43	1	0	0	X
ejpam-214	43	2	.	.	PUNCT
ejpam-214	44	1	the	the	DET
ejpam-214	44	2	min	min	PROPN
ejpam-214	44	3	-	-	ADJ
ejpam-214	44	4	max	max	PROPN
ejpam-214	44	5	problem	problem	NOUN
ejpam-214	44	6	(	(	PUNCT
ejpam-214	44	7	1	1	X
ejpam-214	44	8	)	)	PUNCT
ejpam-214	44	9	has	have	VERB
ejpam-214	44	10	the	the	DET
ejpam-214	44	11	classical	classical	ADJ
ejpam-214	44	12	lagrangian	lagrangian	ADJ
ejpam-214	44	13	function	function	NOUN
ejpam-214	44	14	l	l	NOUN
ejpam-214	44	15	(	(	PUNCT
ejpam-214	44	16	x	x	NOUN
ejpam-214	44	17	,	,	PUNCT
ejpam-214	44	18	λ	λ	NOUN
ejpam-214	44	19	)	)	PUNCT
ejpam-214	44	20	=	=	PUNCT
ejpam-214	45	1	m	m	VERB
ejpam-214	45	2	∑	∑	PUNCT
ejpam-214	45	3	i=1	i=1	PROPN
ejpam-214	45	4	λi	λi	INTJ
ejpam-214	45	5	fi	fi	NOUN
ejpam-214	45	6	(	(	PUNCT
ejpam-214	45	7	x	x	X
ejpam-214	45	8	)	)	PUNCT
ejpam-214	45	9	for	for	ADP
ejpam-214	45	10	each	each	DET
ejpam-214	45	11	x	x	SYM
ejpam-214	45	12	∈	∈	PROPN
ejpam-214	45	13	x	x	X
ejpam-214	45	14	,	,	PUNCT
ejpam-214	45	15	where	where	SCONJ
ejpam-214	45	16	λ	λ	PROPN
ejpam-214	45	17	denotes	denote	VERB
ejpam-214	45	18	the	the	DET
ejpam-214	45	19	lagrangian	lagrangian	ADJ
ejpam-214	45	20	multipliers	multiplier	NOUN
ejpam-214	45	21	that	that	PRON
ejpam-214	45	22	are	be	AUX
ejpam-214	45	23	restricted	restrict	VERB
ejpam-214	45	24	to	to	PART
ejpam-214	45	25	fall	fall	VERB
ejpam-214	45	26	within	within	ADP
ejpam-214	45	27	the	the	DET
ejpam-214	45	28	simplex	simplex	NOUN
ejpam-214	45	29	λ	λ	PROPN
ejpam-214	45	30	≡	≡	PROPN
ejpam-214	45	31	¨	¨	NOUN
ejpam-214	45	32	λ|λ¾	λ|λ¾	PROPN
ejpam-214	45	33	0	0	NUM
ejpam-214	45	34	;	;	PUNCT
ejpam-214	45	35	m	m	VERB
ejpam-214	45	36	∑	∑	ADJ
ejpam-214	45	37	i=1	i=1	PROPN
ejpam-214	45	38	λi	λi	NOUN
ejpam-214	45	39	=	=	NOUN
ejpam-214	45	40	1	1	NUM
ejpam-214	45	41	«	«	PUNCT
ejpam-214	45	42	.	.	PUNCT
ejpam-214	46	1	the	the	DET
ejpam-214	46	2	following	follow	VERB
ejpam-214	46	3	karush	karush	PROPN
ejpam-214	46	4	-	-	PUNCT
ejpam-214	46	5	kuhn	kuhn	PROPN
ejpam-214	46	6	-	-	PUNCT
ejpam-214	46	7	tucker	tucker	PROPN
ejpam-214	46	8	(	(	PUNCT
ejpam-214	46	9	k−k−t	k−k−t	NOUN
ejpam-214	46	10	)	)	PUNCT
ejpam-214	46	11	conditions	condition	NOUN
ejpam-214	46	12	for	for	ADP
ejpam-214	46	13	problem	problem	NOUN
ejpam-214	46	14	(	(	PUNCT
ejpam-214	46	15	1	1	X
ejpam-214	46	16	)	)	PUNCT
ejpam-214	46	17	hold	hold	VERB
ejpam-214	46	18	true	true	ADJ
ejpam-214	46	19	:	:	PUNCT
ejpam-214	46	20			PRON
ejpam-214	46	21			NOUN
ejpam-214	46	22			PROPN
ejpam-214	46	23			PROPN
ejpam-214	46	24			NOUN
ejpam-214	46	25			PROPN
ejpam-214	46	26			PROPN
ejpam-214	46	27			PROPN
ejpam-214	46	28			ADJ
ejpam-214	46	29	∇x	∇x	PROPN
ejpam-214	46	30	l	l	NOUN
ejpam-214	46	31	(	(	PUNCT
ejpam-214	46	32	x∗,λ∗	x∗,λ∗	PROPN
ejpam-214	46	33	)	)	PUNCT
ejpam-214	47	1	=	=	PUNCT
ejpam-214	47	2	m	m	VERB
ejpam-214	47	3	∑	∑	PUNCT
ejpam-214	47	4	i=1	i=1	PROPN
ejpam-214	47	5	λ∗i∇	λ∗i∇	PROPN
ejpam-214	47	6	fi	fi	NOUN
ejpam-214	47	7	(	(	PUNCT
ejpam-214	47	8	x	x	NOUN
ejpam-214	47	9	∗	∗	NOUN
ejpam-214	47	10	)	)	PUNCT
ejpam-214	47	11	=	=	SYM
ejpam-214	47	12	0	0	NUM
ejpam-214	47	13	λ∗i	λ∗i	X
ejpam-214	47	14	≥	≥	NUM
ejpam-214	47	15	0	0	NUM
ejpam-214	47	16	,	,	PUNCT
ejpam-214	47	17	i	i	PRON
ejpam-214	47	18	=	=	NOUN
ejpam-214	47	19	1,2	1,2	NUM
ejpam-214	47	20	,	,	PUNCT
ejpam-214	47	21	·	·	PUNCT
ejpam-214	47	22	·	·	PUNCT
ejpam-214	47	23	·	·	PUNCT
ejpam-214	47	24	,	,	PUNCT
ejpam-214	47	25	m	m	PROPN
ejpam-214	47	26	,	,	PUNCT
ejpam-214	47	27	m	m	VERB
ejpam-214	47	28	∑	∑	PROPN
ejpam-214	47	29	i=1	i=1	PROPN
ejpam-214	47	30	λ∗i	λ∗i	X
ejpam-214	47	31	=	=	SYM
ejpam-214	47	32	1	1	NUM
ejpam-214	47	33	λ∗i	λ∗i	X
ejpam-214	47	34	fi	fi	NOUN
ejpam-214	47	35	(	(	PUNCT
ejpam-214	47	36	x	x	NOUN
ejpam-214	47	37	∗	∗	NOUN
ejpam-214	47	38	)	)	PUNCT
ejpam-214	48	1	=	=	SYM
ejpam-214	48	2	0	0	PUNCT
ejpam-214	49	1	i	i	NOUN
ejpam-214	49	2	=	=	SYM
ejpam-214	49	3	1,2	1,2	NUM
ejpam-214	49	4	,	,	PUNCT
ejpam-214	49	5	·	·	PUNCT
ejpam-214	49	6	·	·	PUNCT
ejpam-214	49	7	·	·	PUNCT
ejpam-214	49	8	,	,	PUNCT
ejpam-214	49	9	m	m	VERB
ejpam-214	49	10	(	(	PUNCT
ejpam-214	49	11	4	4	X
ejpam-214	49	12	)	)	PUNCT
ejpam-214	49	13	let	let	VERB
ejpam-214	49	14	i	i	PRON
ejpam-214	49	15	(	(	PUNCT
ejpam-214	49	16	x∗	x∗	PROPN
ejpam-214	49	17	)	)	PUNCT
ejpam-214	49	18	=	=	SYM
ejpam-214	49	19	�	�	PROPN
ejpam-214	49	20	i|	i|	PROPN
ejpam-214	49	21	fi	fi	NOUN
ejpam-214	49	22	(	(	PUNCT
ejpam-214	49	23	x	x	NOUN
ejpam-214	49	24	∗	∗	NOUN
ejpam-214	49	25	)	)	PUNCT
ejpam-214	49	26	=	=	SYM
ejpam-214	49	27	f(x∗	f(x∗	NOUN
ejpam-214	49	28	)	)	PUNCT
ejpam-214	49	29	is	be	AUX
ejpam-214	49	30	the	the	DET
ejpam-214	49	31	active	active	ADJ
ejpam-214	49	32	set	set	NOUN
ejpam-214	49	33	at	at	ADP
ejpam-214	49	34	point	point	NOUN
ejpam-214	49	35	x∗	x∗	PROPN
ejpam-214	49	36	and	and	CCONJ
ejpam-214	49	37	|i	|i	NOUN
ejpam-214	49	38	(	(	PUNCT
ejpam-214	49	39	x∗)|	x∗)|	NOUN
ejpam-214	50	1	=	=	SYM
ejpam-214	50	2	r	r	NOUN
ejpam-214	50	3	,	,	PUNCT
ejpam-214	50	4	where	where	SCONJ
ejpam-214	50	5	|q|	|q|	NOUN
ejpam-214	50	6	is	be	AUX
ejpam-214	50	7	the	the	DET
ejpam-214	50	8	cardinal	cardinal	ADJ
ejpam-214	50	9	number	number	NOUN
ejpam-214	50	10	of	of	ADP
ejpam-214	50	11	the	the	DET
ejpam-214	50	12	set	set	NOUN
ejpam-214	50	13	q.	q.	PROPN
ejpam-214	50	14	respectively	respectively	ADV
ejpam-214	50	15	,	,	PUNCT
ejpam-214	50	16	∇	∇	X
ejpam-214	50	17	fi	fi	X
ejpam-214	50	18	(	(	PUNCT
ejpam-214	50	19	x	x	NOUN
ejpam-214	50	20	)	)	PUNCT
ejpam-214	51	1	=	=	SYM
ejpam-214	51	2	j	j	PROPN
ejpam-214	51	3	�	�	PROPN
ejpam-214	51	4	fi	fi	PROPN
ejpam-214	51	5	(	(	PUNCT
ejpam-214	51	6	x	x	NOUN
ejpam-214	51	7	)	)	PUNCT
ejpam-214	51	8	�	�	PROPN
ejpam-214	51	9	=	=	SYM
ejpam-214	51	10	�	�	PROPN
ejpam-214	51	11	∇	∇	X
ejpam-214	51	12	fi1	fi1	X
ejpam-214	51	13	(	(	PUNCT
ejpam-214	51	14	x	x	NOUN
ejpam-214	51	15	)	)	PUNCT
ejpam-214	51	16	·	·	PUNCT
ejpam-214	51	17	·	·	PUNCT
ejpam-214	51	18	·	·	PUNCT
ejpam-214	51	19	∇	∇	X
ejpam-214	51	20	fir	fir	NOUN
ejpam-214	51	21	(	(	PUNCT
ejpam-214	51	22	x	x	NOUN
ejpam-214	51	23	)	)	PUNCT
ejpam-214	51	24	�	�	PROPN
ejpam-214	51	25	t	t	PROPN
ejpam-214	51	26	,	,	PUNCT
ejpam-214	51	27	ik	ik	PROPN
ejpam-214	51	28	∈	∈	PROPN
ejpam-214	51	29	i	i	PRON
ejpam-214	51	30	(	(	PUNCT
ejpam-214	51	31	x	x	X
ejpam-214	51	32	)	)	PUNCT
ejpam-214	51	33	k	k	NOUN
ejpam-214	52	1	=	=	SYM
ejpam-214	52	2	1,2	1,2	NUM
ejpam-214	52	3	,	,	PUNCT
ejpam-214	52	4	·	·	PUNCT
ejpam-214	52	5	·	·	PUNCT
ejpam-214	52	6	·	·	PUNCT
ejpam-214	53	1	r	r	X
ejpam-214	53	2	;	;	PUNCT
ejpam-214	53	3	∇	∇	X
ejpam-214	53	4	f	f	X
ejpam-214	53	5	(	(	PUNCT
ejpam-214	53	6	x	x	X
ejpam-214	53	7	)	)	PUNCT
ejpam-214	53	8	=	=	SYM
ejpam-214	53	9	j	j	PROPN
ejpam-214	53	10	�	�	PROPN
ejpam-214	53	11	f	f	PROPN
ejpam-214	53	12	(	(	PUNCT
ejpam-214	53	13	x	x	NOUN
ejpam-214	53	14	)	)	PUNCT
ejpam-214	53	15	�	�	PROPN
ejpam-214	53	16	=	=	SYM
ejpam-214	53	17	�	�	PROPN
ejpam-214	53	18	∇	∇	X
ejpam-214	53	19	f1	f1	PROPN
ejpam-214	53	20	(	(	PUNCT
ejpam-214	53	21	x	x	NOUN
ejpam-214	53	22	)	)	PUNCT
ejpam-214	53	23	·	·	PUNCT
ejpam-214	53	24	·	·	PUNCT
ejpam-214	53	25	·	·	PUNCT
ejpam-214	53	26	∇	∇	X
ejpam-214	53	27	fm	fm	X
ejpam-214	53	28	(	(	PUNCT
ejpam-214	53	29	x	x	X
ejpam-214	53	30	)	)	PUNCT
ejpam-214	53	31	�	�	PROPN
ejpam-214	53	32	t	t	PROPN
ejpam-214	53	33	are	be	AUX
ejpam-214	53	34	their	their	PRON
ejpam-214	53	35	jacobians	jacobian	NOUN
ejpam-214	53	36	.	.	PUNCT
ejpam-214	54	1	∇	∇	PROPN
ejpam-214	54	2	fi	fi	X
ejpam-214	54	3	(	(	PUNCT
ejpam-214	54	4	x	x	NOUN
ejpam-214	54	5	∗	∗	NOUN
ejpam-214	54	6	)	)	PUNCT
ejpam-214	54	7	linear	linear	ADJ
ejpam-214	54	8	independence	independence	NOUN
ejpam-214	54	9	,	,	PUNCT
ejpam-214	54	10	and	and	CCONJ
ejpam-214	54	11	the	the	DET
ejpam-214	54	12	pair	pair	NOUN
ejpam-214	54	13	(	(	PUNCT
ejpam-214	54	14	x∗,λ∗	x∗,λ∗	PROPN
ejpam-214	54	15	)	)	PUNCT
ejpam-214	54	16	satisfies	satisfy	VERB
ejpam-214	54	17	the	the	DET
ejpam-214	54	18	second	second	ADJ
ejpam-214	54	19	order	order	NOUN
ejpam-214	54	20	optimality	optimality	NOUN
ejpam-214	54	21	conditions	condition	NOUN
ejpam-214	54	22	:	:	PUNCT
ejpam-214	55	1	¬	¬	X
ejpam-214	55	2	∇2	∇2	X
ejpam-214	55	3	x	x	SYM
ejpam-214	55	4	x	x	PUNCT
ejpam-214	55	5	l	l	X
ejpam-214	55	6	�	�	PROPN
ejpam-214	55	7	x∗,λ∗	x∗,λ∗	PROPN
ejpam-214	55	8	�	�	PROPN
ejpam-214	56	1	d	d	PROPN
ejpam-214	56	2	,	,	PUNCT
ejpam-214	56	3	d	d	PROPN
ejpam-214	56	4	¶	¶	PROPN
ejpam-214	56	5	≥	≥	PROPN
ejpam-214	56	6	ρ	ρ	PROPN
ejpam-214	56	7	〈	〈	PROPN
ejpam-214	56	8	d	d	PROPN
ejpam-214	56	9	,	,	PUNCT
ejpam-214	56	10	d	d	SYM
ejpam-214	56	11	〉	〉	NOUN
ejpam-214	56	12	,	,	PUNCT
ejpam-214	56	13	ρ	ρ	PROPN
ejpam-214	56	14	>	>	X
ejpam-214	56	15	0,∀d	0,∀d	NUM
ejpam-214	56	16	6=	6=	ADP
ejpam-214	56	17	0	0	NUM
ejpam-214	56	18	:	:	PUNCT
ejpam-214	56	19	∇	∇	X
ejpam-214	56	20	fi	fi	X
ejpam-214	56	21	�	�	PROPN
ejpam-214	56	22	x∗	x∗	PROPN
ejpam-214	56	23	�	�	PROPN
ejpam-214	56	24	t	t	PROPN
ejpam-214	56	25	d	d	PROPN
ejpam-214	56	26	=	=	SYM
ejpam-214	56	27	0	0	NUM
ejpam-214	56	28	(	(	PUNCT
ejpam-214	56	29	5	5	NUM
ejpam-214	56	30	)	)	PUNCT
ejpam-214	56	31	the	the	DET
ejpam-214	56	32	strictly	strictly	ADV
ejpam-214	56	33	complementary	complementary	ADJ
ejpam-214	56	34	condition	condition	NOUN
ejpam-214	56	35	is	be	AUX
ejpam-214	56	36	true	true	ADJ
ejpam-214	56	37	:	:	PUNCT
ejpam-214	56	38	λ∗	λ∗	PROPN
ejpam-214	56	39	∈	∈	PROPN
ejpam-214	56	40	λ	λ	PROPN
ejpam-214	56	41	and	and	CCONJ
ejpam-214	56	42	λ∗i	λ∗i	X
ejpam-214	56	43	>	>	X
ejpam-214	56	44	0	0	NUM
ejpam-214	56	45	,	,	PUNCT
ejpam-214	56	46	i	i	PRON
ejpam-214	56	47	∈	∈	VERB
ejpam-214	56	48	i	i	PRON
ejpam-214	56	49	(	(	PUNCT
ejpam-214	56	50	x∗	x∗	PROPN
ejpam-214	56	51	)	)	PUNCT
ejpam-214	56	52	.	.	PUNCT
ejpam-214	57	1	then	then	ADV
ejpam-214	57	2	the	the	DET
ejpam-214	57	3	max	max	PROPN
ejpam-214	57	4	function	function	NOUN
ejpam-214	57	5	can	can	AUX
ejpam-214	57	6	be	be	AUX
ejpam-214	57	7	obtained	obtain	VERB
ejpam-214	57	8	as	as	ADP
ejpam-214	57	9	f	f	PROPN
ejpam-214	57	10	(	(	PUNCT
ejpam-214	57	11	x	x	X
ejpam-214	57	12	)	)	PUNCT
ejpam-214	58	1	=	=	NOUN
ejpam-214	58	2	max	max	NOUN
ejpam-214	58	3	λ∈λ	λ∈λ	PROPN
ejpam-214	58	4	l	l	PROPN
ejpam-214	58	5	(	(	PUNCT
ejpam-214	58	6	x	x	X
ejpam-214	58	7	,	,	PUNCT
ejpam-214	58	8	λ	λ	PROPN
ejpam-214	58	9	)	)	PUNCT
ejpam-214	58	10	,	,	PUNCT
ejpam-214	58	11	x	x	PUNCT
ejpam-214	58	12	∈	∈	NOUN
ejpam-214	58	13	x	x	SYM
ejpam-214	58	14	(	(	PUNCT
ejpam-214	58	15	6	6	NUM
ejpam-214	58	16	)	)	PUNCT
ejpam-214	58	17	unfortunately	unfortunately	ADV
ejpam-214	58	18	,	,	PUNCT
ejpam-214	58	19	the	the	DET
ejpam-214	58	20	above	above	ADJ
ejpam-214	58	21	maximization	maximization	NOUN
ejpam-214	58	22	rarely	rarely	ADV
ejpam-214	58	23	has	have	VERB
ejpam-214	58	24	an	an	DET
ejpam-214	58	25	explicit	explicit	ADJ
ejpam-214	58	26	solution	solution	NOUN
ejpam-214	58	27	.	.	PUNCT
ejpam-214	59	1	therefore	therefore	ADV
ejpam-214	59	2	the	the	DET
ejpam-214	59	3	regularization	regularization	NOUN
ejpam-214	59	4	methods	method	NOUN
ejpam-214	59	5	add	add	VERB
ejpam-214	59	6	some	some	DET
ejpam-214	59	7	terms	term	NOUN
ejpam-214	59	8	that	that	PRON
ejpam-214	59	9	are	be	AUX
ejpam-214	59	10	called	call	VERB
ejpam-214	59	11	regularization	regularization	NOUN
ejpam-214	59	12	functions	function	NOUN
ejpam-214	59	13	lp	lp	NOUN
ejpam-214	59	14	(	(	PUNCT
ejpam-214	59	15	x	x	NOUN
ejpam-214	59	16	,	,	PUNCT
ejpam-214	59	17	λ	λ	NOUN
ejpam-214	59	18	)	)	PUNCT
ejpam-214	59	19	=	=	SYM
ejpam-214	59	20	l	l	NOUN
ejpam-214	59	21	(	(	PUNCT
ejpam-214	59	22	x	x	NOUN
ejpam-214	59	23	,	,	PUNCT
ejpam-214	59	24	λ	λ	NOUN
ejpam-214	59	25	)	)	PUNCT
ejpam-214	60	1	+	+	CCONJ
ejpam-214	60	2	1	1	NUM
ejpam-214	60	3	p	p	NOUN
ejpam-214	60	4	r	r	NOUN
ejpam-214	60	5	�	�	PROPN
ejpam-214	60	6	λ;µ	λ;µ	X
ejpam-214	60	7	�	�	PROPN
ejpam-214	60	8	(	(	PUNCT
ejpam-214	60	9	7	7	NUM
ejpam-214	60	10	)	)	PUNCT
ejpam-214	60	11	where	where	SCONJ
ejpam-214	60	12	p	p	NOUN
ejpam-214	60	13	>	>	X
ejpam-214	60	14	0	0	NUM
ejpam-214	60	15	is	be	AUX
ejpam-214	60	16	a	a	DET
ejpam-214	60	17	control	control	NOUN
ejpam-214	60	18	parameter	parameter	NOUN
ejpam-214	60	19	,	,	PUNCT
ejpam-214	60	20	r	r	NOUN
ejpam-214	60	21	is	be	AUX
