id	sid	tid	token	lemma	pos
ejpam-819	1	1	10_husain.dvi	10_husain.dvi	NUM
ejpam-819	1	2	european	european	ADJ
ejpam-819	1	3	journal	journal	NOUN
ejpam-819	1	4	of	of	ADP
ejpam-819	1	5	pure	pure	ADJ
ejpam-819	1	6	and	and	CCONJ
ejpam-819	1	7	applied	apply	VERB
ejpam-819	1	8	mathematics	mathematic	NOUN
ejpam-819	1	9	vol	vol	NOUN
ejpam-819	1	10	.	.	PROPN
ejpam-819	1	11	5	5	NUM
ejpam-819	1	12	,	,	PUNCT
ejpam-819	1	13	no	no	INTJ
ejpam-819	1	14	.	.	NOUN
ejpam-819	1	15	3	3	NUM
ejpam-819	1	16	,	,	PUNCT
ejpam-819	1	17	2012	2012	NUM
ejpam-819	1	18	,	,	PUNCT
ejpam-819	1	19	390	390	NUM
ejpam-819	1	20	-	-	SYM
ejpam-819	1	21	400	400	NUM
ejpam-819	1	22	issn	issn	PROPN
ejpam-819	1	23	1307	1307	NUM
ejpam-819	1	24	-	-	SYM
ejpam-819	1	25	5543	5543	NUM
ejpam-819	1	26	–	–	PUNCT
ejpam-819	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-819	1	28	second	second	ADJ
ejpam-819	1	29	-	-	PUNCT
ejpam-819	1	30	order	order	NOUN
ejpam-819	1	31	duality	duality	NOUN
ejpam-819	1	32	for	for	ADP
ejpam-819	1	33	a	a	DET
ejpam-819	1	34	class	class	NOUN
ejpam-819	1	35	of	of	ADP
ejpam-819	1	36	nondifferentiable	nondifferentiable	ADJ
ejpam-819	1	37	continuous	continuous	ADJ
ejpam-819	1	38	programming	programming	NOUN
ejpam-819	1	39	problems	problem	NOUN
ejpam-819	1	40	iqbal	iqbal	PROPN
ejpam-819	1	41	husain1,∗	husain1,∗	PROPN
ejpam-819	1	42	,	,	PUNCT
ejpam-819	1	43	mashoob	mashoob	VERB
ejpam-819	1	44	masoodi2	masoodi2	NOUN
ejpam-819	1	45	1	1	NUM
ejpam-819	1	46	department	department	NOUN
ejpam-819	1	47	of	of	ADP
ejpam-819	1	48	mathematics	mathematics	PROPN
ejpam-819	1	49	,	,	PUNCT
ejpam-819	1	50	jaypee	jaypee	PROPN
ejpam-819	1	51	university	university	PROPN
ejpam-819	1	52	of	of	ADP
ejpam-819	1	53	engineering	engineering	NOUN
ejpam-819	1	54	and	and	CCONJ
ejpam-819	1	55	technology	technology	NOUN
ejpam-819	1	56	,	,	PUNCT
ejpam-819	1	57	guna	guna	PROPN
ejpam-819	1	58	(	(	PUNCT
ejpam-819	1	59	m.p	m.p	PROPN
ejpam-819	1	60	.	.	PROPN
ejpam-819	1	61	)	)	PUNCT
ejpam-819	1	62	,	,	PUNCT
ejpam-819	1	63	india	india	PROPN
ejpam-819	1	64	2	2	NUM
ejpam-819	1	65	department	department	NOUN
ejpam-819	1	66	of	of	ADP
ejpam-819	1	67	statistics	statistic	NOUN
ejpam-819	1	68	,	,	PUNCT
ejpam-819	1	69	university	university	PROPN
ejpam-819	1	70	of	of	ADP
ejpam-819	1	71	kashmir	kashmir	PROPN
ejpam-819	1	72	,	,	PUNCT
ejpam-819	1	73	srinagar	srinagar	PROPN
ejpam-819	1	74	(	(	PUNCT
ejpam-819	1	75	kashmir	kashmir	PROPN
ejpam-819	1	76	)	)	PUNCT
ejpam-819	1	77	,	,	PUNCT
ejpam-819	1	78	india	india	PROPN
ejpam-819	1	79	abstract	abstract	PROPN
ejpam-819	1	80	.	.	PUNCT
ejpam-819	2	1	a	a	DET
ejpam-819	2	2	dual	dual	ADJ
ejpam-819	2	3	problem	problem	NOUN
ejpam-819	2	4	associated	associate	VERB
ejpam-819	2	5	with	with	ADP
ejpam-819	2	6	a	a	DET
ejpam-819	2	7	class	class	NOUN
ejpam-819	2	8	of	of	ADP
ejpam-819	2	9	non	non	ADJ
ejpam-819	2	10	-	-	ADJ
ejpam-819	2	11	differentiable	differentiable	ADJ
ejpam-819	2	12	continuous	continuous	ADJ
ejpam-819	2	13	programming	programming	NOUN
ejpam-819	2	14	problems	problem	NOUN
ejpam-819	2	15	is	be	AUX
ejpam-819	2	16	formulated	formulate	VERB
ejpam-819	2	17	.	.	PUNCT
ejpam-819	3	1	under	under	ADP
ejpam-819	3	2	the	the	DET
ejpam-819	3	3	second	second	ADJ
ejpam-819	3	4	-	-	PUNCT
ejpam-819	3	5	order	order	NOUN
ejpam-819	3	6	pseudo	pseudo	NOUN
ejpam-819	3	7	-	-	NOUN
ejpam-819	3	8	invexity	invexity	NOUN
ejpam-819	3	9	,	,	PUNCT
ejpam-819	3	10	various	various	ADJ
ejpam-819	3	11	duality	duality	NOUN
ejpam-819	3	12	theorems	theorem	NOUN
ejpam-819	3	13	are	be	AUX
ejpam-819	3	14	validated	validate	VERB
ejpam-819	3	15	for	for	ADP
ejpam-819	3	16	this	this	DET
ejpam-819	3	17	pair	pair	NOUN
ejpam-819	3	18	of	of	ADP
ejpam-819	3	19	dual	dual	ADJ
ejpam-819	3	20	problems	problem	NOUN
ejpam-819	3	21	.	.	PUNCT
ejpam-819	4	1	a	a	DET
ejpam-819	4	2	pair	pair	NOUN
ejpam-819	4	3	of	of	ADP
ejpam-819	4	4	dual	dual	ADJ
ejpam-819	4	5	problems	problem	NOUN
ejpam-819	4	6	with	with	ADP
ejpam-819	4	7	natural	natural	ADJ
ejpam-819	4	8	boundary	boundary	ADJ
ejpam-819	4	9	values	value	NOUN
ejpam-819	4	10	is	be	AUX
ejpam-819	4	11	constructed	construct	VERB
ejpam-819	4	12	and	and	CCONJ
ejpam-819	4	13	the	the	DET
ejpam-819	4	14	proofs	proof	NOUN
ejpam-819	4	15	of	of	ADP
ejpam-819	4	16	its	its	PRON
ejpam-819	4	17	various	various	ADJ
ejpam-819	4	18	duality	duality	NOUN
ejpam-819	4	19	results	result	NOUN
ejpam-819	4	20	are	be	AUX
ejpam-819	4	21	merely	merely	ADV
ejpam-819	4	22	indicated	indicate	VERB
ejpam-819	4	23	.	.	PUNCT
ejpam-819	5	1	further	far	ADV
ejpam-819	5	2	,	,	PUNCT
ejpam-819	5	3	it	it	PRON
ejpam-819	5	4	is	be	AUX
ejpam-819	5	5	shown	show	VERB
ejpam-819	5	6	that	that	SCONJ
ejpam-819	5	7	our	our	PRON
ejpam-819	5	8	results	result	NOUN
ejpam-819	5	9	can	can	AUX
ejpam-819	5	10	be	be	AUX
ejpam-819	5	11	viewed	view	VERB
ejpam-819	5	12	as	as	ADP
ejpam-819	5	13	dynamic	dynamic	ADJ
ejpam-819	5	14	generalizations	generalization	NOUN
ejpam-819	5	15	of	of	ADP
ejpam-819	5	16	corresponding	correspond	VERB
ejpam-819	5	17	(	(	PUNCT
ejpam-819	5	18	static	static	ADJ
ejpam-819	5	19	)	)	PUNCT
ejpam-819	5	20	second	second	ADJ
ejpam-819	5	21	-	-	PUNCT
ejpam-819	5	22	order	order	NOUN
ejpam-819	5	23	duality	duality	NOUN
ejpam-819	5	24	theorems	theorem	NOUN
ejpam-819	5	25	for	for	ADP
ejpam-819	5	26	a	a	DET
ejpam-819	5	27	class	class	NOUN
ejpam-819	5	28	of	of	ADP
ejpam-819	5	29	nondifferentiable	nondifferentiable	ADJ
ejpam-819	5	30	nonlinear	nonlinear	ADJ
ejpam-819	5	31	programming	programming	NOUN
ejpam-819	5	32	problems	problem	NOUN
ejpam-819	5	33	existing	exist	VERB
ejpam-819	5	34	in	in	ADP
ejpam-819	5	35	the	the	DET
ejpam-819	5	36	literature	literature	NOUN
ejpam-819	5	37	.	.	PUNCT
ejpam-819	6	1	2010	2010	NUM
ejpam-819	6	2	mathematics	mathematic	NOUN
ejpam-819	6	3	subject	subject	NOUN
ejpam-819	6	4	classifications	classification	NOUN
ejpam-819	6	5	:	:	PUNCT
ejpam-819	6	6	90c30	90c30	NUM
ejpam-819	6	7	,	,	PUNCT
ejpam-819	6	8	90c11	90c11	NUM
ejpam-819	6	9	,	,	PUNCT
ejpam-819	6	10	90c20	90c20	NUM
ejpam-819	6	11	,	,	PUNCT
ejpam-819	6	12	90c26	90c26	NUM
ejpam-819	6	13	.	.	PUNCT
ejpam-819	7	1	key	key	ADJ
ejpam-819	7	2	words	word	NOUN
ejpam-819	7	3	and	and	CCONJ
ejpam-819	7	4	phrases	phrase	NOUN
ejpam-819	7	5	:	:	PUNCT
ejpam-819	7	6	continuous	continuous	ADJ
ejpam-819	7	7	programming	programming	NOUN
ejpam-819	7	8	,	,	PUNCT
ejpam-819	7	9	second	second	ADJ
ejpam-819	7	10	-	-	PUNCT
ejpam-819	7	11	order	order	NOUN
ejpam-819	7	12	invexity	invexity	NOUN
ejpam-819	7	13	,	,	PUNCT
ejpam-819	7	14	second	second	ADJ
ejpam-819	7	15	-	-	PUNCT
ejpam-819	7	16	order	order	NOUN
ejpam-819	7	17	pseudoinvexity	pseudoinvexity	NOUN
ejpam-819	7	18	,	,	PUNCT
ejpam-819	7	19	second	second	ADJ
ejpam-819	7	20	-	-	PUNCT
ejpam-819	7	21	order	order	NOUN
ejpam-819	7	22	duality	duality	NOUN
ejpam-819	7	23	,	,	PUNCT
ejpam-819	7	24	nonlinear	nonlinear	ADJ
ejpam-819	7	25	programming	programming	NOUN
ejpam-819	7	26	1	1	NUM
ejpam-819	7	27	.	.	PUNCT
ejpam-819	8	1	introduction	introduction	NOUN
ejpam-819	8	2	second	second	ADJ
ejpam-819	8	3	-	-	PUNCT
ejpam-819	8	4	order	order	NOUN
ejpam-819	8	5	duality	duality	NOUN
ejpam-819	8	6	in	in	ADP
ejpam-819	8	7	mathematical	mathematical	ADJ
ejpam-819	8	8	programming	programming	NOUN
ejpam-819	8	9	has	have	AUX
ejpam-819	8	10	been	be	AUX
ejpam-819	8	11	extensively	extensively	ADV
ejpam-819	8	12	investigated	investigate	VERB
ejpam-819	8	13	in	in	ADP
ejpam-819	8	14	the	the	DET
ejpam-819	8	15	literature	literature	NOUN
ejpam-819	8	16	.	.	PUNCT
ejpam-819	9	1	a	a	DET
ejpam-819	9	2	second	second	ADJ
ejpam-819	9	3	-	-	PUNCT
ejpam-819	9	4	order	order	NOUN
ejpam-819	9	5	dual	dual	ADJ
ejpam-819	9	6	formulation	formulation	NOUN
ejpam-819	9	7	for	for	ADP
ejpam-819	9	8	a	a	DET
ejpam-819	9	9	non	non	ADJ
ejpam-819	9	10	-	-	ADJ
ejpam-819	9	11	linear	linear	ADJ
ejpam-819	9	12	programming	programming	NOUN
ejpam-819	9	13	problem	problem	NOUN
ejpam-819	9	14	was	be	AUX
ejpam-819	9	15	introduced	introduce	VERB
ejpam-819	9	16	by	by	ADP
ejpam-819	9	17	mangasarian	mangasarian	PROPN
ejpam-819	10	1	[	[	X
ejpam-819	10	2	5	5	NUM
ejpam-819	10	3	]	]	PUNCT
ejpam-819	10	4	.	.	PUNCT
ejpam-819	11	1	later	later	ADV
ejpam-819	11	2	mond	mond	NOUN
ejpam-819	11	3	[	[	X
ejpam-819	11	4	6	6	NUM
ejpam-819	11	5	]	]	PUNCT
ejpam-819	11	6	established	establish	VERB
ejpam-819	11	7	various	various	ADJ
ejpam-819	11	8	duality	duality	NOUN
ejpam-819	11	9	theorems	theorem	NOUN
ejpam-819	11	10	under	under	ADP
ejpam-819	11	11	a	a	DET
ejpam-819	11	12	condition	condition	NOUN
ejpam-819	11	13	which	which	PRON
ejpam-819	11	14	is	be	AUX
ejpam-819	11	15	called	call	VERB
ejpam-819	11	16	"	"	PUNCT
ejpam-819	11	17	second	second	ADJ
ejpam-819	11	18	-	-	PUNCT
ejpam-819	11	19	order	order	NOUN
ejpam-819	11	20	convexity	convexity	NOUN
ejpam-819	11	21	"	"	PUNCT
ejpam-819	11	22	.	.	PUNCT
ejpam-819	12	1	this	this	DET
ejpam-819	12	2	condition	condition	NOUN
ejpam-819	12	3	is	be	AUX
ejpam-819	12	4	much	much	ADV
ejpam-819	12	5	simpler	simple	ADJ
ejpam-819	12	6	than	than	ADP
ejpam-819	12	7	that	that	PRON
ejpam-819	12	8	used	use	VERB
ejpam-819	12	9	by	by	ADP
ejpam-819	12	10	mangasarian	mangasarian	PROPN
ejpam-819	13	1	[	[	X
ejpam-819	13	2	5	5	NUM
ejpam-819	13	3	]	]	PUNCT
ejpam-819	13	4	.	.	PUNCT
ejpam-819	14	1	in	in	ADP
ejpam-819	14	2	[	[	X
ejpam-819	14	3	9	9	NUM
ejpam-819	14	4	]	]	PUNCT
ejpam-819	14	5	,	,	PUNCT
ejpam-819	14	6	mond	mond	PROPN
ejpam-819	14	7	and	and	CCONJ
ejpam-819	14	8	weir	weir	PROPN
ejpam-819	14	9	reconstructed	reconstruct	VERB
ejpam-819	14	10	the	the	DET
ejpam-819	14	11	second	second	ADJ
ejpam-819	14	12	-	-	PUNCT
ejpam-819	14	13	order	order	NOUN
ejpam-819	14	14	duals	dual	NOUN
ejpam-819	14	15	and	and	CCONJ
ejpam-819	14	16	higher	high	ADJ