ejpam-214	60	22	a	a	DET
ejpam-214	60	23	regularization	regularization	NOUN
ejpam-214	60	24	function	function	NOUN
ejpam-214	60	25	,	,	PUNCT
ejpam-214	60	26	and	and	CCONJ
ejpam-214	60	27	µ	µ	NOUN
ejpam-214	60	28	is	be	AUX
ejpam-214	60	29	an	an	DET
ejpam-214	60	30	optional	optional	ADJ
ejpam-214	60	31	parameter	parameter	NOUN
ejpam-214	60	32	vector	vector	NOUN
ejpam-214	60	33	of	of	ADP
ejpam-214	60	34	r.	r.	PROPN
ejpam-214	60	35	then	then	ADV
ejpam-214	60	36	,	,	PUNCT
ejpam-214	60	37	by	by	ADP
ejpam-214	60	38	carefully	carefully	ADV
ejpam-214	60	39	choosing	choose	VERB
ejpam-214	60	40	the	the	DET
ejpam-214	60	41	function	function	NOUN
ejpam-214	60	42	r	r	NOUN
ejpam-214	60	43	,	,	PUNCT
ejpam-214	60	44	maximizing	maximize	VERB
ejpam-214	60	45	the	the	DET
ejpam-214	60	46	lp(x	lp(x	PUNCT
ejpam-214	60	47	,	,	PUNCT
ejpam-214	60	48	λ	λ	X
ejpam-214	60	49	)	)	PUNCT
ejpam-214	60	50	could	could	AUX
ejpam-214	60	51	result	result	VERB
ejpam-214	60	52	in	in	ADP
ejpam-214	60	53	a	a	DET
ejpam-214	60	54	smooth	smooth	ADJ
ejpam-214	60	55	approximation	approximation	NOUN
ejpam-214	60	56	function	function	NOUN
ejpam-214	60	57	.	.	PUNCT
ejpam-214	61	1	when	when	SCONJ
ejpam-214	61	2	r	r	NOUN
ejpam-214	61	3	�	�	PROPN
ejpam-214	61	4	λ,µ	λ,µ	PROPN
ejpam-214	61	5	�	�	PROPN
ejpam-214	61	6	=	=	PUNCT
ejpam-214	61	7	m	m	VERB
ejpam-214	61	8	∑	∑	VERB
ejpam-214	61	9	i=1	i=1	PROPN
ejpam-214	61	10	λi	λi	INTJ
ejpam-214	61	11	ln	ln	NOUN
ejpam-214	61	12	λi	λi	ADP
ejpam-214	61	13	µi	µi	PROPN
ejpam-214	61	14	,	,	PUNCT
ejpam-214	61	15	we	we	PRON
ejpam-214	61	16	have	have	VERB
ejpam-214	61	17	the	the	DET
ejpam-214	61	18	following	follow	VERB
ejpam-214	61	19	cross	cross	ADJ
ejpam-214	61	20	-	-	ADJ
ejpam-214	61	21	entropic	entropic	ADJ
ejpam-214	61	22	regularization	regularization	NOUN
ejpam-214	61	23	formula	formula	NOUN
ejpam-214	61	24	:	:	PUNCT
ejpam-214	61	25	fp	fp	PROPN
ejpam-214	61	26	�	�	PROPN
ejpam-214	61	27	x	x	PROPN
ejpam-214	61	28	,	,	PUNCT
ejpam-214	61	29	µ	µ	X
ejpam-214	61	30	�	�	PROPN
ejpam-214	61	31	≡max	≡max	PROPN
ejpam-214	61	32	λ∈λ	λ∈λ	NOUN
ejpam-214	61	33	(	(	PUNCT
ejpam-214	61	34	l	l	X
ejpam-214	61	35	(	(	PUNCT
ejpam-214	61	36	x	x	SYM
ejpam-214	61	37	,	,	PUNCT
ejpam-214	61	38	λ)−	λ)−	PROPN
ejpam-214	61	39	1	1	NUM
ejpam-214	61	40	p	p	NOUN
ejpam-214	61	41	r	r	NOUN
ejpam-214	61	42	�	�	PROPN
ejpam-214	61	43	λ;µ	λ;µ	X
ejpam-214	61	44	�	�	PROPN
ejpam-214	61	45	=	=	PUNCT
ejpam-214	61	46	m	m	PROPN
ejpam-214	61	47	∑	∑	PUNCT
ejpam-214	61	48	i=1	i=1	PROPN
ejpam-214	61	49	λi	λi	INTJ
ejpam-214	61	50	fi	fi	NOUN
ejpam-214	61	51	(	(	PUNCT
ejpam-214	61	52	x)−	x)−	PROPN
ejpam-214	61	53	1	1	NUM
ejpam-214	61	54	p	p	NOUN
ejpam-214	61	55	m	m	PROPN
ejpam-214	61	56	∑	∑	VERB
ejpam-214	61	57	i=1	i=1	PROPN
ejpam-214	62	1	λi	λi	INTJ
ejpam-214	62	2	ln	ln	NOUN
ejpam-214	62	3	λi	λi	INTJ
ejpam-214	62	4	µi	µi	PROPN
ejpam-214	62	5	)	)	PUNCT
ejpam-214	62	6	(	(	PUNCT
ejpam-214	62	7	8)	8)	NUM
ejpam-214	62	8	where	where	SCONJ
ejpam-214	62	9	µ	µ	NOUN
ejpam-214	62	10	is	be	AUX
ejpam-214	62	11	an	an	DET
ejpam-214	62	12	additional	additional	ADJ
ejpam-214	62	13	control	control	NOUN
ejpam-214	62	14	vector	vector	NOUN
ejpam-214	62	15	representing	represent	VERB
ejpam-214	62	16	some	some	PRON
ejpam-214	62	17	known	know	VERB
ejpam-214	62	18	as	as	ADP
ejpam-214	62	19	priori	priori	ADJ
ejpam-214	62	20	information	information	NOUN
ejpam-214	62	21	(	(	PUNCT
ejpam-214	62	22	distribution	distribution	NOUN
ejpam-214	62	23	)	)	PUNCT
ejpam-214	62	24	.	.	PUNCT
ejpam-214	63	1	l.	l.	PROPN
ejpam-214	63	2	zhang	zhang	PROPN
ejpam-214	63	3	,	,	PUNCT
ejpam-214	63	4	j.	j.	PROPN
ejpam-214	63	5	li	li	PROPN
ejpam-214	63	6	,	,	PUNCT
ejpam-214	63	7	x.	x.	PROPN
ejpam-214	63	8	li	li	PROPN
ejpam-214	63	9	/	/	SYM
ejpam-214	63	10	eur	eur	PROPN
ejpam-214	63	11	.	.	PUNCT
ejpam-214	64	1	j.	j.	PROPN
ejpam-214	64	2	pure	pure	PROPN
ejpam-214	64	3	appl	appl	PROPN
ejpam-214	64	4	.	.	PROPN
ejpam-214	64	5	math	math	PROPN
ejpam-214	64	6	,	,	PUNCT
ejpam-214	64	7	3	3	NUM
ejpam-214	64	8	(	(	PUNCT
ejpam-214	64	9	2010	2010	NUM
ejpam-214	64	10	)	)	PUNCT
ejpam-214	64	11	,	,	PUNCT
ejpam-214	64	12	98	98	NUM
ejpam-214	64	13	-	-	SYM
ejpam-214	64	14	106	106	NUM
ejpam-214	64	15	101	101	NUM
ejpam-214	64	16	a	a	DET
ejpam-214	64	17	simple	simple	ADJ
ejpam-214	64	18	calculation	calculation	NOUN
ejpam-214	64	19	results	result	NOUN
ejpam-214	64	20	in	in	ADP
ejpam-214	64	21	the	the	DET
ejpam-214	64	22	following	follow	VERB
ejpam-214	64	23	solution	solution	NOUN
ejpam-214	64	24	:	:	PUNCT
ejpam-214	64	25	λ∗i	λ∗i	X
ejpam-214	64	26	=	=	SYM
ejpam-214	64	27	µi	µi	PROPN
ejpam-214	64	28	exp	exp	PRON
ejpam-214	64	29	�	�	PROPN
ejpam-214	64	30	p	p	PROPN
ejpam-214	65	1	fi	fi	NOUN
ejpam-214	66	1	(	(	PUNCT
ejpam-214	66	2	x	x	NOUN
ejpam-214	66	3	)	)	PUNCT
ejpam-214	66	4	�	�	PROPN
ejpam-214	66	5	z	z	PROPN
ejpam-214	66	6	,	,	PUNCT
ejpam-214	66	7	i	i	PRON
ejpam-214	66	8	=	=	SYM
ejpam-214	66	9	1,2	1,2	NUM
ejpam-214	66	10	,	,	PUNCT
ejpam-214	66	11	·	·	PUNCT
ejpam-214	66	12	·	·	PUNCT
ejpam-214	66	13	·	·	PUNCT
ejpam-214	66	14	,	,	PUNCT
ejpam-214	66	15	m	m	VERB
ejpam-214	66	16	(	(	PUNCT
ejpam-214	66	17	9	9	NUM
ejpam-214	66	18	)	)	PUNCT
ejpam-214	66	19	where	where	SCONJ
ejpam-214	66	20	z	z	NOUN
ejpam-214	66	21	=	=	X
ejpam-214	66	22	m	m	VERB
ejpam-214	66	23	∑	∑	PUNCT
ejpam-214	66	24	i=1	i=1	PROPN
ejpam-214	66	25	µi	µi	PROPN
ejpam-214	66	26	exp	exp	NOUN
ejpam-214	66	27	�	�	PROPN
ejpam-214	66	28	p	p	PROPN
ejpam-214	66	29	fk	fk	INTJ
ejpam-214	66	30	(	(	PUNCT
ejpam-214	66	31	x	x	NOUN
ejpam-214	66	32	)	)	PUNCT
ejpam-214	66	33	�	�	PROPN
ejpam-214	66	34	.	.	PUNCT
ejpam-214	67	1	substituting	substitute	VERB
ejpam-214	67	2	(	(	PUNCT
ejpam-214	67	3	9	9	NUM
ejpam-214	67	4	)	)	PUNCT
ejpam-214	67	5	into	into	ADP
ejpam-214	67	6	(	(	PUNCT
ejpam-214	67	7	8)	8)	NUM
ejpam-214	67	8	,	,	PUNCT
ejpam-214	67	9	we	we	PRON
ejpam-214	67	10	have	have	VERB
ejpam-214	67	11	the	the	DET
ejpam-214	67	12	smooth	smooth	ADJ
ejpam-214	67	13	approximation	approximation	NOUN
ejpam-214	67	14	function	function	NOUN
ejpam-214	67	15	of	of	ADP
ejpam-214	67	16	multiplier	multipli	ADJ
ejpam-214	67	17	(	(	PUNCT
ejpam-214	67	18	3	3	NUM
ejpam-214	67	19	):	):	PUNCT
ejpam-214	68	1	fp	fp	PROPN
ejpam-214	68	2	�	�	PROPN
ejpam-214	68	3	x	x	PROPN
ejpam-214	68	4	,	,	PUNCT
ejpam-214	68	5	µ	µ	X
ejpam-214	68	6	�	�	X
ejpam-214	68	7	=	=	SYM
ejpam-214	68	8	1	1	NUM
ejpam-214	68	9	p	p	NOUN
ejpam-214	68	10	ln	ln	NOUN
ejpam-214	68	11	m	m	VERB
ejpam-214	68	12	∑	∑	PROPN
ejpam-214	68	13	i=1	i=1	PROPN
ejpam-214	68	14	µi	µi	PROPN
ejpam-214	68	15	exp	exp	DET
ejpam-214	68	16	�	�	PROPN
ejpam-214	68	17	p	p	PROPN
ejpam-214	68	18	fi	fi	NOUN
ejpam-214	68	19	(	(	PUNCT
ejpam-214	68	20	x	x	NOUN
ejpam-214	68	21	)	)	PUNCT
ejpam-214	68	22	�	�	PROPN
ejpam-214	68	23	.	.	PUNCT
ejpam-214	69	1	the	the	DET
ejpam-214	69	2	reason	reason	NOUN
ejpam-214	69	3	for	for	ADP
ejpam-214	69	4	the	the	DET
ejpam-214	69	5	name	name	NOUN
ejpam-214	69	6	of	of	ADP
ejpam-214	69	7	the	the	DET
ejpam-214	69	8	smooth	smooth	ADJ
ejpam-214	69	9	approximation	approximation	NOUN
ejpam-214	69	10	function	function	NOUN
ejpam-214	69	11	of	of	ADP
ejpam-214	69	12	multiplier	multipli	ADJ
ejpam-214	69	13	is	be	AUX
ejpam-214	69	14	that	that	SCONJ
ejpam-214	69	15	if	if	SCONJ
ejpam-214	69	16	the	the	DET
ejpam-214	69	17	pair	pair	NOUN
ejpam-214	69	18	(	(	PUNCT
ejpam-214	69	19	x	x	X
ejpam-214	69	20	l	l	NOUN
ejpam-214	69	21	,	,	PUNCT
ejpam-214	69	22	µl	µl	NOUN
ejpam-214	69	23	)	)	PUNCT
ejpam-214	69	24	have	have	AUX
ejpam-214	69	25	been	be	AUX
ejpam-214	69	26	found	find	VERB
ejpam-214	69	27	already	already	ADV
ejpam-214	69	28	,	,	PUNCT
ejpam-214	69	29	we	we	PRON
ejpam-214	69	30	find	find	VERB
ejpam-214	69	31	the	the	DET
ejpam-214	69	32	next	next	ADJ
ejpam-214	69	33	approximation	approximation	NOUN
ejpam-214	69	34	(	(	PUNCT
ejpam-214	69	35	x	x	SYM
ejpam-214	69	36	l+1,µl+1	l+1,µl+1	PROPN
ejpam-214	69	37	)	)	PUNCT
ejpam-214	69	38	by	by	ADP
ejpam-214	69	39	the	the	DET
ejpam-214	69	40	following	follow	VERB
ejpam-214	69	41	formulas	formula	NOUN
ejpam-214	69	42	:	:	PUNCT
ejpam-214	69	43	x	x	X
ejpam-214	69	44	l+1	l+1	PUNCT
ejpam-214	69	45	=	=	PUNCT
ejpam-214	69	46	arg	arg	NOUN
ejpam-214	69	47	min	min	NOUN
ejpam-214	69	48	x	x	INTJ
ejpam-214	69	49	¦	¦	PROPN
ejpam-214	69	50	fp	fp	PROPN
ejpam-214	69	51	�	�	PROPN
ejpam-214	69	52	x	x	SYM
ejpam-214	69	53	,	,	PUNCT
ejpam-214	69	54	µl	µl	ADP
ejpam-214	69	55	�	�	NOUN
ejpam-214	69	56	©	©	NOUN
ejpam-214	69	57	(	(	PUNCT
ejpam-214	69	58	10	10	NUM
ejpam-214	69	59	)	)	PUNCT
ejpam-214	69	60	µl+1	µl+1	PROPN
ejpam-214	70	1	i	i	PRON
ejpam-214	70	2	=	=	PUNCT
ejpam-214	70	3	µl	µl	ADP
ejpam-214	70	4	i	i	PRON
ejpam-214	70	5	exp	exp	NOUN
ejpam-214	70	6	�	�	PROPN
ejpam-214	70	7	p	p	PROPN
ejpam-214	70	8	fi	fi	NOUN
ejpam-214	70	9	(	(	PUNCT
ejpam-214	70	10	x	x	NOUN
ejpam-214	70	11	)	)	PUNCT
ejpam-214	70	12	�	�	PROPN
ejpam-214	70	13	m	m	VERB
ejpam-214	70	14	∑	∑	ADV
ejpam-214	70	15	k=1	k=1	X
ejpam-214	70	16	µl	µl	ADP
ejpam-214	70	17	k	k	PROPN
ejpam-214	70	18	exp	exp	X
ejpam-214	70	19	�	�	PROPN
ejpam-214	70	20	p	p	PROPN
ejpam-214	70	21	fk	fk	INTJ
ejpam-214	70	22	(	(	PUNCT
ejpam-214	70	23	x	x	NOUN
ejpam-214	70	24	)	)	PUNCT
ejpam-214	70	25	�	�	PROPN
ejpam-214	70	26	,	,	PUNCT
ejpam-214	70	27	i	i	NOUN
ejpam-214	70	28	=	=	SYM
ejpam-214	70	29	1,2	1,2	NUM
ejpam-214	70	30	,	,	PUNCT
ejpam-214	70	31	·	·	PUNCT
ejpam-214	70	32	·	·	PUNCT
ejpam-214	70	33	·	·	PUNCT
ejpam-214	70	34	,	,	PUNCT
ejpam-214	70	35	m	m	VERB
ejpam-214	70	36	(	(	PUNCT
ejpam-214	70	37	11	11	NUM
ejpam-214	70	38	)	)	PUNCT
ejpam-214	70	39	so	so	ADV
ejpam-214	70	40	µ	µ	NOUN
ejpam-214	70	41	is	be	AUX
ejpam-214	70	42	the	the	DET
ejpam-214	70	43	lagrangian	lagrangian	ADJ
ejpam-214	70	44	multiplier	multiplier	NOUN
ejpam-214	70	45	in	in	ADP
ejpam-214	70	46	practice	practice	NOUN
ejpam-214	70	47	,	,	PUNCT
ejpam-214	70	48	we	we	PRON
ejpam-214	70	49	can	can	AUX
ejpam-214	70	50	just	just	ADV
ejpam-214	70	51	denote	denote	VERB
ejpam-214	70	52	the	the	DET
ejpam-214	70	53	smooth	smooth	ADJ
ejpam-214	70	54	approximation	approximation	NOUN
ejpam-214	70	55	function	function	NOUN
ejpam-214	70	56	of	of	ADP
ejpam-214	70	57	multiplier	multipli	ADJ
ejpam-214	70	58	as	as	ADP
ejpam-214	70	59	fp	fp	PROPN
ejpam-214	70	60	(	(	PUNCT
ejpam-214	70	61	x	x	INTJ
ejpam-214	70	62	,	,	PUNCT
ejpam-214	70	63	λ	λ	NOUN
ejpam-214	70	64	)	)	PUNCT
ejpam-214	70	65	=	=	SYM
ejpam-214	71	1	1	1	NUM
ejpam-214	71	2	p	p	NOUN
ejpam-214	71	3	ln	ln	NOUN
ejpam-214	71	4	m	m	VERB
ejpam-214	71	5	∑	∑	PROPN
ejpam-214	71	6	i=1	i=1	PROPN
ejpam-214	71	7	λi	λi	INTJ
ejpam-214	71	8	exp	exp	PRON
ejpam-214	71	9	�	�	PROPN
ejpam-214	71	10	p	p	PROPN
ejpam-214	71	11	fi	fi	NOUN
ejpam-214	71	12	(	(	PUNCT
ejpam-214	71	13	x	x	NOUN
ejpam-214	71	14	)	)	PUNCT
ejpam-214	71	15	�	�	PROPN
ejpam-214	71	16	.	.	PUNCT
ejpam-214	72	1	3	3	X
ejpam-214	72	2	.	.	X
ejpam-214	72	3	main	main	ADJ
ejpam-214	72	4	results	result	NOUN
ejpam-214	72	5	3.1	3.1	NUM
ejpam-214	72	6	.	.	PUNCT
ejpam-214	73	1	first	first	ADJ
ejpam-214	73	2	order	order	NOUN
ejpam-214	73	3	information	information	NOUN
ejpam-214	73	4	:	:	PUNCT
ejpam-214	73	5	subgradient	subgradient	NOUN
ejpam-214	73	6	it	it	PRON
ejpam-214	73	7	is	be	AUX
ejpam-214	73	8	well	well	ADV
ejpam-214	73	9	known	know	VERB
ejpam-214	73	10	that	that	SCONJ
ejpam-214	73	11	the	the	DET
ejpam-214	73	12	max	max	PROPN
ejpam-214	73	13	function	function	PROPN
ejpam-214	73	14	f(x	f(x	PROPN
ejpam-214	73	15	)	)	PUNCT
ejpam-214	73	16	has	have	VERB
ejpam-214	73	17	discontinuous	discontinuous	ADJ
ejpam-214	73	18	first	first	ADJ
ejpam-214	73	19	derivatives	derivative	NOUN
ejpam-214	73	20	at	at	ADP
ejpam-214	73	21	points	point	NOUN
ejpam-214	73	22	where	where	SCONJ
ejpam-214	73	23	two	two	NUM
ejpam-214	73	24	or	or	CCONJ
ejpam-214	73	25	more	more	ADJ
ejpam-214	73	26	of	of	ADP
ejpam-214	73	27	the	the	DET
ejpam-214	73	28	components	component	NOUN
ejpam-214	73	29	fi(x	fi(x	NUM
ejpam-214	73	30	)	)	PUNCT
ejpam-214	73	31	are	be	AUX
ejpam-214	73	32	equal	equal	ADJ
ejpam-214	73	33	to	to	ADP
ejpam-214	73	34	f(x	f(x	PROPN
ejpam-214	73	35	)	)	PUNCT