ejpam-819	14	17	order	order	NOUN
ejpam-819	14	18	dual	dual	ADJ
ejpam-819	14	19	models	model	NOUN
ejpam-819	14	20	to	to	PART
ejpam-819	14	21	drive	drive	VERB
ejpam-819	14	22	usual	usual	ADJ
ejpam-819	14	23	duality	duality	NOUN
ejpam-819	14	24	results	result	NOUN
ejpam-819	14	25	.	.	PUNCT
ejpam-819	15	1	it	it	PRON
ejpam-819	15	2	is	be	AUX
ejpam-819	15	3	remarked	remark	VERB
ejpam-819	15	4	here	here	ADV
ejpam-819	15	5	that	that	SCONJ
ejpam-819	15	6	second	second	ADJ
ejpam-819	15	7	-	-	PUNCT
ejpam-819	15	8	order	order	NOUN
ejpam-819	15	9	dual	dual	ADJ
ejpam-819	15	10	to	to	ADP
ejpam-819	15	11	a	a	DET
ejpam-819	15	12	mathematical	mathematical	ADJ
ejpam-819	15	13	programming	programming	NOUN
ejpam-819	15	14	problem	problem	NOUN
ejpam-819	15	15	presents	present	VERB
ejpam-819	15	16	a	a	DET
ejpam-819	15	17	tighter	tighter	ADV
ejpam-819	15	18	bound	bind	VERB
ejpam-819	15	19	and	and	CCONJ
ejpam-819	15	20	because	because	SCONJ
ejpam-819	15	21	of	of	ADP
ejpam-819	15	22	which	which	PRON
ejpam-819	15	23	it	it	PRON
ejpam-819	15	24	enjoys	enjoy	VERB
ejpam-819	15	25	computational	computational	ADJ
ejpam-819	15	26	advantage	advantage	NOUN
ejpam-819	15	27	over	over	ADP
ejpam-819	15	28	a	a	DET
ejpam-819	15	29	first	first	ADJ
ejpam-819	15	30	order	order	NOUN
ejpam-819	15	31	dual	dual	ADJ
ejpam-819	15	32	.	.	PUNCT
ejpam-819	16	1	duality	duality	NOUN
ejpam-819	16	2	and	and	CCONJ
ejpam-819	16	3	optimality	optimality	NOUN
ejpam-819	16	4	for	for	ADP
ejpam-819	16	5	continuous	continuous	ADJ
ejpam-819	16	6	programming	programming	NOUN
ejpam-819	16	7	have	have	AUX
ejpam-819	16	8	been	be	AUX
ejpam-819	16	9	widely	widely	ADV
ejpam-819	16	10	investigated	investigate	VERB
ejpam-819	16	11	by	by	ADP
ejpam-819	16	12	many	many	ADJ
ejpam-819	16	13	authors	author	NOUN
ejpam-819	16	14	in	in	ADP
ejpam-819	16	15	the	the	DET
ejpam-819	16	16	recent	recent	ADJ
ejpam-819	16	17	past	past	NOUN
ejpam-819	16	18	notably	notably	ADV
ejpam-819	16	19	,	,	PUNCT
ejpam-819	16	20	mond	mond	NOUN
ejpam-819	16	21	and	and	CCONJ
ejpam-819	16	22	hanson	hanson	NOUN
ejpam-819	17	1	[	[	X
ejpam-819	17	2	7	7	NUM
ejpam-819	17	3	]	]	PUNCT
ejpam-819	17	4	,	,	PUNCT
ejpam-819	17	5	bector	bector	NOUN
ejpam-819	17	6	,	,	PUNCT
ejpam-819	17	7	chandra	chandra	PROPN
ejpam-819	17	8	and	and	CCONJ
ejpam-819	17	9	husain	husain	PROPN
ejpam-819	18	1	[	[	X
ejpam-819	18	2	1	1	NUM
ejpam-819	18	3	]	]	PUNCT
ejpam-819	18	4	,	,	PUNCT
ejpam-819	18	5	mond	mond	NOUN
ejpam-819	18	6	and	and	CCONJ
ejpam-819	18	7	husain	husain	NOUN
ejpam-819	19	1	[	[	X
ejpam-819	19	2	8	8	NUM
ejpam-819	19	3	]	]	PUNCT
ejpam-819	19	4	and	and	CCONJ
ejpam-819	19	5	chen	chen	PROPN
ejpam-819	20	1	[	[	X
ejpam-819	20	2	3	3	X
ejpam-819	20	3	]	]	PUNCT
ejpam-819	20	4	and	and	CCONJ
ejpam-819	20	5	other	other	ADJ
ejpam-819	20	6	cited	cite	VERB
ejpam-819	20	7	references	reference	NOUN
ejpam-819	20	8	in	in	ADP
ejpam-819	20	9	these	these	DET
ejpam-819	20	10	expositions	exposition	NOUN
ejpam-819	20	11	.	.	PUNCT
ejpam-819	21	1	chen	chen	PROPN
ejpam-819	22	1	[	[	X
ejpam-819	22	2	3	3	X
ejpam-819	22	3	]	]	PUNCT
ejpam-819	22	4	was	be	AUX
ejpam-819	22	5	the	the	DET
ejpam-819	22	6	first	first	ADJ
ejpam-819	22	7	to	to	PART
ejpam-819	22	8	identify	identify	VERB
ejpam-819	22	9	second	second	ADJ
ejpam-819	22	10	-	-	PUNCT
ejpam-819	22	11	order	order	NOUN
ejpam-819	22	12	dual	dual	ADV
ejpam-819	22	13	formulated	formulate	VERB
ejpam-819	22	14	for	for	ADP
ejpam-819	22	15	a	a	DET
ejpam-819	22	16	constrained	constrain	VERB
ejpam-819	22	17	variational	variational	ADJ
ejpam-819	22	18	problem	problem	NOUN
ejpam-819	22	19	and	and	CCONJ
ejpam-819	22	20	established	establish	VERB
ejpam-819	22	21	various	various	ADJ
ejpam-819	22	22	duality	duality	NOUN
ejpam-819	22	23	results	result	NOUN
ejpam-819	22	24	under	under	ADP
ejpam-819	22	25	an	an	DET
ejpam-819	22	26	involved	involved	ADJ
ejpam-819	22	27	invexitylike	invexitylike	NOUN
ejpam-819	22	28	assumptions	assumption	NOUN
ejpam-819	22	29	.	.	PUNCT
ejpam-819	23	1	recently	recently	ADV
ejpam-819	23	2	,	,	PUNCT
ejpam-819	23	3	husain	husain	PROPN
ejpam-819	23	4	et	et	PROPN
ejpam-819	23	5	al	al	PROPN
ejpam-819	23	6	[	[	X
ejpam-819	23	7	4	4	X
ejpam-819	23	8	]	]	PUNCT
ejpam-819	23	9	have	have	AUX
ejpam-819	23	10	presented	present	VERB
ejpam-819	23	11	mond	mond	PROPN
ejpam-819	23	12	-	-	PUNCT
ejpam-819	23	13	weir	weir	PROPN
ejpam-819	23	14	type	type	NOUN
ejpam-819	23	15	duality	duality	NOUN
ejpam-819	23	16	for	for	ADP
ejpam-819	23	17	the	the	DET
ejpam-819	23	18	problem	problem	NOUN
ejpam-819	23	19	∗corresponding	∗corresponde	VERB
ejpam-819	23	20	author	author	NOUN
ejpam-819	23	21	.	.	PUNCT
ejpam-819	24	1	email	email	NOUN
ejpam-819	24	2	addresses	address	NOUN
ejpam-819	24	3	:	:	PUNCT
ejpam-819	24	4	ihusain11	ihusain11	PROPN
ejpam-819	24	5	�	�	PROPN
ejpam-819	24	6	yahoo	yahoo	PROPN
ejpam-819	24	7	.	.	PUNCT
ejpam-819	25	1	om	om	PROPN
ejpam-819	25	2	(	(	PUNCT
ejpam-819	25	3	i.	i.	PROPN
ejpam-819	25	4	husain	husain	PROPN
ejpam-819	25	5	)	)	PUNCT
ejpam-819	25	6	,	,	PUNCT
ejpam-819	25	7	masoodisaba	masoodisaba	PROPN
ejpam-819	25	8	�	�	PROPN
ejpam-819	25	9	yahoo	yahoo	PROPN
ejpam-819	25	10	.	.	PUNCT
ejpam-819	26	1	om	om	PROPN
ejpam-819	26	2	(	(	PUNCT
ejpam-819	26	3	m.	m.	NOUN
ejpam-819	26	4	masoodi	masoodi	PROPN
ejpam-819	26	5	)	)	PUNCT
ejpam-819	26	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-819	27	1	390	390	NUM
ejpam-819	28	1	c	c	X
ejpam-819	28	2	©	©	PROPN
ejpam-819	28	3	2012	2012	NUM
ejpam-819	28	4	ejpam	ejpam	VERB
ejpam-819	28	5	all	all	DET
ejpam-819	28	6	rights	right	NOUN
ejpam-819	28	7	reserved	reserve	VERB
ejpam-819	28	8	.	.	PUNCT
ejpam-819	29	1	i.	i.	PROPN
ejpam-819	29	2	husain	husain	PROPN
ejpam-819	29	3	,	,	PUNCT
ejpam-819	29	4	m.	m.	NOUN
ejpam-819	29	5	masoodi	masoodi	PROPN
ejpam-819	29	6	/	/	SYM
ejpam-819	29	7	eur	eur	PROPN
ejpam-819	29	8	.	.	PUNCT
ejpam-819	30	1	j.	j.	PROPN
ejpam-819	30	2	pure	pure	PROPN
ejpam-819	30	3	appl	appl	PROPN
ejpam-819	30	4	.	.	PROPN
ejpam-819	30	5	math	math	PROPN
ejpam-819	30	6	,	,	PUNCT
ejpam-819	30	7	5	5	NUM
ejpam-819	30	8	(	(	PUNCT
ejpam-819	30	9	2012	2012	NUM
ejpam-819	30	10	)	)	PUNCT
ejpam-819	30	11	,	,	PUNCT
ejpam-819	30	12	390	390	NUM
ejpam-819	30	13	-	-	SYM
ejpam-819	30	14	400	400	NUM
ejpam-819	30	15	391	391	NUM
ejpam-819	30	16	of	of	ADP
ejpam-819	30	17	[	[	X
ejpam-819	30	18	3	3	NUM
ejpam-819	30	19	]	]	PUNCT
ejpam-819	30	20	and	and	CCONJ
ejpam-819	30	21	by	by	ADP
ejpam-819	30	22	introducing	introduce	VERB
ejpam-819	30	23	continuous	continuous	ADJ
ejpam-819	30	24	-	-	PUNCT
ejpam-819	30	25	time	time	NOUN
ejpam-819	30	26	version	version	NOUN
ejpam-819	30	27	of	of	ADP
ejpam-819	30	28	second	second	ADJ
ejpam-819	30	29	-	-	PUNCT
ejpam-819	30	30	order	order	NOUN
ejpam-819	30	31	invexity	invexity	NOUN
ejpam-819	30	32	and	and	CCONJ
ejpam-819	30	33	generalized	generalize	VERB
ejpam-819	30	34	second	second	ADJ
ejpam-819	30	35	-	-	PUNCT
ejpam-819	30	36	order	order	NOUN
ejpam-819	30	37	invexity	invexity	NOUN
ejpam-819	30	38	,	,	PUNCT
ejpam-819	30	39	validated	validate	VERB
ejpam-819	30	40	various	various	ADJ
ejpam-819	30	41	duality	duality	NOUN
ejpam-819	30	42	results	result	NOUN
ejpam-819	30	43	.	.	PUNCT
ejpam-819	31	1	in	in	ADP
ejpam-819	31	2	this	this	DET
ejpam-819	31	3	paper	paper	NOUN
ejpam-819	31	4	we	we	PRON
ejpam-819	31	5	formulate	formulate	VERB
ejpam-819	31	6	a	a	DET
ejpam-819	31	7	wolfe	wolfe	PROPN
ejpam-819	31	8	type	type	NOUN
ejpam-819	31	9	second	second	ADJ
ejpam-819	31	10	order	order	NOUN
ejpam-819	31	11	dual	dual	ADJ
ejpam-819	31	12	to	to	ADP
ejpam-819	31	13	a	a	DET
ejpam-819	31	14	class	class	NOUN
ejpam-819	31	15	of	of	ADP
ejpam-819	31	16	nondifferentiability	nondifferentiability	NOUN
ejpam-819	31	17	continuous	continuous	ADJ
ejpam-819	31	18	programming	programming	NOUN
ejpam-819	31	19	problems	problem	NOUN
ejpam-819	31	20	where	where	SCONJ
ejpam-819	31	21	nondifferentiability	nondifferentiability	NOUN
ejpam-819	31	22	enters	enter	VERB
ejpam-819	31	23	due	due	ADJ
ejpam-819	31	24	to	to	ADP
ejpam-819	31	25	the	the	DET
ejpam-819	31	26	square	square	ADJ
ejpam-819	31	27	root	root	NOUN
ejpam-819	31	28	of	of	ADP
ejpam-819	31	29	a	a	DET
ejpam-819	31	30	certain	certain	ADJ
ejpam-819	31	31	quadratic	quadratic	ADJ
ejpam-819	31	32	form	form	NOUN
ejpam-819	31	33	appearing	appear	VERB
ejpam-819	31	34	in	in	ADP
ejpam-819	31	35	the	the	DET
ejpam-819	31	36	integrand	integrand	NOUN
ejpam-819	31	37	of	of	ADP
ejpam-819	31	38	the	the	DET
ejpam-819	31	39	objective	objective	ADJ
ejpam-819	31	40	functional	functional	NOUN
ejpam-819	31	41	.	.	PUNCT
ejpam-819	32	1	the	the	DET
ejpam-819	32	2	popularity	popularity	NOUN
ejpam-819	32	3	of	of	ADP
ejpam-819	32	4	this	this	DET
ejpam-819	32	5	type	type	NOUN
ejpam-819	32	6	of	of	ADP
ejpam-819	32	7	problems	problem	NOUN
ejpam-819	32	8	seems	seem	VERB
ejpam-819	32	9	to	to	PART
ejpam-819	32	10	originate	originate	VERB
ejpam-819	32	11	from	from	ADP
ejpam-819	32	12	the	the	DET
ejpam-819	32	13	fact	fact	NOUN
ejpam-819	32	14	that	that	SCONJ
ejpam-819	32	15	,	,	PUNCT
ejpam-819	32	16	even	even	ADV
ejpam-819	32	17	though	though	SCONJ
ejpam-819	32	18	the	the	DET
ejpam-819	32	19	objective	objective	ADJ
ejpam-819	32	20	function	function	NOUN
ejpam-819	32	21	and	and	CCONJ
ejpam-819	32	22	or	or	CCONJ
ejpam-819	32	23	/	/	SYM
ejpam-819	32	24	constraint	constraint	NOUN
ejpam-819	32	25	functions	function	NOUN
ejpam-819	32	26	are	be	AUX
ejpam-819	32	27	non	non	ADJ
ejpam-819	32	28	-	-	ADJ
ejpam-819	32	29	smooth	smooth	ADJ
ejpam-819	32	30	,	,	PUNCT
ejpam-819	32	31	a	a	DET
ejpam-819	32	32	simple	simple	ADJ
ejpam-819	32	33	representation	representation	NOUN
ejpam-819	32	34	of	of	ADP
ejpam-819	32	35	the	the	DET
ejpam-819	32	36	dual	dual	ADJ