ejpam-214	73	36	even	even	ADV
ejpam-214	73	37	if	if	SCONJ
ejpam-214	73	38	each	each	DET
ejpam-214	73	39	fi(x	fi(x	NUM
ejpam-214	73	40	)	)	PUNCT
ejpam-214	73	41	is	be	AUX
ejpam-214	73	42	smooth	smooth	ADJ
ejpam-214	73	43	with	with	ADP
ejpam-214	73	44	any	any	DET
ejpam-214	73	45	order	order	NOUN
ejpam-214	73	46	.	.	PUNCT
ejpam-214	74	1	so	so	ADV
ejpam-214	74	2	we	we	PRON
ejpam-214	74	3	first	first	ADV
ejpam-214	74	4	analyze	analyze	VERB
ejpam-214	74	5	whether	whether	SCONJ
ejpam-214	74	6	the	the	DET
ejpam-214	74	7	approximation	approximation	NOUN
ejpam-214	74	8	function	function	NOUN
ejpam-214	74	9	(	(	PUNCT
ejpam-214	74	10	3	3	X
ejpam-214	74	11	)	)	PUNCT
ejpam-214	74	12	could	could	AUX
ejpam-214	74	13	yield	yield	VERB
ejpam-214	74	14	the	the	DET
ejpam-214	74	15	first	first	ADJ
ejpam-214	74	16	order	order	NOUN
ejpam-214	74	17	information	information	NOUN
ejpam-214	74	18	on	on	ADP
ejpam-214	74	19	the	the	DET
ejpam-214	74	20	behavior	behavior	NOUN
ejpam-214	74	21	of	of	ADP
ejpam-214	74	22	f(x	f(x	PROPN
ejpam-214	74	23	)	)	PUNCT
ejpam-214	74	24	.	.	PUNCT
ejpam-214	75	1	the	the	DET
ejpam-214	75	2	results	result	NOUN
ejpam-214	75	3	reveal	reveal	VERB
ejpam-214	75	4	that	that	SCONJ
ejpam-214	75	5	for	for	ADP
ejpam-214	75	6	the	the	DET
ejpam-214	75	7	convex	convex	ADJ
ejpam-214	75	8	situation	situation	NOUN
ejpam-214	75	9	the	the	DET
ejpam-214	75	10	subgradients	subgradient	NOUN
ejpam-214	75	11	of	of	ADP
ejpam-214	75	12	f(x	f(x	PROPN
ejpam-214	75	13	)	)	PUNCT
ejpam-214	75	14	can	can	AUX
ejpam-214	75	15	be	be	AUX
ejpam-214	75	16	obtained	obtain	VERB
ejpam-214	75	17	from	from	ADP
ejpam-214	75	18	the	the	DET
ejpam-214	75	19	gradients	gradient	NOUN
ejpam-214	75	20	of	of	ADP
ejpam-214	75	21	smooth	smooth	ADJ
ejpam-214	75	22	approximation	approximation	NOUN
ejpam-214	75	23	function	function	NOUN
ejpam-214	75	24	fp(x	fp(x	PROPN
ejpam-214	75	25	)	)	PUNCT
ejpam-214	75	26	.	.	PUNCT
ejpam-214	76	1	the	the	DET
ejpam-214	76	2	first	first	ADJ
ejpam-214	76	3	order	order	NOUN
ejpam-214	76	4	behavior	behavior	NOUN
ejpam-214	76	5	of	of	ADP
ejpam-214	76	6	convex	convex	PROPN
ejpam-214	76	7	non	non	ADJ
ejpam-214	76	8	-	-	ADJ
ejpam-214	76	9	smooth	smooth	ADJ
ejpam-214	76	10	function	function	NOUN
ejpam-214	76	11	around	around	ADP
ejpam-214	76	12	a	a	DET
ejpam-214	76	13	point	point	NOUN
ejpam-214	76	14	x	x	PUNCT
ejpam-214	76	15	is	be	AUX
ejpam-214	76	16	reflected	reflect	VERB
ejpam-214	76	17	by	by	ADP
ejpam-214	76	18	the	the	DET
ejpam-214	76	19	the	the	DET
ejpam-214	76	20	concepts	concept	NOUN
ejpam-214	76	21	of	of	ADP
ejpam-214	76	22	subgradients	subgradient	NOUN
ejpam-214	76	23	and	and	CCONJ
ejpam-214	76	24	subdifferential	subdifferential	ADJ
ejpam-214	76	25	(	(	PUNCT
ejpam-214	76	26	[	[	X
ejpam-214	76	27	17	17	NUM
ejpam-214	76	28	]	]	PUNCT
ejpam-214	76	29	p214	p214	NUM
ejpam-214	76	30	)	)	PUNCT
ejpam-214	76	31	.	.	PUNCT
ejpam-214	77	1	definition	definition	NOUN
ejpam-214	77	2	1	1	NUM
ejpam-214	77	3	.	.	PUNCT
ejpam-214	78	1	a	a	DET
ejpam-214	78	2	vector	vector	NOUN
ejpam-214	78	3	ω	ω	PROPN
ejpam-214	78	4	is	be	AUX
ejpam-214	78	5	said	say	VERB
ejpam-214	78	6	to	to	PART
ejpam-214	78	7	be	be	AUX
ejpam-214	78	8	a	a	DET
ejpam-214	78	9	subgradient	subgradient	NOUN
ejpam-214	78	10	of	of	ADP
ejpam-214	78	11	a	a	DET
ejpam-214	78	12	convex	convex	NOUN
ejpam-214	78	13	function	function	NOUN
ejpam-214	78	14	at	at	ADP
ejpam-214	78	15	a	a	DET
ejpam-214	78	16	point	point	NOUN
ejpam-214	78	17	x	x	PUNCT
ejpam-214	78	18	if	if	SCONJ
ejpam-214	78	19	f	f	PROPN
ejpam-214	78	20	(	(	PUNCT
ejpam-214	78	21	z)−	z)−	PROPN
ejpam-214	78	22	f	f	PROPN
ejpam-214	78	23	(	(	PUNCT
ejpam-214	78	24	x)¾	x)¾	PROPN
ejpam-214	78	25	〈	〈	PROPN
ejpam-214	78	26	ω	ω	PROPN
ejpam-214	78	27	,	,	PUNCT
ejpam-214	78	28	z	z	NOUN
ejpam-214	78	29	−	−	NOUN
ejpam-214	78	30	x	x	SYM
ejpam-214	78	31	〉	〉	NOUN
ejpam-214	78	32	∀z	∀z	X
ejpam-214	78	33	∈	∈	NOUN
ejpam-214	78	34	x	x	SYM
ejpam-214	78	35	(	(	PUNCT
ejpam-214	78	36	12	12	NUM
ejpam-214	78	37	)	)	PUNCT
ejpam-214	78	38	the	the	DET
ejpam-214	78	39	set	set	NOUN
ejpam-214	78	40	of	of	ADP
ejpam-214	78	41	all	all	DET
ejpam-214	78	42	subgradients	subgradient	NOUN
ejpam-214	78	43	of	of	ADP
ejpam-214	78	44	f	f	PROPN
ejpam-214	78	45	at	at	ADP
ejpam-214	78	46	x	x	PROPN
ejpam-214	78	47	is	be	AUX
ejpam-214	78	48	called	call	VERB
ejpam-214	78	49	the	the	DET
ejpam-214	78	50	subdifferential	subdifferential	NOUN
ejpam-214	78	51	of	of	ADP
ejpam-214	78	52	f	f	PROPN
ejpam-214	78	53	at	at	ADP
ejpam-214	78	54	x	x	PUNCT
ejpam-214	78	55	and	and	CCONJ
ejpam-214	78	56	is	be	AUX
ejpam-214	78	57	denoted	denote	VERB
ejpam-214	78	58	by	by	ADP
ejpam-214	78	59	∂	∂	NUM
ejpam-214	78	60	f	f	PROPN
ejpam-214	78	61	(	(	PUNCT
ejpam-214	78	62	x	x	NOUN
ejpam-214	78	63	)	)	PUNCT
ejpam-214	78	64	,	,	PUNCT
ejpam-214	78	65	i.e.	i.e.	X
ejpam-214	78	66	∂	∂	ADJ
ejpam-214	78	67	f	f	X
ejpam-214	78	68	(	(	PUNCT
ejpam-214	78	69	x	x	NOUN
ejpam-214	78	70	)	)	PUNCT
ejpam-214	78	71	:	:	PUNCT
ejpam-214	78	72	=	=	PUNCT
ejpam-214	78	73	�	�	PROPN
ejpam-214	78	74	ω|	ω|	PROPN
ejpam-214	78	75	f	f	X
ejpam-214	79	1	(	(	PUNCT
ejpam-214	79	2	z)−	z)−	PROPN
ejpam-214	79	3	f	f	PROPN
ejpam-214	79	4	(	(	PUNCT
ejpam-214	79	5	x)¾	x)¾	PROPN
ejpam-214	79	6	〈	〈	PROPN
ejpam-214	79	7	ω	ω	PROPN
ejpam-214	79	8	,	,	PUNCT
ejpam-214	79	9	z	z	NOUN
ejpam-214	79	10	−	−	NOUN
ejpam-214	79	11	x	x	SYM
ejpam-214	79	12	〉	〉	NOUN
ejpam-214	79	13	∀z	∀z	X
ejpam-214	79	14	∈	∈	NOUN
ejpam-214	79	15	x	x	SYM
ejpam-214	79	16	(	(	PUNCT
ejpam-214	79	17	13	13	NUM
ejpam-214	79	18	)	)	PUNCT
ejpam-214	79	19	theorem	theorem	NOUN
ejpam-214	79	20	1	1	NUM
ejpam-214	79	21	.	.	PUNCT
ejpam-214	80	1	for	for	ADP
ejpam-214	80	2	the	the	DET
ejpam-214	80	3	max	max	PROPN
ejpam-214	80	4	function	function	PROPN
ejpam-214	80	5	f(x	f(x	PROPN
ejpam-214	80	6	)	)	PUNCT
ejpam-214	80	7	and	and	CCONJ
ejpam-214	80	8	the	the	DET
ejpam-214	80	9	smooth	smooth	ADJ
ejpam-214	80	10	approximation	approximation	NOUN
ejpam-214	80	11	function	function	NOUN
ejpam-214	80	12	of	of	ADP
ejpam-214	80	13	multipliers	multiplier	NOUN
ejpam-214	80	14	fp(x	fp(x	PUNCT
ejpam-214	80	15	,	,	PUNCT
ejpam-214	80	16	λ	λ	PROPN
ejpam-214	80	17	)	)	PUNCT
ejpam-214	80	18	,	,	PUNCT
ejpam-214	80	19	the	the	DET
ejpam-214	80	20	following	follow	VERB
ejpam-214	80	21	statements	statement	NOUN
ejpam-214	80	22	are	be	AUX
ejpam-214	80	23	equivalent	equivalent	ADJ
ejpam-214	80	24	:	:	PUNCT
ejpam-214	80	25	l.	l.	PROPN
ejpam-214	80	26	zhang	zhang	PROPN
ejpam-214	80	27	,	,	PUNCT
ejpam-214	80	28	j.	j.	PROPN
ejpam-214	80	29	li	li	PROPN
ejpam-214	80	30	,	,	PUNCT
ejpam-214	80	31	x.	x.	PROPN
ejpam-214	80	32	li	li	PROPN
ejpam-214	80	33	/	/	SYM
ejpam-214	80	34	eur	eur	PROPN
ejpam-214	80	35	.	.	PUNCT
ejpam-214	81	1	j.	j.	PROPN
ejpam-214	81	2	pure	pure	PROPN
ejpam-214	81	3	appl	appl	PROPN
ejpam-214	81	4	.	.	PROPN
ejpam-214	81	5	math	math	PROPN
ejpam-214	81	6	,	,	PUNCT
ejpam-214	81	7	3	3	NUM
ejpam-214	81	8	(	(	PUNCT
ejpam-214	81	9	2010	2010	NUM
ejpam-214	81	10	)	)	PUNCT
ejpam-214	81	11	,	,	PUNCT
ejpam-214	81	12	98	98	NUM
ejpam-214	81	13	-	-	SYM
ejpam-214	81	14	106	106	NUM
ejpam-214	81	15	102	102	NUM
ejpam-214	81	16	i	i	NOUN
ejpam-214	81	17	)	)	PUNCT
ejpam-214	81	18	ω	ω	PROPN
ejpam-214	81	19	is	be	AUX
ejpam-214	81	20	a	a	DET
ejpam-214	81	21	subgradient	subgradient	NOUN
ejpam-214	81	22	of	of	ADP
ejpam-214	81	23	f	f	PROPN
ejpam-214	81	24	at	at	ADP
ejpam-214	81	25	x	x	PROPN
ejpam-214	81	26	;	;	PUNCT
ejpam-214	81	27	ii	ii	X
ejpam-214	81	28	)	)	PUNCT
ejpam-214	81	29	there	there	PRON
ejpam-214	81	30	is	be	VERB
ejpam-214	81	31	a	a	DET
ejpam-214	81	32	weighted	weighted	ADJ
ejpam-214	81	33	vector	vector	NOUN
ejpam-214	81	34	ξ	ξ	PROPN
ejpam-214	81	35	,	,	PUNCT
ejpam-214	82	1	such	such	ADJ
ejpam-214	82	2	that	that	SCONJ
ejpam-214	82	3	ω	ω	PROPN
ejpam-214	82	4	=	=	SYM
ejpam-214	82	5	∑	∑	PUNCT
ejpam-214	82	6	i∈i(x	i∈i(x	PROPN
ejpam-214	82	7	)	)	PUNCT
ejpam-214	82	8	ξi∇	ξi∇	NUM
ejpam-214	82	9	fi	fi	NOUN
ejpam-214	82	10	(	(	PUNCT
ejpam-214	82	11	x	x	NOUN
ejpam-214	82	12	)	)	PUNCT
ejpam-214	82	13	;	;	PUNCT
ejpam-214	82	14	iii)ω=	iii)ω=	PROPN
ejpam-214	82	15	lim	lim	PROPN
ejpam-214	82	16	p→∞	p→∞	NOUN
ejpam-214	82	17	¦	¦	PROPN
ejpam-214	82	18	∇x	∇x	PROPN
ejpam-214	82	19	fp	fp	INTJ
ejpam-214	82	20	(	(	PUNCT
ejpam-214	82	21	x	x	INTJ
ejpam-214	82	22	,	,	PUNCT
ejpam-214	82	23	λ	λ	NOUN
ejpam-214	82	24	)	)	PUNCT
ejpam-214	82	25	©	©	ADJ
ejpam-214	82	26	proof	proof	NOUN
ejpam-214	82	27	.	.	PUNCT
ejpam-214	83	1	the	the	DET
ejpam-214	83	2	equivalence	equivalence	NOUN
ejpam-214	83	3	between	between	ADP
ejpam-214	83	4	(	(	PUNCT
ejpam-214	83	5	i	i	NOUN
ejpam-214	83	6	)	)	PUNCT
ejpam-214	83	7	and	and	CCONJ
ejpam-214	83	8	(	(	PUNCT
ejpam-214	83	9	ii	ii	NOUN
ejpam-214	83	10	)	)	PUNCT
ejpam-214	83	11	is	be	AUX
ejpam-214	83	12	well	well	ADV
ejpam-214	83	13	known	know	VERB
ejpam-214	83	14	,	,	PUNCT
ejpam-214	83	15	and	and	CCONJ
ejpam-214	83	16	is	be	AUX
ejpam-214	83	17	obtained	obtain	VERB
ejpam-214	83	18	by	by	ADP
ejpam-214	83	19	applying	apply	VERB
ejpam-214	83	20	standard	standard	ADJ
ejpam-214	83	21	calculus	calculus	NOUN
ejpam-214	83	22	rules	rule	NOUN
ejpam-214	83	23	for	for	ADP
ejpam-214	83	24	computing	computing	NOUN
ejpam-214	83	25	subgradients	subgradient	NOUN
ejpam-214	83	26	(	(	PUNCT
ejpam-214	83	27	[	[	X
ejpam-214	83	28	17	17	NUM
ejpam-214	83	29	]	]	NUM
ejpam-214	83	30	)	)	PUNCT
ejpam-214	83	31	.	.	PUNCT
ejpam-214	84	1	lim	lim	PROPN
ejpam-214	84	2	p→∞	p→∞	PART
ejpam-214	84	3	¦	¦	PROPN
ejpam-214	84	4	∇x	∇x	PROPN
ejpam-214	84	5	fp	fp	INTJ
ejpam-214	84	6	(	(	PUNCT
ejpam-214	84	7	x	x	INTJ
ejpam-214	84	8	,	,	PUNCT
ejpam-214	84	9	λ	λ	NOUN
ejpam-214	84	10	)	)	PUNCT
ejpam-214	84	11	©	©	PROPN
ejpam-214	84	12	=	=	SYM
ejpam-214	84	13	lim	lim	PROPN
ejpam-214	84	14	p→∞	p→∞	PRON
ejpam-214	84	15			VERB
ejpam-214	84	16			ADV
ejpam-214	84	17			DET
ejpam-214	84	18			ADJ
ejpam-214	84	19			PROPN
ejpam-214	84	20	m	m	PROPN
ejpam-214	84	21	∑	∑	PROPN
ejpam-214	84	22	i=1	i=1	PROPN
ejpam-214	84	23	λi	λi	INTJ
ejpam-214	84	24	exp	exp	PRON
ejpam-214	84	25	�	�	PROPN
ejpam-214	84	26	p	p	PROPN
ejpam-214	84	27	fi	fi	NOUN
ejpam-214	84	28	(	(	PUNCT
ejpam-214	84	29	x	x	NOUN
ejpam-214	84	30	)	)	PUNCT
ejpam-214	84	31	�	�	PROPN
ejpam-214	84	32	m	m	VERB
ejpam-214	84	33	∑	∑	PROPN
ejpam-214	84	34	k=1	k=1	PROPN
ejpam-214	84	35	λk	λk	PROPN
ejpam-214	84	36	exp	exp	NOUN
ejpam-214	84	37	�	�	PROPN
ejpam-214	84	38	p	p	PROPN
ejpam-214	84	39	fk	fk	INTJ
ejpam-214	84	40	(	(	PUNCT
ejpam-214	84	41	x	x	NOUN
ejpam-214	84	42	)	)	PUNCT
ejpam-214	84	43	�	�	PROPN
ejpam-214	84	44	∇	∇	X
ejpam-214	84	45	fi	fi	X
ejpam-214	84	46	(	(	PUNCT
ejpam-214	84	47	x	x	NOUN
ejpam-214	84	48	)	)	PUNCT
ejpam-214	84	49			PROPN
ejpam-214	84	50			PROPN
ejpam-214	85	1			PROPN
ejpam-214	85	2			ADJ
ejpam-214	85	3			NOUN
ejpam-214	85	4	=	=	SYM
ejpam-214	85	5	∑	∑	NOUN
ejpam-214	85	6	i∈i(x	i∈i(x	PROPN
ejpam-214	85	7	)	)	PUNCT
ejpam-214	85	8	λi∇	λi∇	NUM
ejpam-214	85	9	fi	fi	NOUN
ejpam-214	85	10	(	(	PUNCT
ejpam-214	85	11	x	x	X
ejpam-214	85	12	)	)	PUNCT
ejpam-214	85	13	(	(	PUNCT
ejpam-214	85	14	14	14	NUM
ejpam-214	85	15	)	)	PUNCT
ejpam-214	85	16	as	as	ADP
ejpam-214	85	17	exp	exp	X
ejpam-214	85	18	�	�	PROPN
ejpam-214	85	19	p	p	PROPN
ejpam-214	85	20	fi	fi	NOUN
ejpam-214	85	21	(	(	PUNCT
ejpam-214	85	22	x	x	NOUN
ejpam-214	85	23	)	)	PUNCT
ejpam-214	85	24	�	�	PROPN
ejpam-214	85	25	→	→	SYM
ejpam-214	85	26	p→∞	p→∞	NUM
ejpam-214	85	27	0	0	NUM
ejpam-214	85	28	,	,	PUNCT
ejpam-214	85	29	i	i	PRON
ejpam-214	85	30	/∈	/∈	VERB
ejpam-214	86	1	i	i	PRON
ejpam-214	86	2	(	(	PUNCT
ejpam-214	86	3	x	x	NOUN
ejpam-214	86	4	)	)	PUNCT
ejpam-214	86	5	and	and	CCONJ
ejpam-214	86	6	λ	λ	PROPN
ejpam-214	86	7	∈	∈	PROPN
ejpam-214	86	8	λ	λ	PROPN
ejpam-214	86	9	.	.	PROPN
ejpam-214	86	10	remark	remark	PROPN
ejpam-214	86	11	1	1	NUM
ejpam-214	86	12	.	.	PUNCT
ejpam-214	87	1	in	in	ADP
ejpam-214	87	2	this	this	DET
ejpam-214	87	3	proof	proof	NOUN
ejpam-214	87	4	,	,	PUNCT
ejpam-214	87	5	we	we	PRON
ejpam-214	87	6	use	use	VERB
ejpam-214	87	7	the	the	DET
ejpam-214	87	8	assumption	assumption	NOUN
ejpam-214	87	9	that	that	SCONJ
ejpam-214	87	10	f(x∗	f(x∗	NOUN