ejpam-819	32	37	problem	problem	NOUN
ejpam-819	32	38	may	may	AUX
ejpam-819	32	39	be	be	AUX
ejpam-819	32	40	found	find	VERB
ejpam-819	32	41	.	.	PUNCT
ejpam-819	33	1	the	the	DET
ejpam-819	33	2	theory	theory	NOUN
ejpam-819	33	3	of	of	ADP
ejpam-819	33	4	non	non	ADJ
ejpam-819	33	5	-	-	ADJ
ejpam-819	33	6	smooth	smooth	ADJ
ejpam-819	33	7	mathematical	mathematical	ADJ
ejpam-819	33	8	programming	programming	NOUN
ejpam-819	33	9	deals	deal	NOUN
ejpam-819	33	10	with	with	ADP
ejpam-819	33	11	more	more	ADJ
ejpam-819	33	12	general	general	ADJ
ejpam-819	33	13	type	type	NOUN
ejpam-819	33	14	of	of	ADP
ejpam-819	33	15	functions	function	NOUN
ejpam-819	33	16	by	by	ADP
ejpam-819	33	17	means	mean	NOUN
ejpam-819	33	18	of	of	ADP
ejpam-819	33	19	generalized	generalized	ADJ
ejpam-819	33	20	subdifferentials	subdifferential	NOUN
ejpam-819	33	21	.	.	PUNCT
ejpam-819	34	1	however	however	ADV
ejpam-819	34	2	,	,	PUNCT
ejpam-819	34	3	square	square	ADJ
ejpam-819	34	4	root	root	NOUN
ejpam-819	34	5	of	of	ADP
ejpam-819	34	6	positive	positive	ADJ
ejpam-819	34	7	semi	semi	ADJ
ejpam-819	34	8	-	-	ADJ
ejpam-819	34	9	definite	definite	ADJ
ejpam-819	34	10	quadratic	quadratic	ADJ
ejpam-819	34	11	form	form	NOUN
ejpam-819	34	12	is	be	AUX
ejpam-819	34	13	one	one	NUM
ejpam-819	34	14	of	of	ADP
ejpam-819	34	15	the	the	DET
ejpam-819	34	16	few	few	ADJ
ejpam-819	34	17	cases	case	NOUN
ejpam-819	34	18	of	of	ADP
ejpam-819	34	19	the	the	DET
ejpam-819	34	20	nondifferentiable	nondifferentiable	ADJ
ejpam-819	34	21	functions	function	NOUN
ejpam-819	34	22	for	for	ADP
ejpam-819	34	23	which	which	PRON
ejpam-819	34	24	one	one	PRON
ejpam-819	34	25	can	can	AUX
ejpam-819	34	26	write	write	VERB
ejpam-819	34	27	down	down	ADP
ejpam-819	34	28	the	the	DET
ejpam-819	34	29	sub	sub	ADJ
ejpam-819	34	30	-	-	ADJ
ejpam-819	34	31	or	or	CCONJ
ejpam-819	34	32	quasi	quasi	ADJ
ejpam-819	34	33	-	-	NOUN
ejpam-819	34	34	differentials	differential	NOUN
ejpam-819	34	35	explicitly	explicitly	ADV
ejpam-819	34	36	.	.	PUNCT
ejpam-819	35	1	here	here	ADV
ejpam-819	35	2	,	,	PUNCT
ejpam-819	35	3	various	various	ADJ
ejpam-819	35	4	duality	duality	NOUN
ejpam-819	35	5	theorems	theorem	NOUN
ejpam-819	35	6	for	for	ADP
ejpam-819	35	7	this	this	DET
ejpam-819	35	8	pair	pair	NOUN
ejpam-819	35	9	of	of	ADP
ejpam-819	35	10	wolfe	wolfe	PROPN
ejpam-819	35	11	type	type	PROPN
ejpam-819	35	12	dual	dual	ADJ
ejpam-819	35	13	problems	problem	NOUN
ejpam-819	35	14	are	be	AUX
ejpam-819	35	15	validated	validate	VERB
ejpam-819	35	16	under	under	ADP
ejpam-819	35	17	second	second	ADJ
ejpam-819	35	18	order	order	NOUN
ejpam-819	35	19	pseudo	pseudo	NOUN
ejpam-819	35	20	-	-	ADJ
ejpam-819	35	21	invexity	invexity	NOUN
ejpam-819	35	22	condition	condition	NOUN
ejpam-819	35	23	.	.	PUNCT
ejpam-819	36	1	a	a	DET
ejpam-819	36	2	pair	pair	NOUN
ejpam-819	36	3	of	of	ADP
ejpam-819	36	4	wolfe	wolfe	PROPN
ejpam-819	36	5	type	type	NOUN
ejpam-819	36	6	dual	dual	ADJ
ejpam-819	36	7	variational	variational	ADJ
ejpam-819	36	8	problems	problem	NOUN
ejpam-819	36	9	with	with	ADP
ejpam-819	36	10	natural	natural	ADJ
ejpam-819	36	11	boundary	boundary	ADJ
ejpam-819	36	12	values	value	NOUN
ejpam-819	36	13	rather	rather	ADV
ejpam-819	36	14	than	than	ADP
ejpam-819	36	15	fixed	fix	VERB
ejpam-819	36	16	end	end	NOUN
ejpam-819	36	17	points	point	NOUN
ejpam-819	36	18	is	be	AUX
ejpam-819	36	19	presented	present	VERB
ejpam-819	36	20	and	and	CCONJ
ejpam-819	36	21	the	the	DET
ejpam-819	36	22	proofs	proof	NOUN
ejpam-819	36	23	of	of	ADP
ejpam-819	36	24	its	its	PRON
ejpam-819	36	25	duality	duality	NOUN
ejpam-819	36	26	results	result	NOUN
ejpam-819	36	27	are	be	AUX
ejpam-819	36	28	indicated	indicate	VERB
ejpam-819	36	29	.	.	PUNCT
ejpam-819	37	1	it	it	PRON
ejpam-819	37	2	is	be	AUX
ejpam-819	37	3	also	also	ADV
ejpam-819	37	4	shown	show	VERB
ejpam-819	37	5	that	that	SCONJ
ejpam-819	37	6	our	our	PRON
ejpam-819	37	7	second	second	ADJ
ejpam-819	37	8	-	-	PUNCT
ejpam-819	37	9	order	order	NOUN
ejpam-819	37	10	duality	duality	NOUN
ejpam-819	37	11	results	result	NOUN
ejpam-819	37	12	can	can	AUX
ejpam-819	37	13	be	be	AUX
ejpam-819	37	14	considered	consider	VERB
ejpam-819	37	15	as	as	ADP
ejpam-819	37	16	dynamic	dynamic	ADJ
ejpam-819	37	17	generalizations	generalization	NOUN
ejpam-819	37	18	of	of	ADP
ejpam-819	37	19	corresponding	correspond	VERB
ejpam-819	37	20	(	(	PUNCT
ejpam-819	37	21	static	static	ADJ
ejpam-819	37	22	)	)	PUNCT
ejpam-819	37	23	second	second	ADJ
ejpam-819	37	24	-	-	PUNCT
ejpam-819	37	25	order	order	NOUN
ejpam-819	37	26	duality	duality	NOUN
ejpam-819	37	27	results	result	NOUN
ejpam-819	37	28	established	establish	VERB
ejpam-819	37	29	for	for	ADP
ejpam-819	37	30	nondifferentiable	nondifferentiable	ADJ
ejpam-819	37	31	nonlinear	nonlinear	ADJ
ejpam-819	37	32	programming	programming	NOUN
ejpam-819	37	33	problem	problem	NOUN
ejpam-819	37	34	,	,	PUNCT
ejpam-819	37	35	considered	consider	VERB
ejpam-819	37	36	by	by	ADP
ejpam-819	37	37	zhang	zhang	PROPN
ejpam-819	37	38	and	and	CCONJ
ejpam-819	37	39	mond	mond	VERB
ejpam-819	38	1	[	[	X
ejpam-819	38	2	10	10	NUM
ejpam-819	38	3	]	]	PUNCT
ejpam-819	38	4	.	.	PUNCT
ejpam-819	39	1	2	2	X
ejpam-819	39	2	.	.	X
ejpam-819	39	3	definitions	definition	NOUN
ejpam-819	39	4	and	and	CCONJ
ejpam-819	39	5	related	relate	VERB
ejpam-819	39	6	pre	pre	NOUN
ejpam-819	39	7	-	-	NOUN
ejpam-819	39	8	requistes	requiste	NOUN
ejpam-819	39	9	let	let	VERB
ejpam-819	39	10	i	i	PRON
ejpam-819	39	11	=	=	PUNCT
ejpam-819	40	1	[	[	X
ejpam-819	40	2	a	a	X
ejpam-819	40	3	,	,	PUNCT
ejpam-819	40	4	b	b	AUX
ejpam-819	40	5	]	]	PUNCT
ejpam-819	40	6	be	be	AUX
ejpam-819	40	7	a	a	DET
ejpam-819	40	8	real	real	ADJ
ejpam-819	40	9	interval	interval	NOUN
ejpam-819	40	10	,	,	PUNCT
ejpam-819	40	11	φ	φ	PROPN
ejpam-819	40	12	:	:	PUNCT
ejpam-819	41	1	i	i	PRON
ejpam-819	41	2	×rn×rn	×rn×rn	VERB
ejpam-819	41	3	−→	−→	NOUN
ejpam-819	41	4	r	r	NOUN
ejpam-819	41	5	and	and	CCONJ
ejpam-819	41	6	ψ	ψ	NOUN
ejpam-819	41	7	:	:	PUNCT
ejpam-819	41	8	i	i	PRON
ejpam-819	41	9	×rn×rn	×rn×rn	VERB
ejpam-819	41	10	−→	−→	PROPN
ejpam-819	41	11	rm	rm	PROPN
ejpam-819	41	12	be	be	AUX
ejpam-819	41	13	twice	twice	ADV
ejpam-819	41	14	continuously	continuously	ADV
ejpam-819	41	15	differentiable	differentiable	ADJ
ejpam-819	41	16	functions	function	NOUN
ejpam-819	41	17	.	.	PUNCT
ejpam-819	42	1	in	in	ADP
ejpam-819	42	2	order	order	NOUN
ejpam-819	42	3	to	to	PART
ejpam-819	42	4	consider	consider	VERB
ejpam-819	42	5	φ(t	φ(t	PROPN
ejpam-819	42	6	,	,	PUNCT
ejpam-819	42	7	x(t	x(t	PROPN
ejpam-819	42	8	)	)	PUNCT
ejpam-819	42	9	,	,	PUNCT
ejpam-819	42	10	ẋ(t	ẋ(t	NOUN
ejpam-819	42	11	)	)	PUNCT
ejpam-819	42	12	)	)	PUNCT
ejpam-819	42	13	where	where	SCONJ
ejpam-819	42	14	x	x	X
ejpam-819	42	15	:	:	PUNCT
ejpam-819	42	16	i	i	PRON
ejpam-819	42	17	−→	−→	VERB
ejpam-819	42	18	rn	rn	PROPN
ejpam-819	42	19	is	be	AUX
ejpam-819	42	20	differentiable	differentiable	ADJ
ejpam-819	42	21	with	with	ADP
ejpam-819	42	22	derivative	derivative	PROPN
ejpam-819	42	23	ẋ	ẋ	PROPN
ejpam-819	42	24	,	,	PUNCT
ejpam-819	42	25	denoted	denote	VERB
ejpam-819	42	26	by	by	ADP
ejpam-819	42	27	φx	φx	PROPN
ejpam-819	42	28	and	and	CCONJ
ejpam-819	42	29	φ	φ	PROPN
ejpam-819	42	30	ẋ	ẋ	PROPN
ejpam-819	42	31	,	,	PUNCT
ejpam-819	42	32	the	the	DET
ejpam-819	42	33	first	first	ADJ
ejpam-819	42	34	order	order	NOUN
ejpam-819	42	35	of	of	ADP
ejpam-819	42	36	φ	φ	PROPN
ejpam-819	42	37	with	with	ADP
ejpam-819	42	38	respect	respect	NOUN
ejpam-819	42	39	to	to	ADP
ejpam-819	42	40	x(t	x(t	PROPN
ejpam-819	42	41	)	)	PUNCT
ejpam-819	42	42	and	and	CCONJ
ejpam-819	42	43	ẋ(t	ẋ(t	NOUN
ejpam-819	42	44	)	)	PUNCT
ejpam-819	42	45	,	,	PUNCT
ejpam-819	42	46	respectively	respectively	ADV
ejpam-819	42	47	,	,	PUNCT
ejpam-819	42	48	that	that	ADV
ejpam-819	42	49	is	is	ADV
ejpam-819	42	50	,	,	PUNCT
ejpam-819	42	51	φx	φx	PROPN
ejpam-819	42	52	=	=	SYM
ejpam-819	42	53	�	�	PROPN
ejpam-819	42	54	∂	∂	PROPN
ejpam-819	42	55	φ	φ	PROPN
ejpam-819	42	56	∂	∂	NUM
ejpam-819	42	57	x1	x1	PROPN
ejpam-819	42	58	,	,	PUNCT
ejpam-819	42	59	∂	∂	NUM
ejpam-819	42	60	φ	φ	PROPN
ejpam-819	42	61	∂	∂	PROPN
ejpam-819	42	62	x2	x2	PROPN
ejpam-819	42	63	,	,	PUNCT
ejpam-819	42	64	...	...	PUNCT
ejpam-819	42	65	,	,	PUNCT
ejpam-819	42	66	∂	∂	NUM
ejpam-819	42	67	φ	φ	PROPN
ejpam-819	42	68	∂	∂	PROPN
ejpam-819	42	69	xn	xn	PROPN
ejpam-819	42	70	�	�	PROPN
ejpam-819	42	71	t	t	PROPN
ejpam-819	42	72	,	,	PUNCT
ejpam-819	42	73	φ	φ	PROPN
ejpam-819	42	74	ẋ	ẋ	PUNCT
ejpam-819	43	1	=	=	SYM
ejpam-819	43	2	�	�	PROPN
ejpam-819	43	3	∂	∂	PROPN
ejpam-819	43	4	φ	φ	PROPN
ejpam-819	43	5	∂	∂	NOUN
ejpam-819	44	1	ẋ1	ẋ1	PROPN
ejpam-819	44	2	,	,	PUNCT
ejpam-819	44	3	∂	∂	NUM
ejpam-819	44	4	φ	φ	NOUN
ejpam-819	44	5	∂	∂	X
ejpam-819	45	1	ẋ2	ẋ2	PROPN
ejpam-819	45	2	,	,	PUNCT
ejpam-819	45	3	...	...	PUNCT
ejpam-819	45	4	,	,	PUNCT
ejpam-819	45	5	∂	∂	NUM
ejpam-819	45	6	φ	φ	PROPN
ejpam-819	45	7	∂	∂	NOUN
ejpam-819	45	8	ẋn	ẋn	PROPN
ejpam-819	45	9	�	�	PROPN
ejpam-819	45	10	t	t	PROPN
ejpam-819	45	11	denote	denote	VERB
ejpam-819	45	12	by	by	ADP
ejpam-819	45	13	φx	φx	PROPN
ejpam-819	45	14	x	x	SYM
ejpam-819	45	15	the	the	DET
ejpam-819	45	16	hessian	hessian	ADJ
ejpam-819	45	17	matrix	matrix	NOUN
ejpam-819	45	18	of	of	ADP
ejpam-819	45	19	φ	φ	NUM
ejpam-819	45	20	,	,	PUNCT
ejpam-819	45	21	and	and	CCONJ
ejpam-819	45	22	ψx	ψx	VERB
ejpam-819	45	23	the	the	DET
ejpam-819	45	24	m×	m×	PROPN
ejpam-819	45	25	n	n	CCONJ
ejpam-819	45	26	jacobian	jacobian	ADJ
ejpam-819	45	27	matrix	matrix	NOUN
ejpam-819	45	28	respectively	respectively	ADV
ejpam-819	45	29	,	,	PUNCT
ejpam-819	45	30	that	that	ADV
ejpam-819	45	31	is	is	ADV
ejpam-819	45	32	,	,	PUNCT
ejpam-819	45	33	with	with	ADP
ejpam-819	45	34	respect	respect	NOUN
ejpam-819	45	35	to	to	ADP
ejpam-819	45	36	x(t	x(t	PROPN