ejpam-214	87	11	)	)	PUNCT
ejpam-214	87	12	=	=	SYM
ejpam-214	88	1	0	0	X
ejpam-214	88	2	.	.	PUNCT
ejpam-214	89	1	in	in	ADP
ejpam-214	89	2	fact	fact	NOUN
ejpam-214	89	3	,	,	PUNCT
ejpam-214	89	4	without	without	ADP
ejpam-214	89	5	this	this	DET
ejpam-214	89	6	assumption	assumption	NOUN
ejpam-214	89	7	,	,	PUNCT
ejpam-214	89	8	we	we	PRON
ejpam-214	89	9	can	can	AUX
ejpam-214	89	10	also	also	ADV
ejpam-214	89	11	obtain	obtain	VERB
ejpam-214	89	12	the	the	DET
ejpam-214	89	13	result	result	NOUN
ejpam-214	89	14	in	in	ADP
ejpam-214	89	15	theorem	theorem	NOUN
ejpam-214	89	16	1	1	NUM
ejpam-214	89	17	by	by	ADP
ejpam-214	89	18	subtracting	subtract	VERB
ejpam-214	89	19	f(x	f(x	PROPN
ejpam-214	89	20	)	)	PUNCT
ejpam-214	89	21	both	both	PRON
ejpam-214	89	22	in	in	ADP
ejpam-214	89	23	the	the	DET
ejpam-214	89	24	numerator	numerator	NOUN
ejpam-214	89	25	and	and	CCONJ
ejpam-214	89	26	denominator	denominator	NOUN
ejpam-214	89	27	in	in	ADP
ejpam-214	89	28	the	the	DET
ejpam-214	89	29	middle	middle	ADJ
ejpam-214	89	30	part	part	NOUN
ejpam-214	89	31	in	in	ADP
ejpam-214	89	32	formula	formula	NOUN
ejpam-214	89	33	(	(	PUNCT
ejpam-214	89	34	14	14	NUM
ejpam-214	89	35	)	)	PUNCT
ejpam-214	89	36	.	.	PUNCT
ejpam-214	90	1	3.2	3.2	NUM
ejpam-214	90	2	.	.	PUNCT
ejpam-214	90	3	basic	basic	ADJ
ejpam-214	90	4	properties	property	NOUN
ejpam-214	90	5	for	for	ADP
ejpam-214	90	6	approximation	approximation	NOUN
ejpam-214	90	7	function	function	NOUN
ejpam-214	90	8	(	(	PUNCT
ejpam-214	90	9	3	3	NUM
ejpam-214	90	10	)	)	PUNCT
ejpam-214	90	11	,	,	PUNCT
ejpam-214	90	12	the	the	DET
ejpam-214	90	13	following	follow	VERB
ejpam-214	90	14	results	result	NOUN
ejpam-214	90	15	establish	establish	VERB
ejpam-214	90	16	the	the	DET
ejpam-214	90	17	basic	basic	ADJ
ejpam-214	90	18	properties	property	NOUN
ejpam-214	90	19	of	of	ADP
ejpam-214	90	20	this	this	DET
ejpam-214	90	21	function	function	NOUN
ejpam-214	90	22	at	at	ADP
ejpam-214	90	23	any	any	DET
ejpam-214	90	24	k	k	NOUN
ejpam-214	90	25	−	−	PROPN
ejpam-214	90	26	k	k	PROPN
ejpam-214	90	27	−	−	PROPN
ejpam-214	90	28	t	t	PROPN
ejpam-214	90	29	pair	pair	NOUN
ejpam-214	90	30	(	(	PUNCT
ejpam-214	90	31	x∗,λ∗	x∗,λ∗	PROPN
ejpam-214	90	32	):	):	PUNCT
ejpam-214	90	33	lemma	lemma	PROPN
ejpam-214	90	34	1	1	NUM
ejpam-214	90	35	.	.	PUNCT
ejpam-214	91	1	for	for	ADP
ejpam-214	91	2	any	any	DET
ejpam-214	91	3	k	k	NOUN
ejpam-214	91	4	−	−	PROPN
ejpam-214	91	5	k	k	PROPN
ejpam-214	92	1	−	−	PROPN
ejpam-214	92	2	t	t	PROPN
ejpam-214	92	3	pair	pair	NOUN
ejpam-214	92	4	(	(	PUNCT
ejpam-214	92	5	x∗,λ∗	x∗,λ∗	PROPN
ejpam-214	92	6	)	)	PUNCT
ejpam-214	92	7	,	,	PUNCT
ejpam-214	92	8	the	the	DET
ejpam-214	92	9	following	follow	VERB
ejpam-214	92	10	hold	hold	NOUN
ejpam-214	92	11	for	for	ADP
ejpam-214	92	12	any	any	DET
ejpam-214	92	13	p	p	PRON
ejpam-214	92	14	≥	≥	NOUN
ejpam-214	92	15	0	0	NUM
ejpam-214	92	16	:	:	PUNCT
ejpam-214	92	17	i	i	NOUN
ejpam-214	92	18	)	)	PUNCT
ejpam-214	93	1	fp	fp	PROPN
ejpam-214	93	2	(	(	PUNCT
ejpam-214	93	3	x	x	PROPN
ejpam-214	93	4	∗,λ∗	∗,λ∗	NOUN
ejpam-214	93	5	)	)	PUNCT
ejpam-214	94	1	=	=	SYM
ejpam-214	94	2	f	f	PROPN
ejpam-214	94	3	(	(	PUNCT
ejpam-214	94	4	x∗	x∗	X
ejpam-214	94	5	)	)	PUNCT
ejpam-214	94	6	=	=	SYM
ejpam-214	94	7	0	0	NUM
ejpam-214	94	8	;	;	PUNCT
ejpam-214	94	9	ii)∇x	ii)∇x	NOUN
ejpam-214	94	10	fp	fp	PROPN
ejpam-214	94	11	�	�	PROPN
ejpam-214	94	12	x∗,λ∗	x∗,λ∗	PROPN
ejpam-214	94	13	,	,	PUNCT
ejpam-214	94	14	p	p	PROPN
ejpam-214	94	15	�	�	PROPN
ejpam-214	94	16	=	=	SYM
ejpam-214	94	17	0	0	NUM
ejpam-214	94	18	proof	proof	NOUN
ejpam-214	94	19	.	.	PUNCT
ejpam-214	95	1	i)using	i)use	VERB
ejpam-214	95	2	the	the	DET
ejpam-214	95	3	k	k	PROPN
ejpam-214	95	4	−	−	PROPN
ejpam-214	95	5	k	k	PROPN
ejpam-214	95	6	−	−	PROPN
ejpam-214	95	7	t	t	NOUN
ejpam-214	95	8	condition	condition	NOUN
ejpam-214	95	9	(	(	PUNCT
ejpam-214	95	10	4	4	NUM
ejpam-214	95	11	)	)	PUNCT
ejpam-214	95	12	directly	directly	ADV
ejpam-214	95	13	.	.	PUNCT
ejpam-214	96	1	ii	ii	X
ejpam-214	96	2	)	)	PUNCT
ejpam-214	96	3	as	as	ADP
ejpam-214	96	4	the	the	DET
ejpam-214	96	5	computation	computation	NOUN
ejpam-214	96	6	in	in	ADP
ejpam-214	96	7	subsection	subsection	NOUN
ejpam-214	96	8	3.1	3.1	NUM
ejpam-214	96	9	we	we	PRON
ejpam-214	96	10	have	have	VERB
ejpam-214	96	11	∇x	∇x	PROPN
ejpam-214	96	12	fp	fp	PART
ejpam-214	96	13	(	(	PUNCT
ejpam-214	96	14	x	x	INTJ
ejpam-214	96	15	,	,	PUNCT
ejpam-214	96	16	λ	λ	NOUN
ejpam-214	96	17	)	)	PUNCT
ejpam-214	96	18	=	=	PUNCT
ejpam-214	97	1	m	m	VERB
ejpam-214	97	2	∑	∑	VERB
ejpam-214	97	3	i=1	i=1	PROPN
ejpam-214	97	4	λi	λi	INTJ
ejpam-214	97	5	exp	exp	PRON
ejpam-214	97	6	�	�	PROPN
ejpam-214	97	7	p	p	PROPN
ejpam-214	97	8	fi	fi	NOUN
ejpam-214	97	9	(	(	PUNCT
ejpam-214	97	10	x	x	NOUN
ejpam-214	97	11	)	)	PUNCT
ejpam-214	97	12	�	�	PROPN
ejpam-214	97	13	m	m	VERB
ejpam-214	97	14	∑	∑	PROPN
ejpam-214	97	15	k=1	k=1	PROPN
ejpam-214	97	16	λk	λk	PROPN
ejpam-214	97	17	exp	exp	NOUN
ejpam-214	97	18	�	�	PROPN
ejpam-214	97	19	p	p	PROPN
ejpam-214	97	20	fk	fk	INTJ
ejpam-214	97	21	(	(	PUNCT
ejpam-214	97	22	x	x	NOUN
ejpam-214	97	23	)	)	PUNCT
ejpam-214	97	24	�	�	PROPN
ejpam-214	97	25	∇	∇	X
ejpam-214	97	26	fi	fi	X
ejpam-214	97	27	(	(	PUNCT
ejpam-214	97	28	x	x	NOUN
ejpam-214	97	29	)	)	PUNCT
ejpam-214	97	30	=	=	PUNCT
ejpam-214	97	31	m	m	VERB
ejpam-214	97	32	∑	∑	PUNCT
ejpam-214	97	33	i=1	i=1	PROPN
ejpam-214	97	34	λi∇	λi∇	NUM
ejpam-214	97	35	fi	fi	NOUN
ejpam-214	97	36	(	(	PUNCT
ejpam-214	97	37	x	x	X
ejpam-214	97	38	)	)	PUNCT
ejpam-214	97	39	m	m	VERB
ejpam-214	97	40	∑	∑	NOUN
ejpam-214	97	41	k=1	k=1	X
ejpam-214	97	42	λk	λk	PROPN
ejpam-214	97	43	�	�	PROPN
ejpam-214	97	44	exp	exp	X
ejpam-214	97	45	�	�	PROPN
ejpam-214	97	46	p	p	PROPN
ejpam-214	97	47	fk	fk	INTJ
ejpam-214	97	48	(	(	PUNCT
ejpam-214	97	49	x	x	NOUN
ejpam-214	97	50	)	)	PUNCT
ejpam-214	97	51	�	�	PROPN
ejpam-214	97	52	−	−	PROPN
ejpam-214	97	53	exp	exp	NOUN
ejpam-214	97	54	�	�	PROPN
ejpam-214	97	55	p	p	PROPN
ejpam-214	97	56	fi	fi	NOUN
ejpam-214	97	57	(	(	PUNCT
ejpam-214	97	58	x	x	NOUN
ejpam-214	97	59	)	)	PUNCT
ejpam-214	97	60	�	�	PROPN
ejpam-214	97	61	�	�	PROPN
ejpam-214	97	62	(	(	PUNCT
ejpam-214	97	63	15	15	NUM
ejpam-214	97	64	)	)	PUNCT
ejpam-214	97	65	applying	apply	VERB
ejpam-214	97	66	the	the	DET
ejpam-214	97	67	k	k	PROPN
ejpam-214	97	68	−	−	PROPN
ejpam-214	97	69	k	k	PROPN
ejpam-214	97	70	−	−	PROPN
ejpam-214	97	71	t	t	NOUN
ejpam-214	97	72	condition	condition	NOUN
ejpam-214	97	73	,	,	PUNCT
ejpam-214	97	74	we	we	PRON
ejpam-214	97	75	have	have	VERB
ejpam-214	97	76	∇x	∇x	PROPN
ejpam-214	98	1	fp	fp	PRON
ejpam-214	98	2	�	�	PROPN
ejpam-214	98	3	x∗,λ∗	x∗,λ∗	PROPN
ejpam-214	98	4	�	�	PROPN
ejpam-214	98	5	=	=	PUNCT
ejpam-214	98	6	m	m	VERB
ejpam-214	98	7	∑	∑	PUNCT
ejpam-214	98	8	i=1	i=1	PROPN
ejpam-214	98	9	λ∗	λ∗	PROPN
ejpam-214	98	10	i	i	PRON
ejpam-214	98	11	∇	∇	VERB
ejpam-214	98	12	fi	fi	X
ejpam-214	98	13	(	(	PUNCT
ejpam-214	98	14	x	x	NOUN
ejpam-214	98	15	∗	∗	NOUN
ejpam-214	98	16	)	)	PUNCT
ejpam-214	98	17	m	m	VERB
ejpam-214	98	18	∑	∑	PUNCT
ejpam-214	98	19	k=1	k=1	X
ejpam-214	98	20	λ∗	λ∗	PROPN
ejpam-214	98	21	k	k	PROPN
ejpam-214	98	22	�	�	PROPN
ejpam-214	98	23	exp	exp	NOUN
ejpam-214	98	24	�	�	PROPN
ejpam-214	98	25	p	p	PROPN
ejpam-214	98	26	fk	fk	INTJ
ejpam-214	98	27	(	(	PUNCT
ejpam-214	98	28	x	x	NOUN
ejpam-214	98	29	∗	∗	PROPN
ejpam-214	98	30	)	)	PUNCT
ejpam-214	98	31	�	�	PROPN
ejpam-214	98	32	−	−	PROPN
ejpam-214	98	33	exp	exp	NOUN
ejpam-214	98	34	�	�	PROPN
ejpam-214	98	35	p	p	PROPN
ejpam-214	98	36	fi	fi	NOUN
ejpam-214	98	37	(	(	PUNCT
ejpam-214	98	38	x	x	NOUN
ejpam-214	98	39	∗	∗	NOUN
ejpam-214	98	40	)	)	PUNCT
ejpam-214	98	41	�	�	PROPN
ejpam-214	98	42	�	�	PROPN
ejpam-214	98	43	=	=	SYM
ejpam-214	98	44	0	0	NUM
ejpam-214	98	45	(	(	PUNCT
ejpam-214	98	46	16	16	NUM
ejpam-214	98	47	)	)	PUNCT
ejpam-214	98	48	l.	l.	PROPN
ejpam-214	98	49	zhang	zhang	PROPN
ejpam-214	98	50	,	,	PUNCT
ejpam-214	98	51	j.	j.	PROPN
ejpam-214	98	52	li	li	PROPN
ejpam-214	98	53	,	,	PUNCT
ejpam-214	98	54	x.	x.	PROPN
ejpam-214	98	55	li	li	PROPN
ejpam-214	98	56	/	/	SYM
ejpam-214	98	57	eur	eur	PROPN
ejpam-214	98	58	.	.	PUNCT
ejpam-214	99	1	j.	j.	PROPN
ejpam-214	99	2	pure	pure	PROPN
ejpam-214	99	3	appl	appl	PROPN
ejpam-214	99	4	.	.	PROPN
ejpam-214	99	5	math	math	PROPN
ejpam-214	99	6	,	,	PUNCT
ejpam-214	99	7	3	3	NUM
ejpam-214	99	8	(	(	PUNCT
ejpam-214	99	9	2010	2010	NUM
ejpam-214	99	10	)	)	PUNCT
ejpam-214	99	11	,	,	PUNCT
ejpam-214	99	12	98	98	NUM
ejpam-214	99	13	-	-	SYM
ejpam-214	99	14	106	106	NUM
ejpam-214	99	15	103	103	NUM
ejpam-214	99	16	theorem	theorem	NOUN
ejpam-214	99	17	2	2	NUM
ejpam-214	99	18	.	.	PUNCT
ejpam-214	100	1	let	let	AUX
ejpam-214	100	2	(	(	PUNCT
ejpam-214	100	3	x∗,λ∗	x∗,λ∗	PROPN
ejpam-214	100	4	)	)	PUNCT
ejpam-214	100	5	be	be	VERB
ejpam-214	100	6	k	k	NOUN
ejpam-214	100	7	−	−	PROPN
ejpam-214	101	1	k	k	INTJ
ejpam-214	101	2	−	−	PROPN
ejpam-214	101	3	t	t	PROPN
ejpam-214	101	4	pair	pair	NOUN
ejpam-214	101	5	of	of	ADP
ejpam-214	101	6	min	min	ADJ
ejpam-214	101	7	-	-	ADJ
ejpam-214	101	8	max	max	PROPN
ejpam-214	101	9	problem	problem	NOUN
ejpam-214	101	10	(	(	PUNCT
ejpam-214	101	11	1	1	NUM
ejpam-214	101	12	)	)	PUNCT
ejpam-214	101	13	.	.	PUNCT
ejpam-214	102	1	assume	assume	VERB
ejpam-214	102	2	that	that	SCONJ
ejpam-214	102	3	∇	∇	PROPN
ejpam-214	102	4	fi	fi	X
ejpam-214	102	5	(	(	PUNCT
ejpam-214	102	6	x	x	NOUN
ejpam-214	102	7	∗	∗	NOUN
ejpam-214	102	8	)	)	PUNCT
ejpam-214	102	9	,	,	PUNCT
ejpam-214	102	10	i	i	PRON
ejpam-214	102	11	∈	∈	VERB
ejpam-214	102	12	i	i	PRON
ejpam-214	102	13	(	(	PUNCT
ejpam-214	102	14	x∗	x∗	PROPN
ejpam-214	102	15	)	)	PUNCT
ejpam-214	102	16	are	be	AUX
ejpam-214	102	17	linearly	linearly	ADV
ejpam-214	102	18	independent	independent	ADJ
ejpam-214	102	19	and	and	CCONJ
ejpam-214	102	20	x∗	x∗	PROPN
ejpam-214	102	21	satisfy	satisfy	VERB
ejpam-214	102	22	the	the	DET
ejpam-214	102	23	second	second	ADJ
ejpam-214	102	24	-	-	PUNCT
ejpam-214	102	25	order	order	NOUN
ejpam-214	102	26	sufficiency	sufficiency	NOUN
ejpam-214	102	27	condition	condition	NOUN
ejpam-214	102	28	.	.	PUNCT
ejpam-214	103	1	then	then	ADV
ejpam-214	103	2	the	the	DET
ejpam-214	103	3	following	follow	VERB
ejpam-214	103	4	hold	hold	NOUN
ejpam-214	103	5	:	:	PUNCT
ejpam-214	103	6	there	there	PRON
ejpam-214	103	7	exists	exist	VERB
ejpam-214	103	8	ρ	ρ	PROPN
ejpam-214	103	9	>	>	X
ejpam-214	103	10	0	0	PUNCT
ejpam-214	103	11	and	and	CCONJ
ejpam-214	103	12	p0	p0	NOUN
ejpam-214	103	13	>	>	X
ejpam-214	103	14	0	0	NUM
ejpam-214	103	15	,	,	PUNCT
ejpam-214	103	16	¬	¬	PROPN
ejpam-214	103	17	∇2	∇2	X
ejpam-214	103	18	x	x	PUNCT
ejpam-214	103	19	x	x	PUNCT
ejpam-214	103	20	fp	fp	PROPN
ejpam-214	103	21	�	�	PROPN
ejpam-214	103	22	x∗,λ∗	x∗,λ∗	PROPN
ejpam-214	103	23	�	�	PROPN
ejpam-214	104	1	d	d	PROPN
ejpam-214	104	2	,	,	PUNCT
ejpam-214	104	3	d	d	PROPN
ejpam-214	104	4	¶	¶	PROPN
ejpam-214	104	5	≥	≥	PROPN
ejpam-214	104	6	ρ	ρ	PROPN
ejpam-214	104	7	〈	〈	PROPN
ejpam-214	104	8	d	d	PROPN
ejpam-214	104	9	,	,	PUNCT
ejpam-214	104	10	d	d	SYM
ejpam-214	104	11	〉	〉	X
ejpam-214	104	12	(	(	PUNCT
ejpam-214	104	13	17	17	NUM
ejpam-214	104	14	)	)	PUNCT
ejpam-214	104	15	for	for	ADP
ejpam-214	104	16	any	any	DET
ejpam-214	104	17	fixed	fix	VERB
ejpam-214	104	18	p	p	NOUN
ejpam-214	104	19	≥	≥	NOUN
ejpam-214	104	20	p0	p0	NOUN
ejpam-214	104	21	and	and	CCONJ
ejpam-214	104	22	d	d	PROPN
ejpam-214	104	23	∈	∈	PROPN
ejpam-214	104	24	rn	rn	PROPN
ejpam-214	104	25	.	.	PUNCT
ejpam-214	104	26	proof	proof	NOUN
ejpam-214	104	27	.	.	PUNCT
ejpam-214	105	1	∇2	∇2	X
ejpam-214	105	2	x	x	PUNCT
ejpam-214	105	3	x	x	SYM
ejpam-214	105	4	fp	fp	INTJ
ejpam-214	105	5	(	(	PUNCT
ejpam-214	105	6	x	x	INTJ
ejpam-214	105	7	,	,	PUNCT
ejpam-214	105	8	λ	λ	NOUN
ejpam-214	105	9	)	)	PUNCT
ejpam-214	105	10	=	=	PUNCT
ejpam-214	106	1	m	m	VERB
ejpam-214	106	2	∑	∑	VERB
ejpam-214	106	3	i=1	i=1	PROPN
ejpam-214	106	4	λi	λi	INTJ
ejpam-214	106	5	exp	exp	PRON
ejpam-214	106	6	�	�	PROPN
ejpam-214	106	7	p	p	PROPN
ejpam-214	106	8	fi	fi	NOUN
ejpam-214	106	9	(	(	PUNCT
ejpam-214	106	10	x	x	NOUN
ejpam-214	106	11	)	)	PUNCT
ejpam-214	106	12	�	�	PROPN
ejpam-214	106	13	m	m	VERB
ejpam-214	106	14	∑	∑	PROPN
ejpam-214	106	15	k=1	k=1	PROPN
ejpam-214	106	16	λk	λk	PROPN
ejpam-214	106	17	exp	exp	NOUN
ejpam-214	106	18	�	�	PROPN
ejpam-214	106	19	p	p	PROPN
ejpam-214	106	20	fk	fk	INTJ
ejpam-214	106	21	(	(	PUNCT
ejpam-214	106	22	x	x	NOUN
ejpam-214	106	23	)	)	PUNCT
ejpam-214	106	24	�	�	PROPN
ejpam-214	106	25	∇2	∇2	PROPN
ejpam-214	106	26	fi	fi	NOUN
ejpam-214	106	27	(	(	PUNCT
ejpam-214	106	28	x)+	x)+	PROPN
ejpam-214	106	29	p	p	X
ejpam-214	106	30	m	m	VERB
ejpam-214	106	31	∑	∑	VERB
ejpam-214	106	32	i=1	i=1	PROPN
ejpam-214	106	33	λi	λi	INTJ
ejpam-214	106	34	exp	exp	PRON
ejpam-214	106	35	�	�	PROPN
ejpam-214	106	36	p	p	PROPN
ejpam-214	106	37	fi	fi	NOUN
ejpam-214	106	38	(	(	PUNCT
ejpam-214	106	39	x	x	NOUN
ejpam-214	106	40	)	)	PUNCT
ejpam-214	106	41	�	�	PROPN
ejpam-214	106	42	∇	∇	X
ejpam-214	106	43	fi	fi	X
ejpam-214	106	44	(	(	PUNCT
ejpam-214	106	45	x	x	X
ejpam-214	106	46	)	)	PUNCT
ejpam-214	106	47	t	t	PROPN
ejpam-214	106	48	∇	∇	X
ejpam-214	106	49	fi	fi	X
ejpam-214	106	50	(	(	PUNCT
ejpam-214	106	51	x	x	X
ejpam-214	106	52	)	)	PUNCT
ejpam-214	106	53	m	m	VERB
ejpam-214	106	54	∑	∑	NOUN
ejpam-214	106	55	k=1	k=1	X
ejpam-214	106	56	λk	λk	PROPN
ejpam-214	106	57	exp	exp	NOUN
ejpam-214	106	58	�	�	PROPN
ejpam-214	106	59	p	p	PROPN
ejpam-214	106	60	fk	fk	INTJ
ejpam-214	106	61	(	(	PUNCT
ejpam-214	106	62	x	x	NOUN
ejpam-214	106	63	)	)	PUNCT
ejpam-214	106	64	�	�	PROPN
ejpam-214	106	65	−	−	PROPN
ejpam-214	106	66	p	p	PROPN
ejpam-214	106	67	�	�	PROPN
ejpam-214	106	68	m	m	PROPN
ejpam-214	106	69	∑	∑	PROPN
ejpam-214	106	70	i=1	i=1	PROPN
ejpam-214	106	71	λi	λi	INTJ
ejpam-214	106	72	exp	exp	PRON
ejpam-214	106	73	�	�	PROPN
ejpam-214	106	74	p	p	PROPN
ejpam-214	106	75	fi	fi	NOUN
ejpam-214	106	76	(	(	PUNCT
ejpam-214	106	77	x	x	NOUN
ejpam-214	106	78	)	)	PUNCT
ejpam-214	106	79	�	�	PROPN
ejpam-214	106	80	∇	∇	X
ejpam-214	106	81	fi	fi	X
ejpam-214	106	82	(	(	PUNCT
ejpam-214	106	83	x	x	NOUN
ejpam-214	106	84	)	)	PUNCT
ejpam-214	106	85	�	�	PROPN
ejpam-214	106	86	t	t	PROPN
ejpam-214	106	87	m	m	VERB
ejpam-214	106	88	∑	∑	PROPN
ejpam-214	106	89	i=1	i=1	PROPN
ejpam-214	106	90	λi	λi	INTJ
ejpam-214	106	91	exp	exp	PRON
ejpam-214	106	92	�	�	PROPN
ejpam-214	106	93	p	p	PROPN
ejpam-214	106	94	fi	fi	NOUN
ejpam-214	106	95	(	(	PUNCT
ejpam-214	106	96	x	x	NOUN
ejpam-214	106	97	)	)	PUNCT
ejpam-214	106	98	�	�	PROPN
ejpam-214	106	99	∇	∇	X
ejpam-214	106	100	fi	fi	X
ejpam-214	106	101	(	(	PUNCT
ejpam-214	106	102	x	x	NOUN
ejpam-214	106	103	)	)	PUNCT
ejpam-214	106	104	�	�	PROPN
ejpam-214	106	105	m	m	VERB
ejpam-214	106	106	∑	∑	PROPN
ejpam-214	106	107	k=1	k=1	PROPN
ejpam-214	106	108	λk	λk	PROPN
ejpam-214	106	109	exp	exp	NOUN
ejpam-214	106	110	�	�	PROPN
ejpam-214	106	111	p	p	PROPN
ejpam-214	106	112	fk	fk	INTJ
ejpam-214	106	113	(	(	PUNCT
ejpam-214	106	114	x	x	NOUN
ejpam-214	106	115	)	)	PUNCT
ejpam-214	106	116	�	�	PROPN
ejpam-214	106	117	�	�	PROPN
ejpam-214	106	118	2	2	NUM
ejpam-214	106	119	(	(	PUNCT
ejpam-214	106	120	18	18	NUM
ejpam-214	106	121	)	)	PUNCT
ejpam-214	106	122	and	and	CCONJ
ejpam-214	106	123	∇2	∇2	PROPN
ejpam-214	106	124	x	x	SYM
ejpam-214	106	125	x	x	VERB
ejpam-214	106	126	fp	fp	PROPN
ejpam-214	106	127	�	�	PROPN
ejpam-214	106	128	x∗,λ∗	x∗,λ∗	PROPN
ejpam-214	106	129	�	�	PROPN
ejpam-214	107	1	=	=	PUNCT
ejpam-214	107	2	m	m	PROPN
ejpam-214	107	3	∑	∑	VERB
ejpam-214	107	4	i=1	i=1	PROPN
ejpam-214	107	5	λ∗i	λ∗i	PROPN
ejpam-214	107	6	exp	exp	PRON
ejpam-214	107	7	�	�	PROPN
ejpam-214	107	8	p	p	PROPN
ejpam-214	107	9	fi	fi	NOUN
ejpam-214	107	10	(	(	PUNCT
ejpam-214	107	11	x	x	NOUN
ejpam-214	107	12	∗	∗	PROPN
ejpam-214	107	13	)	)	PUNCT
ejpam-214	107	14	�	�	PROPN
ejpam-214	107	15	m	m	VERB
ejpam-214	107	16	∑	∑	PROPN
ejpam-214	107	17	k=1	k=1	X
ejpam-214	107	18	λ∗	λ∗	PROPN
ejpam-214	108	1	k	k	PROPN
ejpam-214	108	2	exp	exp	X
ejpam-214	108	3	�	�	PROPN
ejpam-214	108	4	p	p	PROPN
ejpam-214	108	5	fk	fk	INTJ
ejpam-214	108	6	(	(	PUNCT
ejpam-214	108	7	x	x	NOUN
ejpam-214	108	8	∗	∗	PROPN
ejpam-214	108	9	)	)	PUNCT
ejpam-214	108	10	�	�	PROPN
ejpam-214	108	11	∇2	∇2	PROPN
ejpam-214	108	12	fi	fi	NOUN
ejpam-214	108	13	�	�	PROPN
ejpam-214	108	14	x∗	x∗	PROPN
ejpam-214	108	15	�	�	PROPN
ejpam-214	109	1	+	+	CCONJ
ejpam-214	109	2	p	p	PROPN
ejpam-214	109	3	m	m	PROPN
ejpam-214	109	4	∑	∑	PROPN
ejpam-214	109	5	i=1	i=1	PROPN
ejpam-214	109	6	λ∗i	λ∗i	PROPN
ejpam-214	109	7	exp	exp	PRON
ejpam-214	109	8	�	�	PROPN
ejpam-214	109	9	p	p	PROPN
ejpam-214	109	10	fi	fi	NOUN
ejpam-214	109	11	(	(	PUNCT
ejpam-214	109	12	x	x	NOUN
ejpam-214	109	13	∗	∗	PROPN
ejpam-214	109	14	)	)	PUNCT
ejpam-214	109	15	�	�	PROPN
ejpam-214	109	16	∇	∇	X
ejpam-214	109	17	fi	fi	NOUN
ejpam-214	109	18	(	(	PUNCT
ejpam-214	109	19	x	x	NOUN
ejpam-214	109	20	∗	∗	NOUN
ejpam-214	109	21	)	)	PUNCT
ejpam-214	109	22	t	t	PROPN
ejpam-214	109	23	∇	∇	X
ejpam-214	109	24	fi	fi	X
ejpam-214	109	25	(	(	PUNCT
ejpam-214	109	26	x	x	NOUN
ejpam-214	109	27	∗	∗	NOUN
ejpam-214	109	28	)	)	PUNCT
ejpam-214	109	29	m	m	VERB
ejpam-214	109	30	∑	∑	PUNCT
ejpam-214	109	31	k=1	k=1	X
ejpam-214	109	32	λ∗	λ∗	PROPN
ejpam-214	110	1	k	k	PROPN
ejpam-214	110	2	exp	exp	X
ejpam-214	110	3	�	�	PROPN
ejpam-214	110	4	p	p	PROPN
ejpam-214	110	5	fk	fk	INTJ
ejpam-214	110	6	(	(	PUNCT
ejpam-214	110	7	x	x	NOUN
ejpam-214	110	8	∗	∗	PROPN
ejpam-214	110	9	)	)	PUNCT
ejpam-214	110	10	�	�	PROPN
ejpam-214	110	11	−	−	PROPN
ejpam-214	110	12	p	p	PROPN
ejpam-214	110	13	�	�	PROPN
ejpam-214	110	14	m	m	VERB
ejpam-214	110	15	∑	∑	PROPN
ejpam-214	110	16	i=1	i=1	PROPN
ejpam-214	110	17	λ∗	λ∗	PROPN
ejpam-214	110	18	i	i	PRON
ejpam-214	110	19	exp	exp	VERB
ejpam-214	110	20	�	�	PROPN
ejpam-214	110	21	p	p	PROPN
ejpam-214	110	22	fi	fi	NOUN
ejpam-214	110	23	(	(	PUNCT
ejpam-214	110	24	x	x	NOUN
ejpam-214	110	25	∗	∗	PROPN
ejpam-214	110	26	)	)	PUNCT
ejpam-214	110	27	�	�	PROPN
ejpam-214	110	28	∇	∇	X
ejpam-214	110	29	fi	fi	NOUN
ejpam-214	110	30	(	(	PUNCT
ejpam-214	110	31	x	x	NOUN
ejpam-214	110	32	∗	∗	NOUN
ejpam-214	110	33	)	)	PUNCT
ejpam-214	110	34	�	�	PROPN
ejpam-214	110	35	t	t	PROPN
ejpam-214	110	36	m	m	VERB
ejpam-214	110	37	∑	∑	PROPN
ejpam-214	110	38	i=1	i=1	PROPN
ejpam-214	110	39	λ∗	λ∗	PROPN
ejpam-214	111	1	i	i	PRON
ejpam-214	111	2	exp	exp	VERB
ejpam-214	111	3	�	�	PROPN
ejpam-214	111	4	p	p	PROPN
ejpam-214	111	5	fi	fi	NOUN
ejpam-214	111	6	(	(	PUNCT
ejpam-214	111	7	x	x	NOUN
ejpam-214	111	8	∗	∗	PROPN
ejpam-214	111	9	)	)	PUNCT
ejpam-214	111	10	�	�	PROPN
ejpam-214	111	11	∇	∇	X
ejpam-214	111	12	fi	fi	NOUN
ejpam-214	111	13	(	(	PUNCT
ejpam-214	111	14	x	x	NOUN
ejpam-214	111	15	∗	∗	PROPN
ejpam-214	111	16	)	)	PUNCT
ejpam-214	111	17	�	�	PROPN
ejpam-214	111	18	m	m	VERB
ejpam-214	111	19	∑	∑	PROPN
ejpam-214	111	20	k=1	k=1	X
ejpam-214	111	21	λ∗	λ∗	PROPN
ejpam-214	112	1	k	k	PROPN
ejpam-214	112	2	exp	exp	X
ejpam-214	112	3	�	�	PROPN
ejpam-214	112	4	p	p	PROPN
ejpam-214	112	5	fk	fk	INTJ
ejpam-214	112	6	(	(	PUNCT
ejpam-214	112	7	x	x	NOUN
ejpam-214	112	8	∗	∗	PROPN
ejpam-214	112	9	)	)	PUNCT
ejpam-214	112	10	�	�	PROPN
ejpam-214	112	11	�	�	PROPN
ejpam-214	112	12	2	2	NUM
ejpam-214	112	13	(	(	PUNCT
ejpam-214	112	14	19	19	NUM
ejpam-214	112	15	)	)	PUNCT
ejpam-214	112	16	=	=	NOUN
ejpam-214	112	17	∇2	∇2	NOUN
ejpam-214	112	18	x	x	SYM
ejpam-214	112	19	x	x	PUNCT
ejpam-214	112	20	l	l	X
ejpam-214	112	21	�	�	PROPN
ejpam-214	112	22	x∗,λ∗	x∗,λ∗	PROPN
ejpam-214	112	23	�	�	PROPN
ejpam-214	113	1	+	+	CCONJ
ejpam-214	113	2	p	p	PROPN
ejpam-214	113	3	∑	∑	PROPN
ejpam-214	113	4	i∈i(x∗	i∈i(x∗	PROPN
ejpam-214	113	5	)	)	PUNCT
ejpam-214	113	6	λ∗i∇	λ∗i∇	PROPN
ejpam-214	113	7	fi	fi	NOUN
ejpam-214	113	8	�	�	PROPN
ejpam-214	113	9	x∗	x∗	PROPN
ejpam-214	113	10	�	�	PROPN
ejpam-214	113	11	t	t	PROPN
ejpam-214	113	12	∇	∇	X
ejpam-214	113	13	fi	fi	X
ejpam-214	113	14	�	�	PROPN
ejpam-214	113	15	x∗	x∗	PROPN
ejpam-214	113	16	�	�	PROPN
ejpam-214	114	1	−	−	ADP
ejpam-214	114	2	p	p	NOUN
ejpam-214	114	3			NOUN
ejpam-214	114	4			NOUN
ejpam-214	114	5			PROPN
ejpam-214	114	6	∑	∑	PROPN
ejpam-214	114	7	i∈i(x∗	i∈i(x∗	PROPN
ejpam-214	114	8	)	)	PUNCT
ejpam-214	114	9	λ∗i∇	λ∗i∇	PROPN
ejpam-214	114	10	fi	fi	NOUN
ejpam-214	114	11	�	�	PROPN
ejpam-214	114	12	x∗	x∗	PROPN
ejpam-214	114	13	�	�	PROPN
ejpam-214	114	14			PROPN
ejpam-214	114	15			NOUN
ejpam-214	114	16			PUNCT
ejpam-214	115	1	t	t	PROPN
ejpam-214	115	2			VERB
ejpam-214	115	3			NOUN
ejpam-214	115	4	∑	∑	PROPN
ejpam-214	115	5	i∈i(x∗	i∈i(x∗	PROPN
ejpam-214	115	6	)	)	PUNCT
ejpam-214	115	7	λ∗i∇	λ∗i∇	PROPN
ejpam-214	115	8	fi	fi	NOUN
ejpam-214	115	9	�	�	PROPN
ejpam-214	115	10	x∗	x∗	PROPN
ejpam-214	115	11	�	�	PROPN
ejpam-214	115	12			PROPN
ejpam-214	115	13			VERB
ejpam-214	115	14			PUNCT
ejpam-214	116	1	(	(	PUNCT
ejpam-214	116	2	20	20	NUM
ejpam-214	116	3	)	)	PUNCT
ejpam-214	116	4	l.	l.	PROPN
ejpam-214	116	5	zhang	zhang	PROPN
ejpam-214	116	6	,	,	PUNCT
ejpam-214	116	7	j.	j.	PROPN
ejpam-214	116	8	li	li	PROPN
ejpam-214	116	9	,	,	PUNCT
ejpam-214	116	10	x.	x.	PROPN
ejpam-214	116	11	li	li	PROPN
ejpam-214	116	12	/	/	SYM
ejpam-214	116	13	eur	eur	PROPN
ejpam-214	116	14	.	.	PUNCT
ejpam-214	117	1	j.	j.	PROPN
ejpam-214	117	2	pure	pure	PROPN
ejpam-214	117	3	appl	appl	PROPN
ejpam-214	117	4	.	.	PROPN
ejpam-214	117	5	math	math	PROPN
ejpam-214	117	6	,	,	PUNCT
ejpam-214	117	7	3	3	NUM
ejpam-214	117	8	(	(	PUNCT
ejpam-214	117	9	2010	2010	NUM
ejpam-214	117	10	)	)	PUNCT
ejpam-214	117	11	,	,	PUNCT
ejpam-214	117	12	98	98	NUM
ejpam-214	117	13	-	-	SYM
ejpam-214	117	14	106	106	NUM
ejpam-214	117	15	104	104	NUM
ejpam-214	117	16	as	as	ADP
ejpam-214	117	17	the	the	DET
ejpam-214	117	18	convexity	convexity	NOUN
ejpam-214	117	19	of	of	ADP
ejpam-214	117	20	the	the	DET
ejpam-214	117	21	quadratic	quadratic	ADJ
ejpam-214	117	22	function	function	NOUN
ejpam-214	118	1	,	,	PUNCT
ejpam-214	118	2	we	we	PRON
ejpam-214	118	3	have	have	VERB
ejpam-214	118	4	the	the	DET
ejpam-214	118	5	inequality	inequality	NOUN
ejpam-214	118	6	∑	∑	VERB
ejpam-214	118	7	i∈i(x∗	i∈i(x∗	PROPN
ejpam-214	118	8	)	)	PUNCT
ejpam-214	118	9	λ∗i∇	λ∗i∇	PROPN
ejpam-214	118	10	fi	fi	NOUN
ejpam-214	118	11	�	�	PROPN
ejpam-214	118	12	x∗	x∗	PROPN
ejpam-214	118	13	�	�	PROPN
ejpam-214	118	14	t	t	PROPN
ejpam-214	118	15	∇	∇	X
ejpam-214	118	16	fi	fi	X
ejpam-214	118	17	�	�	PROPN
ejpam-214	118	18	x∗	x∗	PROPN
ejpam-214	118	19	�	�	PROPN
ejpam-214	118	20	≥	≥	PROPN
ejpam-214	118	21			PROPN
ejpam-214	118	22			NOUN
ejpam-214	118	23			PROPN
ejpam-214	118	24	∑	∑	PROPN
ejpam-214	118	25	i∈i(x∗	i∈i(x∗	PROPN
ejpam-214	118	26	)	)	PUNCT
ejpam-214	118	27	λ∗i∇	λ∗i∇	PROPN
ejpam-214	118	28	fi	fi	NOUN
ejpam-214	118	29	�	�	PROPN
ejpam-214	118	30	x∗	x∗	PROPN
ejpam-214	118	31	�	�	PROPN
ejpam-214	118	32			PROPN
ejpam-214	118	33			NOUN
ejpam-214	118	34			PUNCT
ejpam-214	119	1	t	t	PROPN
ejpam-214	119	2			VERB
ejpam-214	119	3			NOUN
ejpam-214	119	4	∑	∑	PROPN
ejpam-214	119	5	i∈i(x∗	i∈i(x∗	PROPN
ejpam-214	119	6	)	)	PUNCT
ejpam-214	119	7	λ∗i∇	λ∗i∇	PROPN
ejpam-214	119	8	fi	fi	NOUN
ejpam-214	119	9	�	�	PROPN
ejpam-214	119	10	x∗	x∗	PROPN
ejpam-214	119	11	�	�	PROPN
ejpam-214	119	12			PROPN
ejpam-214	119	13			VERB
ejpam-214	119	14			PUNCT
ejpam-214	120	1	(	(	PUNCT
ejpam-214	120	2	21	21	NUM
ejpam-214	120	3	)	)	PUNCT
ejpam-214	120	4	combining	combine	VERB
ejpam-214	120	5	the	the	DET
ejpam-214	120	6	second	second	ADJ
ejpam-214	120	7	order	order	NOUN
ejpam-214	120	8	optimality	optimality	NOUN
ejpam-214	120	9	condition	condition	NOUN
ejpam-214	120	10	we	we	PRON
ejpam-214	120	11	have	have	VERB
ejpam-214	120	12	¬	¬	PROPN
ejpam-214	120	13	∇2	∇2	X
ejpam-214	120	14	x	x	PUNCT
ejpam-214	120	15	x	x	PUNCT
ejpam-214	120	16	fp	fp	PROPN
ejpam-214	120	17	�	�	PROPN
ejpam-214	120	18	x∗,λ∗	x∗,λ∗	PROPN
ejpam-214	120	19	�	�	PROPN
ejpam-214	121	1	d	d	PROPN
ejpam-214	121	2	,	,	PUNCT
ejpam-214	121	3	d	d	PROPN
ejpam-214	121	4	¶	¶	PROPN
ejpam-214	121	5	≥	≥	NOUN
ejpam-214	121	6	¬	¬	PROPN
ejpam-214	121	7	∇2	∇2	X
ejpam-214	121	8	x	x	SYM
ejpam-214	121	9	x	x	PUNCT
ejpam-214	121	10	l	l	X
ejpam-214	121	11	�	�	PROPN
ejpam-214	121	12	x∗,λ∗	x∗,λ∗	PROPN
ejpam-214	121	13	�	�	PROPN
ejpam-214	122	1	d	d	PROPN
ejpam-214	122	2	,	,	PUNCT
ejpam-214	122	3	d	d	PROPN
ejpam-214	122	4	¶	¶	PROPN
ejpam-214	122	5	≥	≥	PROPN
ejpam-214	122	6	ρ	ρ	PROPN
ejpam-214	122	7	〈	〈	PROPN
ejpam-214	122	8	d	d	PROPN
ejpam-214	122	9	,	,	PUNCT
ejpam-214	122	10	d	d	SYM
ejpam-214	122	11	〉	〉	X
ejpam-214	122	12	(	(	PUNCT
ejpam-214	122	13	22	22	NUM