ejpam-819	45	37	)	)	PUNCT
ejpam-819	45	38	,	,	PUNCT
ejpam-819	45	39	that	that	ADV
ejpam-819	45	40	is	is	ADV
ejpam-819	45	41	,	,	PUNCT
ejpam-819	45	42	φx	φx	PROPN
ejpam-819	45	43	x	x	X
ejpam-819	45	44	=	=	PRON
ejpam-819	45	45	(	(	PUNCT
ejpam-819	45	46	∂	∂	NUM
ejpam-819	45	47	2φ	2φ	NUM
ejpam-819	45	48	∂	∂	NOUN
ejpam-819	45	49	x	x	VERB
ejpam-819	45	50	i∂	i∂	VERB
ejpam-819	45	51	x	x	SYM
ejpam-819	45	52	j	j	PROPN
ejpam-819	45	53	)	)	PUNCT
ejpam-819	45	54	,	,	PUNCT
ejpam-819	46	1	i	i	PRON
ejpam-819	46	2	,	,	PUNCT
ejpam-819	46	3	j	j	PROPN
ejpam-819	46	4	=	=	SYM
ejpam-819	46	5	1,2	1,2	NUM
ejpam-819	46	6	,	,	PUNCT
ejpam-819	46	7	...	...	PUNCT
ejpam-819	46	8	n	n	CCONJ
ejpam-819	46	9	,	,	PUNCT
ejpam-819	46	10	ψx	ψx	VERB
ejpam-819	46	11	the	the	DET
ejpam-819	46	12	m×	m×	PROPN
ejpam-819	46	13	n	n	CCONJ
ejpam-819	46	14	jacobian	jacobian	ADJ
ejpam-819	46	15	matrix	matrix	NOUN
ejpam-819	46	16	ψx	ψx	ADP
ejpam-819	46	17	=	=	SYM
ejpam-819	46	18			PROPN
ejpam-819	46	19			NOUN
ejpam-819	46	20			NOUN
ejpam-819	46	21			NOUN
ejpam-819	46	22			NOUN
ejpam-819	46	23			NOUN
ejpam-819	46	24			NOUN
ejpam-819	46	25	∂	∂	NUM
ejpam-819	46	26	ψ1	ψ1	NOUN
ejpam-819	46	27	∂	∂	PUNCT
ejpam-819	46	28	x1	x1	NOUN
ejpam-819	46	29	∂	∂	NUM
ejpam-819	46	30	ψ1	ψ1	NOUN
ejpam-819	46	31	∂	∂	PUNCT
ejpam-819	46	32	x2	x2	NOUN
ejpam-819	46	33	·	·	PUNCT
ejpam-819	46	34	·	·	PUNCT
ejpam-819	46	35	·	·	PUNCT
ejpam-819	46	36	∂	∂	NUM
ejpam-819	46	37	ψ1	ψ1	NOUN
ejpam-819	46	38	∂	∂	NOUN
ejpam-819	46	39	xn	xn	PROPN
ejpam-819	46	40	∂	∂	NUM
ejpam-819	46	41	ψ2	ψ2	NOUN
ejpam-819	46	42	∂	∂	NUM
ejpam-819	46	43	x1	x1	NUM
ejpam-819	46	44	∂	∂	NUM
ejpam-819	46	45	ψ2	ψ2	NOUN
ejpam-819	46	46	∂	∂	NUM
ejpam-819	46	47	x2	x2	X
ejpam-819	46	48	·	·	PUNCT
ejpam-819	46	49	·	·	PUNCT
ejpam-819	46	50	·	·	PUNCT
ejpam-819	46	51	∂	∂	NUM
ejpam-819	46	52	ψ2	ψ2	NOUN
ejpam-819	46	53	∂	∂	NUM
ejpam-819	46	54	xn	xn	NUM
ejpam-819	46	55	...	...	PUNCT
ejpam-819	46	56	...	...	PUNCT
ejpam-819	46	57	...	...	PUNCT
ejpam-819	47	1	∂	∂	NUM
ejpam-819	47	2	ψm	ψm	SYM
ejpam-819	47	3	∂	∂	PROPN
ejpam-819	48	1	x1	x1	PROPN
ejpam-819	48	2	∂	∂	PROPN
ejpam-819	48	3	ψm	ψm	PROPN
ejpam-819	48	4	∂	∂	NOUN
ejpam-819	48	5	x2	x2	PROPN
ejpam-819	48	6	·	·	PUNCT
ejpam-819	48	7	·	·	PUNCT
ejpam-819	48	8	·	·	PUNCT
ejpam-819	48	9	∂	∂	NUM
ejpam-819	48	10	ψm	ψm	SYM
ejpam-819	48	11	∂	∂	PROPN
ejpam-819	48	12	xn	xn	PROPN
ejpam-819	48	13			PROPN
ejpam-819	48	14			NOUN
ejpam-819	48	15			VERB
ejpam-819	48	16			NOUN
ejpam-819	48	17			NOUN
ejpam-819	48	18			NOUN
ejpam-819	48	19			PUNCT
ejpam-819	49	1	n×n	n×n	PROPN
ejpam-819	49	2	the	the	DET
ejpam-819	49	3	symbols	symbol	NOUN
ejpam-819	49	4	φ	φ	PROPN
ejpam-819	49	5	ẋ	ẋ	PROPN
ejpam-819	49	6	,	,	PUNCT
ejpam-819	49	7	φ	φ	PROPN
ejpam-819	49	8	ẋ	ẋ	PROPN
ejpam-819	50	1	x	x	X
ejpam-819	50	2	,	,	PUNCT
ejpam-819	50	3	φx	φx	PROPN
ejpam-819	50	4	ẋ	ẋ	PROPN
ejpam-819	50	5	and	and	CCONJ
ejpam-819	50	6	ψ	ψ	PROPN
ejpam-819	50	7	ẋ	ẋ	PROPN
ejpam-819	50	8	have	have	VERB
ejpam-819	50	9	analogous	analogous	ADJ
ejpam-819	50	10	representations	representation	NOUN
ejpam-819	50	11	.	.	PUNCT
ejpam-819	51	1	designate	designate	ADJ
ejpam-819	51	2	by	by	ADP
ejpam-819	51	3	x	x	PROPN
ejpam-819	51	4	the	the	DET
ejpam-819	51	5	space	space	NOUN
ejpam-819	51	6	of	of	ADP
ejpam-819	51	7	piecewise	piecewise	NOUN
ejpam-819	51	8	smooth	smooth	ADJ
ejpam-819	51	9	functions	function	NOUN
ejpam-819	51	10	x	x	PUNCT
ejpam-819	51	11	:	:	PUNCT
ejpam-819	51	12	i	i	PRON
ejpam-819	51	13	−→	−→	VERB
ejpam-819	51	14	rn	rn	PROPN
ejpam-819	51	15	,	,	PUNCT
ejpam-819	51	16	with	with	SCONJ
ejpam-819	51	17	the	the	DET
ejpam-819	51	18	norm	norm	NOUN
ejpam-819	51	19	‖x‖=	‖x‖=	VERB
ejpam-819	51	20	‖x‖∞+	‖x‖∞+	X
ejpam-819	52	1	‖dx‖∞	‖dx‖∞	PROPN
ejpam-819	52	2	,	,	PUNCT
ejpam-819	52	3	where	where	SCONJ
ejpam-819	52	4	the	the	DET
ejpam-819	52	5	differentiation	differentiation	NOUN
ejpam-819	52	6	operator	operator	NOUN
ejpam-819	52	7	d	d	NOUN
ejpam-819	52	8	is	be	AUX
ejpam-819	52	9	given	give	VERB
ejpam-819	52	10	by	by	ADP
ejpam-819	52	11	u	u	NOUN
ejpam-819	52	12	=	=	PROPN
ejpam-819	52	13	dx	dx	PROPN
ejpam-819	52	14	⇐	⇐	ADJ
ejpam-819	52	15	⇒	⇒	PROPN
ejpam-819	52	16	x(t	x(t	PROPN
ejpam-819	52	17	)	)	PUNCT
ejpam-819	53	1	=	=	SYM
ejpam-819	53	2	∫	∫	PROPN
ejpam-819	53	3	t	t	PROPN
ejpam-819	53	4	a	a	DET
ejpam-819	53	5	u(s)ds	u(s)ds	PROPN
ejpam-819	53	6	,	,	PUNCT
ejpam-819	53	7	i.	i.	PROPN
ejpam-819	53	8	husain	husain	PROPN
ejpam-819	53	9	,	,	PUNCT
ejpam-819	53	10	m.	m.	NOUN
ejpam-819	53	11	masoodi	masoodi	PROPN
ejpam-819	53	12	/	/	SYM
ejpam-819	53	13	eur	eur	PROPN
ejpam-819	53	14	.	.	PUNCT
ejpam-819	54	1	j.	j.	PROPN
ejpam-819	54	2	pure	pure	PROPN
ejpam-819	54	3	appl	appl	PROPN
ejpam-819	54	4	.	.	PROPN
ejpam-819	54	5	math	math	PROPN
ejpam-819	54	6	,	,	PUNCT
ejpam-819	54	7	5	5	NUM
ejpam-819	54	8	(	(	PUNCT
ejpam-819	54	9	2012	2012	NUM
ejpam-819	54	10	)	)	PUNCT