ejpam-214	122	14	)	)	PUNCT
ejpam-214	122	15	corollary	corollary	NOUN
ejpam-214	122	16	1	1	NUM
ejpam-214	122	17	.	.	PUNCT
ejpam-214	123	1	if	if	SCONJ
ejpam-214	123	2	fi	fi	NOUN
ejpam-214	123	3	∈	∈	PROPN
ejpam-214	123	4	c2	c2	PROPN
ejpam-214	123	5	,	,	PUNCT
ejpam-214	123	6	∇	∇	X
ejpam-214	123	7	fi	fi	NOUN
ejpam-214	123	8	(	(	PUNCT
ejpam-214	123	9	x	x	NOUN
ejpam-214	123	10	∗	∗	NOUN
ejpam-214	123	11	)	)	PUNCT
ejpam-214	123	12	,	,	PUNCT
ejpam-214	123	13	i	i	PRON
ejpam-214	123	14	∈	∈	VERB
ejpam-214	123	15	i	i	PRON
ejpam-214	123	16	(	(	PUNCT
ejpam-214	123	17	x∗	x∗	PROPN
ejpam-214	123	18	)	)	PUNCT
ejpam-214	123	19	are	be	AUX
ejpam-214	123	20	linearly	linearly	ADV
ejpam-214	123	21	independent	independent	ADJ
ejpam-214	123	22	and	and	CCONJ
ejpam-214	123	23	the	the	DET
ejpam-214	123	24	second	second	ADJ
ejpam-214	123	25	order	order	NOUN
ejpam-214	123	26	sufficiently	sufficiently	ADV
ejpam-214	123	27	condition	condition	NOUN
ejpam-214	123	28	is	be	AUX
ejpam-214	123	29	satisfied	satisfied	ADJ
ejpam-214	123	30	,	,	PUNCT
ejpam-214	123	31	then	then	ADV
ejpam-214	123	32	for	for	ADP
ejpam-214	123	33	any	any	DET
ejpam-214	123	34	λ	λ	PROPN
ejpam-214	123	35	>	>	X
ejpam-214	123	36	0	0	PUNCT
ejpam-214	124	1	and	and	CCONJ
ejpam-214	124	2	p	p	X
ejpam-214	124	3	>	>	X
ejpam-214	124	4	0	0	PROPN
ejpam-214	124	5	,	,	PUNCT
ejpam-214	124	6	the	the	DET
ejpam-214	124	7	hessian	hessian	NOUN
ejpam-214	124	8	of	of	ADP
ejpam-214	124	9	fp	fp	PROPN
ejpam-214	124	10	(	(	PUNCT
ejpam-214	124	11	x	x	INTJ
ejpam-214	124	12	,	,	PUNCT
ejpam-214	124	13	λ	λ	NOUN
ejpam-214	124	14	)	)	PUNCT
ejpam-214	124	15	is	be	AUX
ejpam-214	124	16	positive	positive	ADJ
ejpam-214	124	17	definite	definite	ADJ
ejpam-214	124	18	for	for	ADP
ejpam-214	124	19	any	any	DET
ejpam-214	124	20	x	x	PROPN
ejpam-214	124	21	∈	∈	PROPN
ejpam-214	124	22	rn	rn	PROPN
ejpam-214	124	23	,	,	PUNCT
ejpam-214	124	24	i.e.	i.e.	X
ejpam-214	124	25	fp	fp	X
ejpam-214	124	26	(	(	PUNCT
ejpam-214	124	27	x	x	INTJ
ejpam-214	124	28	,	,	PUNCT
ejpam-214	124	29	λ	λ	X
ejpam-214	124	30	)	)	PUNCT
ejpam-214	124	31	is	be	AUX
ejpam-214	124	32	strictly	strictly	ADV
ejpam-214	124	33	convex	convex	ADJ
ejpam-214	124	34	in	in	ADP
ejpam-214	124	35	rn	rn	PROPN
ejpam-214	124	36	and	and	CCONJ
ejpam-214	124	37	strongly	strongly	ADV
ejpam-214	124	38	convex	convex	VERB
ejpam-214	124	39	on	on	ADP
ejpam-214	124	40	any	any	DET
ejpam-214	124	41	bounded	bounded	ADJ
ejpam-214	124	42	set	set	NOUN
ejpam-214	124	43	in	in	ADP
ejpam-214	124	44	rn	rn	PROPN
ejpam-214	124	45	.	.	PROPN
ejpam-214	124	46	remark	remark	PROPN
ejpam-214	124	47	2	2	NUM
ejpam-214	124	48	.	.	PUNCT
ejpam-214	125	1	as	as	SCONJ
ejpam-214	125	2	the	the	DET
ejpam-214	125	3	approximation	approximation	NOUN
ejpam-214	125	4	function	function	NOUN
ejpam-214	125	5	(	(	PUNCT
ejpam-214	125	6	3	3	X
ejpam-214	125	7	)	)	PUNCT
ejpam-214	125	8	is	be	AUX
ejpam-214	125	9	obtained	obtain	VERB
ejpam-214	125	10	by	by	ADP
ejpam-214	125	11	the	the	DET
ejpam-214	125	12	cross	cross	ADJ
ejpam-214	125	13	-	-	ADJ
ejpam-214	125	14	entropic	entropic	ADJ
ejpam-214	125	15	regularization	regularization	NOUN
ejpam-214	125	16	of	of	ADP
ejpam-214	125	17	classical	classical	ADJ
ejpam-214	125	18	lagrangian	lagrangian	NOUN
ejpam-214	125	19	,	,	PUNCT
ejpam-214	125	20	so	so	CCONJ
ejpam-214	125	21	when	when	SCONJ
ejpam-214	125	22	we	we	PRON
ejpam-214	125	23	treat	treat	VERB
ejpam-214	125	24	function	function	NOUN
ejpam-214	125	25	(	(	PUNCT
ejpam-214	125	26	3	3	NUM
ejpam-214	125	27	)	)	PUNCT
ejpam-214	125	28	as	as	ADP
ejpam-214	125	29	a	a	DET
ejpam-214	125	30	nonlinear	nonlinear	ADJ
ejpam-214	125	31	lagrangian	lagrangian	ADJ
ejpam-214	125	32	function	function	NOUN
ejpam-214	125	33	of	of	ADP
ejpam-214	125	34	the	the	DET
ejpam-214	125	35	min	min	PROPN
ejpam-214	125	36	-	-	ADJ
ejpam-214	125	37	max	max	PROPN
ejpam-214	125	38	problem	problem	NOUN
ejpam-214	125	39	,	,	PUNCT
ejpam-214	125	40	under	under	ADP
ejpam-214	125	41	the	the	DET
ejpam-214	125	42	same	same	ADJ
ejpam-214	125	43	conditions	condition	NOUN
ejpam-214	125	44	in	in	ADP
ejpam-214	125	45	theorem	theorem	NOUN
ejpam-214	125	46	2	2	NUM
ejpam-214	125	47	,	,	PUNCT
ejpam-214	125	48	for	for	ADP
ejpam-214	125	49	p	p	PROPN
ejpam-214	125	50	>	>	X
ejpam-214	125	51	p0	p0	NOUN
ejpam-214	125	52	we	we	PRON
ejpam-214	125	53	can	can	AUX
ejpam-214	125	54	have	have	VERB
ejpam-214	125	55	the	the	DET
ejpam-214	125	56	similar	similar	ADJ
ejpam-214	125	57	saddle	saddle	NOUN
ejpam-214	125	58	point	point	NOUN
ejpam-214	125	59	result	result	VERB
ejpam-214	125	60	fp	fp	PROPN
ejpam-214	125	61	�	�	PROPN
ejpam-214	125	62	x	x	SYM
ejpam-214	125	63	,	,	PUNCT
ejpam-214	125	64	λ∗	λ∗	PROPN
ejpam-214	125	65	�	�	PROPN
ejpam-214	125	66	≥	≥	PROPN
ejpam-214	125	67	fp	fp	PROPN
ejpam-214	125	68	�	�	PROPN
ejpam-214	125	69	x∗,λ∗	x∗,λ∗	PROPN
ejpam-214	125	70	�	�	PROPN
ejpam-214	125	71	≥	≥	PROPN
ejpam-214	125	72	fp	fp	PROPN
ejpam-214	125	73	�	�	PROPN
ejpam-214	125	74	x∗,λ	x∗,λ	PROPN
ejpam-214	125	75	�	�	PROPN
ejpam-214	125	76	,	,	PUNCT
ejpam-214	125	77	∀x	∀x	NOUN
ejpam-214	125	78	∈	∈	PROPN
ejpam-214	125	79	u	u	NOUN
ejpam-214	125	80	(	(	PUNCT
ejpam-214	125	81	x	x	INTJ
ejpam-214	125	82	,	,	PUNCT
ejpam-214	125	83	ǫ	ǫ	NOUN
ejpam-214	125	84	)	)	PUNCT
ejpam-214	125	85	(	(	PUNCT
ejpam-214	125	86	23	23	NUM
ejpam-214	125	87	)	)	PUNCT
ejpam-214	125	88	3.3	3.3	NUM
ejpam-214	125	89	.	.	PUNCT
ejpam-214	126	1	condition	condition	NOUN
ejpam-214	126	2	number	number	NOUN
ejpam-214	126	3	based	base	VERB
ejpam-214	126	4	on	on	ADP
ejpam-214	126	5	the	the	DET
ejpam-214	126	6	analysis	analysis	NOUN
ejpam-214	126	7	in	in	ADP
ejpam-214	126	8	subsection	subsection	NOUN
ejpam-214	126	9	3.2	3.2	NUM
ejpam-214	126	10	,	,	PUNCT
ejpam-214	126	11	we	we	PRON
ejpam-214	126	12	give	give	VERB
ejpam-214	126	13	the	the	DET
ejpam-214	126	14	following	follow	VERB
ejpam-214	126	15	result	result	NOUN
ejpam-214	126	16	about	about	ADP
ejpam-214	126	17	the	the	DET
ejpam-214	126	18	condition	condition	NOUN
ejpam-214	126	19	number	number	NOUN
ejpam-214	126	20	.	.	PUNCT
ejpam-214	127	1	theorem	theorem	NOUN
ejpam-214	127	2	3	3	X
ejpam-214	127	3	.	.	PUNCT
ejpam-214	128	1	let	let	AUX
ejpam-214	128	2	(	(	PUNCT
ejpam-214	128	3	x∗,λ∗	x∗,λ∗	PROPN
ejpam-214	128	4	)	)	PUNCT
ejpam-214	128	5	be	be	VERB
ejpam-214	128	6	k	k	NOUN
ejpam-214	128	7	−	−	PROPN
ejpam-214	129	1	k	k	INTJ
ejpam-214	129	2	−	−	PROPN
ejpam-214	129	3	t	t	PROPN
ejpam-214	129	4	pair	pair	NOUN
ejpam-214	129	5	of	of	ADP
ejpam-214	129	6	min	min	ADJ
ejpam-214	129	7	-	-	ADJ
ejpam-214	129	8	max	max	PROPN
ejpam-214	129	9	problem	problem	NOUN
ejpam-214	129	10	(	(	PUNCT
ejpam-214	129	11	1	1	NUM
ejpam-214	129	12	)	)	PUNCT
ejpam-214	130	1	,	,	PUNCT
ejpam-214	130	2	assume	assume	VERB
ejpam-214	130	3	that	that	SCONJ
ejpam-214	130	4	∇	∇	X
ejpam-214	130	5	fi	fi	X
ejpam-214	130	6	(	(	PUNCT
ejpam-214	130	7	x	x	NOUN
ejpam-214	130	8	∗	∗	NOUN
ejpam-214	130	9	)	)	PUNCT
ejpam-214	130	10	,	,	PUNCT
ejpam-214	130	11	i	i	PRON
ejpam-214	130	12	∈	∈	VERB
ejpam-214	130	13	i	i	PRON
ejpam-214	130	14	(	(	PUNCT
ejpam-214	130	15	x∗	x∗	PROPN
ejpam-214	130	16	)	)	PUNCT
ejpam-214	130	17	are	be	AUX
ejpam-214	130	18	linearly	linearly	ADV
ejpam-214	130	19	independent	independent	ADJ
ejpam-214	130	20	and	and	CCONJ
ejpam-214	130	21	the	the	DET
ejpam-214	130	22	second	second	ADJ
ejpam-214	130	23	-	-	PUNCT
ejpam-214	130	24	order	order	NOUN
ejpam-214	130	25	sufficiency	sufficiency	NOUN
ejpam-214	130	26	condition	condition	NOUN
ejpam-214	130	27	is	be	AUX
ejpam-214	130	28	satisfied	satisfied	ADJ
ejpam-214	130	29	,	,	PUNCT
ejpam-214	130	30	then	then	ADV
ejpam-214	130	31	there	there	PRON
ejpam-214	130	32	exists	exist	VERB
ejpam-214	130	33	p0	p0	NOUN
ejpam-214	130	34	and	and	CCONJ
ejpam-214	130	35	m0	m0	PROPN
ejpam-214	131	1	≥	≥	NUM
ejpam-214	131	2	τ0	τ0	NOUN
ejpam-214	131	3	≥	≥	PRON
ejpam-214	131	4	0	0	NUM
ejpam-214	132	1	that	that	SCONJ
ejpam-214	132	2	m0	m0	PROPN
ejpam-214	132	3	〈	〈	PROPN
ejpam-214	132	4	d	d	PROPN
ejpam-214	132	5	,	,	PUNCT
ejpam-214	132	6	d	d	X
ejpam-214	132	7	〉	〉	ADJ
ejpam-214	132	8	¾	¾	NOUN
ejpam-214	132	9	¬	¬	NOUN
ejpam-214	132	10	∇2	∇2	X
ejpam-214	132	11	x	x	PUNCT
ejpam-214	132	12	x	x	PUNCT
ejpam-214	132	13	fp	fp	PROPN
ejpam-214	132	14	�	�	PROPN
ejpam-214	132	15	x∗,λ∗	x∗,λ∗	PROPN
ejpam-214	132	16	�	�	PROPN
ejpam-214	132	17	d	d	PROPN
ejpam-214	132	18	,	,	PUNCT
ejpam-214	132	19	d	d	PROPN
ejpam-214	132	20	¶	¶	PROPN
ejpam-214	132	21	¾	¾	PROPN
ejpam-214	132	22	τ0	τ0	NOUN
ejpam-214	132	23	〈	〈	PROPN
ejpam-214	132	24	d	d	NOUN
ejpam-214	132	25	,	,	PUNCT
ejpam-214	132	26	d	d	SYM
ejpam-214	132	27	〉	〉	X
ejpam-214	132	28	(	(	PUNCT
ejpam-214	132	29	24	24	NUM
ejpam-214	132	30	)	)	PUNCT
ejpam-214	132	31	is	be	AUX
ejpam-214	132	32	true	true	ADJ
ejpam-214	132	33	for	for	ADP
ejpam-214	132	34	any	any	DET
ejpam-214	132	35	fixed	fix	VERB
ejpam-214	132	36	p	p	NOUN
ejpam-214	132	37	≥	≥	NOUN
ejpam-214	132	38	p0	p0	NOUN
ejpam-214	132	39	.	.	PUNCT
ejpam-214	133	1	proof	proof	NOUN
ejpam-214	133	2	.	.	PUNCT
ejpam-214	134	1	the	the	DET
ejpam-214	134	2	right	right	ADJ
ejpam-214	134	3	inequality	inequality	NOUN
ejpam-214	134	4	is	be	AUX
ejpam-214	134	5	the	the	DET
ejpam-214	134	6	result	result	NOUN
ejpam-214	134	7	in	in	ADP
ejpam-214	134	8	theorem	theorem	NOUN
ejpam-214	134	9	2	2	NUM
ejpam-214	134	10	,	,	PUNCT
ejpam-214	134	11	and	and	CCONJ
ejpam-214	134	12	the	the	DET
ejpam-214	134	13	left	left	ADJ
ejpam-214	134	14	inequality	inequality	NOUN
ejpam-214	134	15	follows	follow	VERB
ejpam-214	134	16	from	from	ADP
ejpam-214	134	17	the	the	DET
ejpam-214	134	18	formulas	formula	NOUN
ejpam-214	134	19	(	(	PUNCT
ejpam-214	134	20	20	20	NUM
ejpam-214	134	21	)	)	PUNCT
ejpam-214	134	22	and	and	CCONJ
ejpam-214	134	23	(	(	PUNCT
ejpam-214	134	24	21	21	NUM
ejpam-214	134	25	)	)	PUNCT
ejpam-214	134	26	if	if	SCONJ
ejpam-214	134	27	p	p	PROPN
ejpam-214	134	28	≥	≥	NOUN
ejpam-214	134	29	p0	p0	NOUN
ejpam-214	134	30	and	and	CCONJ
ejpam-214	134	31	p0	p0	NOUN
ejpam-214	134	32	large	large	ADJ
ejpam-214	134	33	enough	enough	ADV
ejpam-214	134	34	.	.	PUNCT
ejpam-214	135	1	corollary	corollary	ADJ
ejpam-214	135	2	2	2	NUM
ejpam-214	135	3	.	.	PUNCT
ejpam-214	136	1	if	if	SCONJ
ejpam-214	136	2	fi(x	fi(x	NUM
ejpam-214	136	3	)	)	PUNCT
ejpam-214	136	4	are	be	AUX
ejpam-214	136	5	twice	twice	ADV
ejpam-214	136	6	continuous	continuous	ADJ
ejpam-214	136	7	differentiable	differentiable	NOUN
ejpam-214	136	8	and	and	CCONJ
ejpam-214	136	9	ǫ	ǫ	DET
ejpam-214	136	10	≥	≥	NOUN
ejpam-214	136	11	0	0	NUM
ejpam-214	136	12	is	be	AUX
ejpam-214	136	13	small	small	ADJ
ejpam-214	136	14	enough	enough	ADV
ejpam-214	136	15	then	then	ADV
ejpam-214	136	16	for	for	ADP
ejpam-214	136	17	any	any	DET
ejpam-214	136	18	fixed	fix	VERB
ejpam-214	136	19	p	p	NOUN
ejpam-214	136	20	≥	≥	NOUN
ejpam-214	136	21	p0	p0	NOUN
ejpam-214	136	22	,	,	PUNCT
ejpam-214	136	23	there	there	PRON
ejpam-214	136	24	exists	exist	VERB
ejpam-214	136	25	m	m	VERB
ejpam-214	136	26	≥	≥	NOUN
ejpam-214	136	27	τ	τ	X
ejpam-214	136	28	≥	≥	NOUN
ejpam-214	136	29	0	0	NUM
ejpam-214	136	30	such	such	ADJ
ejpam-214	136	31	that	that	PRON
ejpam-214	136	32	for	for	ADP
ejpam-214	136	33	any	any	DET
ejpam-214	136	34	pair	pair	NOUN
ejpam-214	136	35	ω	ω	NOUN
ejpam-214	136	36	=	=	SYM
ejpam-214	136	37	(	(	PUNCT
ejpam-214	136	38	x	x	INTJ
ejpam-214	136	39	,	,	PUNCT
ejpam-214	136	40	λ	λ	NOUN
ejpam-214	136	41	)	)	PUNCT
ejpam-214	136	42	∈	∈	PROPN
ejpam-214	136	43	u	u	NOUN
ejpam-214	136	44	(	(	PUNCT
ejpam-214	136	45	ω∗,ǫ	ω∗,ǫ	NOUN
ejpam-214	136	46	)	)	PUNCT
ejpam-214	136	47	=	=	PRON
ejpam-214	137	1	{	{	PUNCT
ejpam-214	137	2	ω|ω−ω∗|	ω|ω−ω∗|	NUM
ejpam-214	137	3	¶	¶	NOUN
ejpam-214	137	4	ǫ	ǫ	NOUN
ejpam-214	137	5	}	}	PUNCT
ejpam-214	137	6	the	the	DET
ejpam-214	137	7	following	follow	VERB
ejpam-214	137	8	inequalities	inequality	NOUN
ejpam-214	137	9	m	m	VERB
ejpam-214	137	10	〈	〈	PROPN
ejpam-214	137	11	d	d	PROPN
ejpam-214	137	12	,	,	PUNCT
ejpam-214	137	13	d	d	X
ejpam-214	137	14	〉	〉	ADJ
ejpam-214	137	15	¾	¾	NOUN
ejpam-214	137	16	¬	¬	NOUN
ejpam-214	137	17	∇2	∇2	X
ejpam-214	137	18	x	x	PUNCT
ejpam-214	137	19	x	x	PUNCT
ejpam-214	137	20	fp	fp	PROPN
ejpam-214	137	21	�	�	PROPN
ejpam-214	137	22	x∗,λ∗	x∗,λ∗	PROPN
ejpam-214	137	23	�	�	PROPN
ejpam-214	138	1	d	d	PROPN
ejpam-214	138	2	,	,	PUNCT
ejpam-214	138	3	d	d	PROPN
ejpam-214	138	4	¶	¶	PROPN
ejpam-214	138	5	¾	¾	PROPN
ejpam-214	138	6	τ	τ	PROPN
ejpam-214	138	7	〈	〈	PROPN
ejpam-214	138	8	d	d	PROPN
ejpam-214	138	9	,	,	PUNCT
ejpam-214	138	10	d	d	SYM
ejpam-214	138	11	〉	〉	NOUN
ejpam-214	138	12	,	,	PUNCT
ejpam-214	138	13	∀d	∀d	PROPN
ejpam-214	138	14	∈	∈	PROPN
ejpam-214	138	15	rn	rn	PROPN
ejpam-214	138	16	(	(	PUNCT
ejpam-214	138	17	25	25	NUM
ejpam-214	138	18	)	)	PUNCT
ejpam-214	138	19	hold	hold	VERB
ejpam-214	138	20	true	true	ADJ
ejpam-214	138	21	.	.	PUNCT
ejpam-214	139	1	references	reference	NOUN
ejpam-214	139	2	105	105	NUM
ejpam-214	140	1	so	so	SCONJ
ejpam-214	140	2	the	the	DET
ejpam-214	140	3	theorem	theorem	NOUN
ejpam-214	140	4	3	3	NUM
ejpam-214	140	5	and	and	CCONJ
ejpam-214	140	6	the	the	DET
ejpam-214	140	7	corollary	corollary	ADJ
ejpam-214	140	8	2	2	NUM
ejpam-214	140	9	mean	mean	VERB
ejpam-214	140	10	that	that	SCONJ
ejpam-214	140	11	in	in	ADP
ejpam-214	140	12	the	the	DET
ejpam-214	140	13	neighborhood	neighborhood	NOUN
ejpam-214	140	14	of	of	ADP
ejpam-214	140	15	the	the	DET
ejpam-214	140	16	k−k−	k−k−	PROPN
ejpam-214	140	17	t	t	PROPN
ejpam-214	140	18	pair	pair	NOUN
ejpam-214	140	19	(	(	PUNCT
ejpam-214	140	20	x∗,λ∗	x∗,λ∗	PROPN
ejpam-214	140	21	)	)	PUNCT
ejpam-214	140	22	the	the	DET
ejpam-214	140	23	condition	condition	NOUN
ejpam-214	140	24	number	number	NOUN
ejpam-214	140	25	cond∇2	cond∇2	PROPN
ejpam-214	140	26	x	x	PROPN
ejpam-214	140	27	x	x	SYM
ejpam-214	140	28	fp	fp	INTJ
ejpam-214	140	29	(	(	PUNCT
ejpam-214	140	30	x	x	INTJ
ejpam-214	140	31	,	,	PUNCT
ejpam-214	140	32	λ)¶	λ)¶	PROPN
ejpam-214	140	33	τ	τ	PROPN
ejpam-214	140	34	m	m	VERB
ejpam-214	140	35	is	be	AUX
ejpam-214	140	36	stable	stable	ADJ
ejpam-214	140	37	for	for	ADP
ejpam-214	140	38	any	any	DET
ejpam-214	140	39	fixed	fix	VERB
ejpam-214	140	40	p	p	NOUN
ejpam-214	140	41	≥	≥	NOUN
ejpam-214	140	42	p0	p0	NOUN
ejpam-214	140	43	.	.	PUNCT
ejpam-214	141	1	remark	remark	PROPN
ejpam-214	141	2	3	3	NUM
ejpam-214	141	3	.	.	PUNCT
ejpam-214	142	1	only	only	ADV
ejpam-214	142	2	the	the	DET
ejpam-214	142	3	first	first	ADJ
ejpam-214	142	4	order	order	NOUN
ejpam-214	142	5	information	information	NOUN
ejpam-214	142	6	results	result	NOUN
ejpam-214	142	7	in	in	ADP
ejpam-214	142	8	subsection	subsection	NOUN
ejpam-214	142	9	3.1	3.1	NUM
ejpam-214	142	10	need	need	VERB
ejpam-214	142	11	the	the	DET
ejpam-214	142	12	convexity	convexity	NOUN
ejpam-214	142	13	assumption	assumption	NOUN
ejpam-214	142	14	.	.	PUNCT
ejpam-214	143	1	the	the	DET
ejpam-214	143	2	results	result	NOUN
ejpam-214	143	3	in	in	ADP
ejpam-214	143	4	subsection	subsection	NOUN
ejpam-214	143	5	3.2	3.2	NUM
ejpam-214	143	6	and	and	CCONJ
ejpam-214	143	7	3.3	3.3	NUM
ejpam-214	143	8	are	be	AUX
ejpam-214	143	9	true	true	ADJ
ejpam-214	143	10	whether	whether	SCONJ
ejpam-214	143	11	f(x	f(x	PROPN
ejpam-214	143	12	)	)	PUNCT
ejpam-214	143	13	and	and	CCONJ
ejpam-214	143	14	all	all	DET
ejpam-214	143	15	fi(x	fi(x	NUM
ejpam-214	143	16	)	)	PUNCT
ejpam-214	143	17	are	be	AUX
ejpam-214	143	18	convex	convex	ADJ
ejpam-214	143	19	or	or	CCONJ
ejpam-214	143	20	not	not	PART
ejpam-214	143	21	.	.	PUNCT
ejpam-214	144	1	4	4	X
ejpam-214	144	2	.	.	X
ejpam-214	144	3	concluding	conclude	VERB
ejpam-214	144	4	remarks	remark	NOUN
ejpam-214	144	5	as	as	ADP
ejpam-214	144	6	the	the	DET
ejpam-214	144	7	uniform	uniform	ADJ
ejpam-214	144	8	convergence	convergence	NOUN
ejpam-214	144	9	and	and	CCONJ
ejpam-214	144	10	the	the	DET
ejpam-214	144	11	algorithm	algorithm	NOUN
ejpam-214	144	12	are	be	AUX
ejpam-214	144	13	well	well	ADV
ejpam-214	144	14	known	know	VERB
ejpam-214	144	15	concepts	concept	NOUN
ejpam-214	144	16	,	,	PUNCT
ejpam-214	144	17	in	in	ADP
ejpam-214	144	18	this	this	DET
ejpam-214	144	19	paper	paper	NOUN
ejpam-214	144	20	we	we	PRON
ejpam-214	144	21	have	have	AUX
ejpam-214	144	22	given	give	VERB
ejpam-214	144	23	some	some	DET
ejpam-214	144	24	basic	basic	ADJ
ejpam-214	144	25	results	result	NOUN
ejpam-214	144	26	that	that	PRON
ejpam-214	144	27	are	be	AUX
ejpam-214	144	28	required	require	VERB
ejpam-214	144	29	for	for	ADP
ejpam-214	144	30	the	the	DET
ejpam-214	144	31	analysis	analysis	NOUN
ejpam-214	144	32	of	of	ADP
ejpam-214	144	33	this	this	DET
ejpam-214	144	34	research	research	NOUN
ejpam-214	144	35	.	.	PUNCT
ejpam-214	145	1	it	it	PRON
ejpam-214	145	2	should	should	AUX
ejpam-214	145	3	be	be	AUX
ejpam-214	145	4	noticed	notice	VERB
ejpam-214	145	5	that	that	SCONJ
ejpam-214	145	6	the	the	DET
ejpam-214	145	7	efficiency	efficiency	NOUN
ejpam-214	145	8	of	of	ADP
ejpam-214	145	9	this	this	DET
ejpam-214	145	10	smoothing	smoothing	NOUN
ejpam-214	145	11	method	method	NOUN
ejpam-214	145	12	of	of	ADP
ejpam-214	145	13	multipliers	multiplier	NOUN
ejpam-214	145	14	depends	depend	VERB
ejpam-214	145	15	on	on	ADP
ejpam-214	145	16	the	the	DET
ejpam-214	145	17	parameter	parameter	NOUN
ejpam-214	145	18	p.	p.	PROPN
ejpam-214	145	19	a	a	DET
ejpam-214	145	20	similar	similar	ADJ
ejpam-214	145	21	parameter	parameter	NOUN
ejpam-214	145	22	analysis	analysis	NOUN
ejpam-214	145	23	in	in	ADP
ejpam-214	145	24	the	the	DET
ejpam-214	145	25	nonlinear	nonlinear	ADJ
ejpam-214	145	26	rescaling	rescaling	NOUN
ejpam-214	145	27	method	method	NOUN
ejpam-214	145	28	for	for	ADP
ejpam-214	145	29	the	the	DET
ejpam-214	145	30	constrained	constrain	VERB
ejpam-214	145	31	optimization	optimization	NOUN
ejpam-214	145	32	problems	problem	NOUN
ejpam-214	145	33	is	be	AUX
ejpam-214	145	34	discussed	discuss	VERB
ejpam-214	145	35	in	in	ADP
ejpam-214	145	36	[	[	X
ejpam-214	145	37	18	18	NUM
ejpam-214	145	38	]	]	PUNCT
ejpam-214	145	39	.	.	PUNCT
ejpam-214	146	1	for	for	ADP
ejpam-214	146	2	this	this	PRON
ejpam-214	146	3	,	,	PUNCT
ejpam-214	146	4	some	some	DET
ejpam-214	146	5	problems	problem	NOUN
ejpam-214	146	6	are	be	AUX
ejpam-214	146	7	investigated	investigate	VERB
ejpam-214	146	8	,	,	PUNCT
ejpam-214	146	9	such	such	ADJ
ejpam-214	146	10	as	as	ADP
ejpam-214	146	11	,	,	PUNCT
ejpam-214	146	12	for	for	ADP
ejpam-214	146	13	the	the	DET
ejpam-214	146	14	min	min	PROPN
ejpam-214	146	15	-	-	ADJ
ejpam-214	146	16	max	max	PROPN
ejpam-214	146	17	problem	problem	NOUN
ejpam-214	146	18	to	to	PART
ejpam-214	146	19	find	find	VERB
ejpam-214	146	20	an	an	DET
ejpam-214	146	21	explicit	explicit	ADJ
ejpam-214	146	22	general	general	ADJ
ejpam-214	146	23	threshold	threshold	NOUN
ejpam-214	146	24	value	value	NOUN
ejpam-214	146	25	of	of	ADP
ejpam-214	146	26	p.	p.	NOUN
ejpam-214	146	27	the	the	DET
ejpam-214	146	28	smoothing	smooth	VERB
ejpam-214	146	29	approximation	approximation	NOUN
ejpam-214	146	30	has	have	VERB
ejpam-214	146	31	some	some	DET
ejpam-214	146	32	properties	property	NOUN
ejpam-214	146	33	that	that	PRON
ejpam-214	146	34	are	be	AUX
ejpam-214	146	35	related	relate	VERB
ejpam-214	146	36	to	to	ADP
ejpam-214	146	37	the	the	DET
ejpam-214	146	38	parameter	parameter	NOUN
ejpam-214	147	1	p.	p.	PROPN
ejpam-214	147	2	the	the	DET
ejpam-214	147	3	research	research	NOUN
ejpam-214	147	4	(	(	PUNCT
ejpam-214	147	5	including	include	VERB
ejpam-214	147	6	the	the	DET
ejpam-214	147	7	implementations	implementation	NOUN
ejpam-214	147	8	,	,	PUNCT
ejpam-214	147	9	properties	property	NOUN
ejpam-214	147	10	and	and	CCONJ
ejpam-214	147	11	so	so	ADV
ejpam-214	147	12	on	on	ADV
ejpam-214	147	13	)	)	PUNCT
ejpam-214	147	14	of	of	ADP
ejpam-214	147	15	the	the	DET
ejpam-214	147	16	smoothing	smoothing	NOUN
ejpam-214	147	17	method	method	NOUN
ejpam-214	147	18	of	of	ADP
ejpam-214	147	19	multipliers	multiplier	NOUN
ejpam-214	147	20	leads	lead	VERB
ejpam-214	147	21	to	to	ADP
ejpam-214	147	22	an	an	DET
ejpam-214	147	23	important	important	ADJ
ejpam-214	147	24	subject	subject	NOUN
ejpam-214	147	25	for	for	ADP
ejpam-214	147	26	research	research	NOUN
ejpam-214	147	27	.	.	PUNCT
ejpam-214	148	1	acknowledgements	acknowledgement	NOUN
ejpam-214	148	2	the	the	DET
ejpam-214	148	3	authors	author	NOUN
ejpam-214	148	4	would	would	AUX
ejpam-214	148	5	like	like	VERB
ejpam-214	148	6	to	to	PART
ejpam-214	148	7	thank	thank	VERB
ejpam-214	148	8	the	the	DET
ejpam-214	148	9	referees	referee	NOUN
ejpam-214	148	10	for	for	ADP
ejpam-214	148	11	their	their	PRON
ejpam-214	148	12	helpful	helpful	ADJ
ejpam-214	148	13	suggestions	suggestion	NOUN
ejpam-214	148	14	.	.	PUNCT
ejpam-214	149	1	this	this	DET
ejpam-214	149	2	work	work	NOUN
ejpam-214	149	3	is	be	AUX
ejpam-214	149	4	supported	support	VERB
ejpam-214	149	5	by	by	ADP
ejpam-214	149	6	the	the	DET
ejpam-214	149	7	national	national	ADJ
ejpam-214	149	8	natural	natural	PROPN
ejpam-214	149	9	science	science	PROPN
ejpam-214	149	10	foundation	foundation	PROPN
ejpam-214	149	11	of	of	ADP
ejpam-214	149	12	china	china	PROPN
ejpam-214	149	13	grant(no	grant(no	PROPN
ejpam-214	149	14	.	.	PUNCT
ejpam-214	150	1	10902077	10902077	NUM
ejpam-214	150	2	,	,	PUNCT
ejpam-214	150	3	60675046	60675046	NUM
ejpam-214	150	4	)	)	PUNCT
ejpam-214	150	5	.	.	PUNCT
ejpam-214	151	1	references	reference	NOUN
ejpam-214	151	2	[	[	X
ejpam-214	151	3	1	1	NUM
ejpam-214	151	4	]	]	PUNCT
ejpam-214	151	5	d.p.bertsekas	d.p.bertseka	NOUN
ejpam-214	151	6	,	,	PUNCT
ejpam-214	151	7	constrained	constrain	VERB
ejpam-214	151	8	optimization	optimization	NOUN
ejpam-214	151	9	and	and	CCONJ
ejpam-214	151	10	lagrange	lagrange	NOUN
ejpam-214	151	11	multiplier	multipli	ADJ
ejpam-214	151	12	methods	method	NOUN
ejpam-214	151	13	,	,	PUNCT
ejpam-214	151	14	academic	academic	ADJ
ejpam-214	151	15	press	press	NOUN
ejpam-214	151	16	,	,	PUNCT
ejpam-214	151	17	boston	boston	PROPN
ejpam-214	151	18	,	,	PUNCT
ejpam-214	151	19	ma	ma	PROPN
ejpam-214	151	20	,	,	PUNCT
ejpam-214	151	21	1982	1982	NUM
ejpam-214	151	22	.	.	PUNCT
ejpam-214	152	1	[	[	X
ejpam-214	152	2	2	2	NUM
ejpam-214	152	3	]	]	X
ejpam-214	152	4	c.charalammbous	c.charalammbous	ADJ
ejpam-214	152	5	,	,	PUNCT
ejpam-214	152	6	a.r.conn	a.r.conn	NOUN
ejpam-214	152	7	,	,	PUNCT
ejpam-214	152	8	an	an	DET
ejpam-214	152	9	efficient	efficient	ADJ
ejpam-214	152	10	method	method	NOUN
ejpam-214	152	11	to	to	PART
ejpam-214	152	12	solve	solve	VERB
ejpam-214	152	13	the	the	DET
ejpam-214	152	14	minimax	minimax	NOUN
ejpam-214	152	15	problem	problem	NOUN
ejpam-214	152	16	directly	directly	ADV
ejpam-214	152	17	,	,	PUNCT
ejpam-214	152	18	siam	siam	ADJ
ejpam-214	152	19	journal	journal	NOUN
ejpam-214	152	20	on	on	ADP
ejpam-214	152	21	numerical	numerical	ADJ
ejpam-214	152	22	analysis	analysis	NOUN
ejpam-214	152	23	,	,	PUNCT
ejpam-214	152	24	15	15	NUM
ejpam-214	152	25	:	:	SYM
ejpam-214	152	26	162	162	NUM
ejpam-214	152	27	-	-	SYM
ejpam-214	152	28	187	187	NUM
ejpam-214	152	29	(	(	PUNCT
ejpam-214	152	30	1978	1978	NUM
ejpam-214	152	31	)	)	PUNCT
ejpam-214	152	32	.	.	PUNCT
ejpam-214	153	1	[	[	X
ejpam-214	153	2	3	3	X
ejpam-214	153	3	]	]	X
ejpam-214	153	4	e.polak	e.polak	NOUN
ejpam-214	153	5	,	,	PUNCT
ejpam-214	153	6	d.q.mayne	d.q.mayne	NOUN
ejpam-214	153	7	,	,	PUNCT
ejpam-214	153	8	j.e.higgins	j.e.higgin	NOUN
ejpam-214	153	9	,	,	PUNCT
ejpam-214	153	10	superlinearly	superlinearly	ADV
ejpam-214	153	11	convergent	convergent	ADJ
ejpam-214	153	12	algorithm	algorithm	NOUN
ejpam-214	153	13	for	for	ADP
ejpam-214	153	14	min	min	PROPN
ejpam-214	153	15	-	-	ADJ
ejpam-214	153	16	max	max	PROPN
ejpam-214	153	17	problems	problem	NOUN
ejpam-214	153	18	,	,	PUNCT
ejpam-214	153	19	journal	journal	NOUN
ejpam-214	153	20	of	of	ADP
ejpam-214	153	21	optimization	optimization	NOUN
ejpam-214	153	22	theory	theory	NOUN
ejpam-214	153	23	and	and	CCONJ
ejpam-214	153	24	applications	application	NOUN
ejpam-214	153	25	,	,	PUNCT
ejpam-214	153	26	69(3	69(3	NUM
ejpam-214	153	27	):	):	PUNCT
ejpam-214	153	28	407	407	NUM
ejpam-214	153	29	-	-	SYM
ejpam-214	153	30	439	439	NUM
ejpam-214	153	31	(	(	PUNCT
ejpam-214	153	32	1991	1991	NUM
ejpam-214	153	33	)	)	PUNCT
ejpam-214	153	34	.	.	PUNCT
ejpam-214	154	1	[	[	X
ejpam-214	154	2	4	4	NUM
ejpam-214	154	3	]	]	SYM
ejpam-214	154	4	a.ben	a.ben	NOUN
ejpam-214	154	5	-	-	PUNCT
ejpam-214	154	6	tal	tal	ADJ
ejpam-214	154	7	,	,	PUNCT
ejpam-214	154	8	a.nemirovsky	a.nemirovsky	ADV
ejpam-214	154	9	,	,	PUNCT
ejpam-214	154	10	convex	convex	ADJ
ejpam-214	154	11	optimization	optimization	NOUN
ejpam-214	154	12	in	in	ADP
ejpam-214	154	13	engineering	engineering	NOUN
ejpam-214	154	14	:	:	PUNCT
ejpam-214	154	15	modeling	model	VERB
ejpam-214	154	16	analysis	analysis	NOUN
ejpam-214	154	17	,	,	PUNCT
ejpam-214	154	18	algorithms	algorithm	NOUN
ejpam-214	154	19	,	,	PUNCT
ejpam-214	154	20	technion	technion	PROPN
ejpam-214	154	21	,	,	PUNCT
ejpam-214	154	22	israel	israel	PROPN
ejpam-214	154	23	,	,	PUNCT
ejpam-214	154	24	1998	1998	NUM
ejpam-214	154	25	.	.	PUNCT
ejpam-214	155	1	[	[	X
ejpam-214	155	2	5	5	NUM
ejpam-214	155	3	]	]	PUNCT
ejpam-214	155	4	v.f.demyanov	v.f.demyanov	PROPN
ejpam-214	155	5	,	,	PUNCT
ejpam-214	155	6	v.n.molozemov	v.n.molozemov	NOUN
ejpam-214	155	7	,	,	PUNCT
ejpam-214	155	8	introduction	introduction	NOUN
ejpam-214	155	9	to	to	ADP
ejpam-214	155	10	minimax	minimax	NOUN
ejpam-214	155	11	,	,	PUNCT
ejpam-214	155	12	wiley	wiley	NOUN
ejpam-214	155	13	,	,	PUNCT
ejpam-214	155	14	new	new	PROPN
ejpam-214	155	15	york	york	PROPN
ejpam-214	155	16	,	,	PUNCT
ejpam-214	155	17	1974	1974	NUM
ejpam-214	155	18	.	.	PUNCT
ejpam-214	156	1	[	[	X
ejpam-214	156	2	6	6	NUM
ejpam-214	156	3	]	]	X
ejpam-214	156	4	d.z.du	d.z.du	PROPN
ejpam-214	156	5	,	,	PUNCT
ejpam-214	156	6	p.m.pardalos	p.m.pardalo	NOUN
ejpam-214	156	7	,	,	PUNCT
ejpam-214	156	8	minimax	minimax	NOUN
ejpam-214	156	9	and	and	CCONJ
ejpam-214	156	10	applications	application	NOUN
ejpam-214	156	11	,	,	PUNCT
ejpam-214	156	12	kluwer	kluwer	NOUN
ejpam-214	156	13	academic	academic	ADJ
ejpam-214	156	14	publishers	publisher	NOUN
ejpam-214	156	15	,	,	PUNCT
ejpam-214	156	16	dordrecht	dordrecht	PROPN
ejpam-214	156	17	,	,	PUNCT
ejpam-214	156	18	1995	1995	NUM
ejpam-214	156	19	.	.	PUNCT
ejpam-214	157	1	[	[	X
ejpam-214	157	2	7	7	X
ejpam-214	157	3	]	]	X
ejpam-214	157	4	e.polak	e.polak	NOUN
ejpam-214	157	5	,	,	PUNCT
ejpam-214	157	6	optimization	optimization	NOUN
ejpam-214	157	7	:	:	PUNCT
ejpam-214	157	8	algorithm	algorithm	NOUN
ejpam-214	157	9	and	and	CCONJ
ejpam-214	157	10	consistent	consistent	ADJ
ejpam-214	157	11	approximations	approximation	NOUN
ejpam-214	157	12	,	,	PUNCT
ejpam-214	157	13	springer	springer	NOUN
ejpam-214	157	14	verlag	verlag	PROPN
ejpam-214	157	15	,	,	PUNCT
ejpam-214	157	16	new	new	PROPN
ejpam-214	157	17	york	york	PROPN
ejpam-214	157	18	,	,	PUNCT
ejpam-214	157	19	1997	1997	NUM
ejpam-214	157	20	.	.	PUNCT
ejpam-214	158	1	references	reference	NOUN
ejpam-214	158	2	106	106	NUM
ejpam-214	159	1	[	[	NOUN
ejpam-214	159	2	8	8	NUM
ejpam-214	159	3	]	]	PUNCT
ejpam-214	159	4	r.polyak	r.polyak	NOUN
ejpam-214	159	5	,	,	PUNCT
ejpam-214	159	6	on	on	ADP
ejpam-214	159	7	the	the	DET
ejpam-214	159	8	best	good	ADJ
ejpam-214	159	9	convex	convex	NOUN
ejpam-214	159	10	chebichev	chebichev	NOUN
ejpam-214	159	11	approximation	approximation	NOUN
ejpam-214	159	12	,	,	PUNCT
ejpam-214	159	13	soviet	soviet	PROPN
ejpam-214	159	14	mathematics	mathematics	PROPN
ejpam-214	159	15	doklady	doklady	PROPN
ejpam-214	159	16	,	,	PUNCT
ejpam-214	159	17	12	12	NUM
ejpam-214	159	18	:	:	SYM
ejpam-214	159	19	1441	1441	NUM
ejpam-214	159	20	-	-	SYM
ejpam-214	159	21	1444	1444	NUM
ejpam-214	159	22	(	(	PUNCT
ejpam-214	159	23	1971	1971	NUM
ejpam-214	159	24	)	)	PUNCT
ejpam-214	159	25	.	.	PUNCT
ejpam-214	160	1	[	[	X
ejpam-214	160	2	9	9	NUM
ejpam-214	160	3	]	]	SYM
ejpam-214	160	4	g.di.phillo	g.di.phillo	NOUN
ejpam-214	160	5	,	,	PUNCT
ejpam-214	160	6	p.l.grippo	p.l.grippo	NOUN
ejpam-214	160	7	,	,	PUNCT
ejpam-214	160	8	s.lucidi	s.lucidi	NOUN
ejpam-214	160	9	,	,	PUNCT
ejpam-214	160	10	a	a	DET
ejpam-214	160	11	smooth	smooth	ADJ
ejpam-214	160	12	method	method	NOUN
ejpam-214	160	13	for	for	ADP
ejpam-214	160	14	the	the	DET
ejpam-214	160	15	finite	finite	ADJ
ejpam-214	160	16	minimax	minimax	NOUN
ejpam-214	160	17	problem	problem	NOUN
ejpam-214	160	18	,	,	PUNCT
ejpam-214	160	19	mathematical	mathematical	ADJ
ejpam-214	160	20	programming	programming	NOUN
ejpam-214	160	21	,	,	PUNCT
ejpam-214	160	22	60	60	NUM
ejpam-214	160	23	:	:	PUNCT
ejpam-214	160	24	187	187	NUM
ejpam-214	160	25	-	-	SYM
ejpam-214	160	26	214	214	NUM
ejpam-214	160	27	(	(	PUNCT
ejpam-214	160	28	1993	1993	NUM
ejpam-214	160	29	)	)	PUNCT
ejpam-214	160	30	.	.	PUNCT
ejpam-214	161	1	[	[	X
ejpam-214	161	2	10	10	NUM
ejpam-214	161	3	]	]	SYM
ejpam-214	161	4	c.gigola	c.gigola	NOUN
ejpam-214	161	5	,	,	PUNCT
ejpam-214	161	6	s.gomez	s.gomez	NOUN
ejpam-214	161	7	,	,	PUNCT
ejpam-214	161	8	a	a	DET
ejpam-214	161	9	regularization	regularization	NOUN
ejpam-214	161	10	method	method	NOUN
ejpam-214	161	11	for	for	ADP
ejpam-214	161	12	solving	solve	VERB
ejpam-214	161	13	the	the	DET
ejpam-214	161	14	finite	finite	PROPN
ejpam-214	161	15	convex	convex	PROPN
ejpam-214	161	16	min	min	PROPN
ejpam-214	161	17	-	-	ADJ
ejpam-214	161	18	max	max	PROPN
ejpam-214	161	19	problem	problem	NOUN
ejpam-214	161	20	,	,	PUNCT
ejpam-214	161	21	siam	siam	ADJ
ejpam-214	161	22	journal	journal	NOUN
ejpam-214	161	23	on	on	ADP
ejpam-214	161	24	numerical	numerical	ADJ
ejpam-214	161	25	analysis	analysis	NOUN
ejpam-214	161	26	,	,	PUNCT
ejpam-214	161	27	27	27	NUM
ejpam-214	161	28	:	:	SYM
ejpam-214	161	29	1621	1621	NUM
ejpam-214	161	30	-	-	SYM
ejpam-214	161	31	1634	1634	NUM
ejpam-214	161	32	(	(	PUNCT
ejpam-214	161	33	1990	1990	NUM
ejpam-214	161	34	)	)	PUNCT
ejpam-214	161	35	.	.	PUNCT
ejpam-214	162	1	[	[	X
ejpam-214	162	2	11	11	NUM
ejpam-214	162	3	]	]	PUNCT
ejpam-214	162	4	r.a.polyak	r.a.polyak	NOUN
ejpam-214	162	5	,	,	PUNCT
ejpam-214	162	6	smooth	smooth	ADJ
ejpam-214	162	7	optimization	optimization	NOUN
ejpam-214	162	8	methods	method	NOUN
ejpam-214	162	9	for	for	ADP
ejpam-214	162	10	minimax	minimax	NOUN
ejpam-214	162	11	problems	problem	NOUN
ejpam-214	162	12	,	,	PUNCT
ejpam-214	162	13	siam	siam	ADJ
ejpam-214	162	14	journal	journal	NOUN
ejpam-214	162	15	on	on	ADP
ejpam-214	162	16	control	control	NOUN
ejpam-214	162	17	and	and	CCONJ
ejpam-214	162	18	optimization	optimization	NOUN
ejpam-214	162	19	,	,	PUNCT
ejpam-214	162	20	26	26	NUM
ejpam-214	162	21	:	:	SYM
ejpam-214	162	22	1274	1274	NUM
ejpam-214	162	23	-	-	SYM
ejpam-214	162	24	1286	1286	NUM
ejpam-214	162	25	(	(	PUNCT
ejpam-214	162	26	1988	1988	NUM
ejpam-214	162	27	)	)	PUNCT
ejpam-214	162	28	.	.	PUNCT
ejpam-214	163	1	[	[	X
ejpam-214	163	2	12	12	NUM
ejpam-214	163	3	]	]	PUNCT
ejpam-214	163	4	a.vardi	a.vardi	NOUN
ejpam-214	163	5	,	,	PUNCT
ejpam-214	163	6	new	new	ADJ
ejpam-214	163	7	minimax	minimax	NOUN
ejpam-214	163	8	algorithm	algorithm	NOUN
ejpam-214	163	9	,	,	PUNCT
ejpam-214	163	10	journal	journal	NOUN
ejpam-214	163	11	of	of	ADP
ejpam-214	163	12	optimization	optimization	NOUN
ejpam-214	163	13	theory	theory	NOUN
ejpam-214	163	14	and	and	CCONJ
ejpam-214	163	15	applications	application	NOUN
ejpam-214	163	16	,	,	PUNCT
ejpam-214	163	17	75	75	NUM
ejpam-214	163	18	:	:	PUNCT
ejpam-214	163	19	613	613	NUM
ejpam-214	163	20	-	-	SYM
ejpam-214	163	21	633	633	NUM
ejpam-214	163	22	(	(	PUNCT
ejpam-214	163	23	1992	1992	NUM
ejpam-214	163	24	)	)	PUNCT
ejpam-214	163	25	.	.	PUNCT
ejpam-214	164	1	[	[	X
ejpam-214	164	2	13	13	NUM
ejpam-214	164	3	]	]	SYM
ejpam-214	164	4	i.zang	i.zang	X
ejpam-214	164	5	,	,	PUNCT
ejpam-214	164	6	a	a	DET
ejpam-214	164	7	smoothing	smooth	VERB
ejpam-214	164	8	out	out	ADP
ejpam-214	164	9	technique	technique	NOUN
ejpam-214	164	10	for	for	ADP
ejpam-214	164	11	min	min	NOUN
ejpam-214	164	12	-	-	ADJ
ejpam-214	164	13	max	max	PROPN
ejpam-214	164	14	optimization	optimization	NOUN
ejpam-214	164	15	,	,	PUNCT
ejpam-214	164	16	mathematical	mathematical	ADJ
ejpam-214	164	17	programming	programming	NOUN
ejpam-214	164	18	,	,	PUNCT
ejpam-214	164	19	19	19	NUM
ejpam-214	164	20	:	:	SYM
ejpam-214	164	21	61	61	NUM
ejpam-214	164	22	-	-	SYM
ejpam-214	164	23	77	77	NUM
ejpam-214	164	24	(	(	PUNCT
ejpam-214	164	25	1980	1980	NUM
ejpam-214	164	26	)	)	PUNCT
ejpam-214	164	27	.	.	PUNCT
ejpam-214	165	1	[	[	X
ejpam-214	165	2	14	14	NUM
ejpam-214	165	3	]	]	X
ejpam-214	165	4	j.b.hiriart	j.b.hiriart	ADJ
ejpam-214	165	5	-	-	PUNCT
ejpam-214	165	6	urruty	urruty	ADJ
ejpam-214	165	7	,	,	PUNCT
ejpam-214	165	8	c.lemarechal	c.lemarechal	NOUN
ejpam-214	165	9	,	,	PUNCT
ejpam-214	165	10	convex	convex	VERB
ejpam-214	165	11	analysis	analysis	NOUN
ejpam-214	165	12	and	and	CCONJ
ejpam-214	165	13	minimization	minimization	NOUN
ejpam-214	165	14	algorithm	algorithm	NOUN
ejpam-214	165	15	,	,	PUNCT
ejpam-214	165	16	springerverlag	springerverlag	NOUN
ejpam-214	165	17	,	,	PUNCT
ejpam-214	165	18	berlin	berlin	PROPN
ejpam-214	165	19	,	,	PUNCT
ejpam-214	165	20	1993	1993	NUM
ejpam-214	165	21	.	.	PUNCT
ejpam-214	166	1	[	[	X
ejpam-214	166	2	15	15	NUM
ejpam-214	166	3	]	]	X
ejpam-214	166	4	x	x	X
ejpam-214	166	5	s	s	PROPN
ejpam-214	166	6	li	li	PROPN
ejpam-214	166	7	,	,	PUNCT
ejpam-214	166	8	entropy	entropy	NOUN
ejpam-214	166	9	and	and	CCONJ
ejpam-214	166	10	optimization	optimization	NOUN
ejpam-214	166	11	,	,	PUNCT
ejpam-214	166	12	ph.d.thesis	ph.d.thesis	PROPN
ejpam-214	166	13	,	,	PUNCT
ejpam-214	166	14	university	university	NOUN
ejpam-214	166	15	of	of	ADP
ejpam-214	166	16	livepool	livepool	PROPN
ejpam-214	166	17	,	,	PUNCT
ejpam-214	166	18	united	united	ADJ
ejpam-214	166	19	kingdom	kingdom	PROPN
ejpam-214	166	20	,	,	PUNCT
ejpam-214	166	21	1987	1987	NUM
ejpam-214	166	22	.	.	PUNCT
ejpam-214	167	1	[	[	X
ejpam-214	167	2	16	16	NUM
ejpam-214	167	3	]	]	PUNCT
ejpam-214	167	4	x	x	X
ejpam-214	167	5	s	s	X
ejpam-214	167	6	li	li	PROPN
ejpam-214	167	7	,	,	PUNCT
ejpam-214	167	8	s	s	PART
ejpam-214	167	9	c	c	NOUN
ejpam-214	167	10	fang	fang	X
ejpam-214	167	11	,	,	PUNCT
ejpam-214	167	12	on	on	ADP
ejpam-214	167	13	the	the	DET
ejpam-214	167	14	entropic	entropic	ADJ
ejpam-214	167	15	regularization	regularization	NOUN
ejpam-214	167	16	method	method	NOUN
ejpam-214	167	17	for	for	ADP
ejpam-214	167	18	solving	solve	VERB
ejpam-214	167	19	min	min	PROPN
ejpam-214	167	20	-	-	ADJ
ejpam-214	167	21	max	max	PROPN
ejpam-214	167	22	problems	problem	NOUN
ejpam-214	167	23	with	with	ADP
ejpam-214	167	24	applications	application	NOUN
ejpam-214	167	25	,	,	PUNCT
ejpam-214	167	26	mathematical	mathematical	ADJ
ejpam-214	167	27	methods	method	NOUN
ejpam-214	167	28	of	of	ADP
ejpam-214	167	29	operations	operation	NOUN
ejpam-214	167	30	research	research	NOUN
ejpam-214	167	31	,	,	PUNCT
ejpam-214	167	32	46	46	NUM
ejpam-214	167	33	:	:	SYM
ejpam-214	167	34	119	119	NUM
ejpam-214	167	35	-	-	SYM
ejpam-214	167	36	130	130	NUM
ejpam-214	167	37	(	(	PUNCT
ejpam-214	167	38	1997	1997	NUM
ejpam-214	167	39	)	)	PUNCT
ejpam-214	167	40	.	.	PUNCT
ejpam-214	168	1	[	[	X
ejpam-214	168	2	17	17	NUM
ejpam-214	168	3	]	]	SYM
ejpam-214	168	4	r.t.rockafellar	r.t.rockafellar	ADJ
ejpam-214	168	5	,	,	PUNCT
ejpam-214	168	6	convex	convex	ADJ
ejpam-214	168	7	analysis	analysis	NOUN
ejpam-214	168	8	,	,	PUNCT
ejpam-214	168	9	princeton	princeton	PROPN
ejpam-214	168	10	university	university	PROPN
ejpam-214	168	11	press	press	NOUN
ejpam-214	168	12	,	,	PUNCT
ejpam-214	168	13	new	new	PROPN
ejpam-214	168	14	jersey	jersey	PROPN
ejpam-214	168	15	,	,	PUNCT
ejpam-214	168	16	1970	1970	NUM
ejpam-214	168	17	.	.	PUNCT
ejpam-214	169	1	[	[	X
ejpam-214	169	2	18	18	NUM
ejpam-214	169	3	]	]	SYM
ejpam-214	169	4	i.griva	i.griva	ADJ
ejpam-214	169	5	,	,	PUNCT
ejpam-214	169	6	r.a.polyak	r.a.polyak	NOUN
ejpam-214	169	7	,	,	PUNCT
ejpam-214	169	8	primal	primal	ADJ
ejpam-214	169	9	-	-	PUNCT
ejpam-214	169	10	dual	dual	ADJ
ejpam-214	169	11	nonlinear	nonlinear	ADJ
ejpam-214	169	12	rescaling	rescaling	NOUN
ejpam-214	169	13	method	method	NOUN
ejpam-214	169	14	with	with	ADP
ejpam-214	169	15	dynamic	dynamic	ADJ
ejpam-214	169	16	scaling	scaling	NOUN
ejpam-214	169	17	parameter	parameter	NOUN
ejpam-214	169	18	update	update	NOUN
ejpam-214	169	19	,	,	PUNCT
ejpam-214	169	20	mathematical	mathematical	ADJ
ejpam-214	169	21	programming	programming	NOUN
ejpam-214	169	22	,	,	PUNCT
ejpam-214	169	23	106	106	NUM
ejpam-214	169	24	:	:	SYM
ejpam-214	169	25	237	237	NUM
ejpam-214	169	26	-	-	SYM
ejpam-214	169	27	259	259	NUM
ejpam-214	169	28	(	(	PUNCT
ejpam-214	169	29	2006	2006	NUM
ejpam-214	169	30	)	)	PUNCT
ejpam-214	169	31	.	.	PUNCT