ejpam-819	54	11	,	,	PUNCT
ejpam-819	54	12	390	390	NUM
ejpam-819	54	13	-	-	SYM
ejpam-819	54	14	400	400	NUM
ejpam-819	54	15	392	392	NUM
ejpam-819	55	1	thus	thus	ADV
ejpam-819	55	2	d	d	PROPN
ejpam-819	55	3	d	d	X
ejpam-819	55	4	t	t	PROPN
ejpam-819	55	5	=	=	PUNCT
ejpam-819	55	6	d	d	PROPN
ejpam-819	55	7	except	except	SCONJ
ejpam-819	55	8	at	at	ADP
ejpam-819	55	9	discontinuities	discontinuity	NOUN
ejpam-819	55	10	.	.	PUNCT
ejpam-819	56	1	we	we	PRON
ejpam-819	56	2	incorporate	incorporate	VERB
ejpam-819	56	3	the	the	DET
ejpam-819	56	4	following	follow	VERB
ejpam-819	56	5	definitions	definition	NOUN
ejpam-819	56	6	which	which	PRON
ejpam-819	56	7	are	be	AUX
ejpam-819	56	8	required	require	VERB
ejpam-819	56	9	in	in	ADP
ejpam-819	56	10	the	the	DET
ejpam-819	56	11	subsequent	subsequent	ADJ
ejpam-819	56	12	analysis	analysis	NOUN
ejpam-819	56	13	.	.	PUNCT
ejpam-819	57	1	definition	definition	NOUN
ejpam-819	57	2	1	1	NUM
ejpam-819	57	3	(	(	PUNCT
ejpam-819	57	4	second	second	ADJ
ejpam-819	57	5	order	order	NOUN
ejpam-819	57	6	invex	invex	NOUN
ejpam-819	57	7	)	)	PUNCT
ejpam-819	57	8	.	.	PUNCT
ejpam-819	58	1	if	if	SCONJ
ejpam-819	58	2	there	there	PRON
ejpam-819	58	3	exists	exist	VERB
ejpam-819	58	4	a	a	DET
ejpam-819	58	5	vector	vector	NOUN
ejpam-819	58	6	function	function	NOUN
ejpam-819	58	7	η	η	PROPN
ejpam-819	58	8	=	=	SYM
ejpam-819	58	9	η(t	η(t	NOUN
ejpam-819	58	10	,	,	PUNCT
ejpam-819	58	11	x	x	SYM
ejpam-819	58	12	,	,	PUNCT
ejpam-819	58	13	x̄	x̄	PROPN
ejpam-819	58	14	)	)	PUNCT
ejpam-819	59	1	∈	∈	PROPN
ejpam-819	59	2	rn	rn	PROPN
ejpam-819	59	3	where	where	SCONJ
ejpam-819	59	4	η	η	PROPN
ejpam-819	59	5	:	:	PUNCT
ejpam-819	59	6	i	i	PRON
ejpam-819	59	7	×	×	VERB
ejpam-819	59	8	rn×rn	rn×rn	PROPN
ejpam-819	59	9	−→	−→	PROPN
ejpam-819	59	10	rn	rn	PROPN
ejpam-819	59	11	with	with	ADP
ejpam-819	59	12	η	η	PROPN
ejpam-819	59	13	=	=	PROPN
ejpam-819	59	14	0	0	PROPN
ejpam-819	59	15	at	at	ADP
ejpam-819	59	16	t	t	NOUN
ejpam-819	59	17	=	=	SYM
ejpam-819	59	18	a	a	PROPN
ejpam-819	59	19	and	and	CCONJ
ejpam-819	59	20	t	t	NOUN
ejpam-819	59	21	=	=	SYM
ejpam-819	59	22	b	b	PROPN
ejpam-819	59	23	,	,	PUNCT
ejpam-819	59	24	such	such	ADJ
ejpam-819	59	25	that	that	PRON
ejpam-819	59	26	for	for	ADP
ejpam-819	59	27	a	a	DET
ejpam-819	59	28	scalar	scalar	ADJ
ejpam-819	59	29	function	function	NOUN
ejpam-819	59	30	φ(t	φ(t	PROPN
ejpam-819	59	31	,	,	PUNCT
ejpam-819	59	32	x	x	X
ejpam-819	59	33	,	,	PUNCT
ejpam-819	59	34	ẋ	ẋ	PROPN
ejpam-819	59	35	)	)	PUNCT
ejpam-819	59	36	,	,	PUNCT
ejpam-819	59	37	the	the	DET
ejpam-819	59	38	functional	functional	ADJ
ejpam-819	59	39	∫	∫	PROPN
ejpam-819	59	40	i	i	PROPN
ejpam-819	59	41	φ(t	φ(t	PROPN
ejpam-819	59	42	,	,	PUNCT
ejpam-819	59	43	x	x	INTJ
ejpam-819	59	44	,	,	PUNCT
ejpam-819	59	45	ẋ)d	ẋ)d	PROPN
ejpam-819	59	46	t	t	PROPN
ejpam-819	59	47	where	where	SCONJ
ejpam-819	59	48	φ	φ	PROPN
ejpam-819	59	49	:	:	PUNCT
ejpam-819	60	1	i	i	PRON
ejpam-819	60	2	×	×	VERB
ejpam-819	60	3	rn×	rn×	NOUN
ejpam-819	60	4	rn	rn	INTJ
ejpam-819	60	5	−→	−→	NOUN
ejpam-819	60	6	r	r	NOUN
ejpam-819	60	7	satisfies	satisfie	NOUN
ejpam-819	60	8	∫	∫	PROPN
ejpam-819	60	9	i	i	PROPN
ejpam-819	60	10	φ(t	φ(t	PROPN
ejpam-819	60	11	,	,	PUNCT
ejpam-819	60	12	x	x	INTJ
ejpam-819	60	13	,	,	PUNCT
ejpam-819	60	14	ẋ)d	ẋ)d	X
ejpam-819	61	1	t−	t−	X
ejpam-819	61	2	∫	∫	PROPN
ejpam-819	61	3	i	i	PRON
ejpam-819	61	4	{	{	PUNCT
ejpam-819	61	5	φ(t	φ(t	PROPN
ejpam-819	61	6	,	,	PUNCT
ejpam-819	61	7	x̄	x̄	NOUN
ejpam-819	61	8	,	,	PUNCT
ejpam-819	61	9	˙̄x)−	˙̄x)−	PROPN
ejpam-819	61	10	1	1	NUM
ejpam-819	61	11	2	2	NUM
ejpam-819	61	12	pt	pt	NOUN
ejpam-819	61	13	(	(	PUNCT
ejpam-819	61	14	t)gp(t)}d	t)gp(t)}d	PROPN
ejpam-819	61	15	t	t	PROPN
ejpam-819	61	16	≥	≥	X
ejpam-819	61	17	∫	∫	PROPN
ejpam-819	62	1	i	i	PRON
ejpam-819	62	2	{	{	PUNCT
ejpam-819	62	3	ηtφx	ηtφx	PROPN
ejpam-819	62	4	(	(	PUNCT
ejpam-819	62	5	t	t	PROPN
ejpam-819	62	6	,	,	PUNCT
ejpam-819	62	7	x̄	x̄	NOUN
ejpam-819	62	8	,	,	PUNCT
ejpam-819	62	9	˙̄x	˙̄x	PUNCT
ejpam-819	62	10	)	)	PUNCT
ejpam-819	63	1	+	+	CCONJ
ejpam-819	63	2	(	(	PUNCT
ejpam-819	63	3	dη)tφ	dη)tφ	NOUN
ejpam-819	63	4	ẋ(t	ẋ(t	NOUN
ejpam-819	63	5	,	,	PUNCT
ejpam-819	63	6	x̄	x̄	NOUN
ejpam-819	63	7	,	,	PUNCT
ejpam-819	63	8	˙̄x)+ηt	˙̄x)+ηt	PROPN
ejpam-819	63	9	gp(t)}d	gp(t)}d	PROPN
ejpam-819	64	1	t	t	PROPN
ejpam-819	64	2	then	then	ADV
ejpam-819	64	3	∫	∫	PROPN
ejpam-819	64	4	i	i	PROPN
ejpam-819	64	5	φ(t	φ(t	PROPN
ejpam-819	64	6	,	,	PUNCT
ejpam-819	64	7	x	x	PRON
ejpam-819	64	8	,	,	PUNCT
ejpam-819	64	9	ẋ)d	ẋ)d	PROPN
ejpam-819	64	10	t	t	PROPN
ejpam-819	64	11	is	be	AUX
ejpam-819	64	12	second	second	ADJ
ejpam-819	64	13	-	-	PUNCT
ejpam-819	64	14	order	order	NOUN
ejpam-819	64	15	invex	invex	NOUN
ejpam-819	64	16	with	with	ADP
ejpam-819	64	17	respect	respect	NOUN
ejpam-819	64	18	to	to	ADP
ejpam-819	64	19	η	η	PROPN
ejpam-819	64	20	where	where	SCONJ
ejpam-819	64	21	g	g	NOUN
ejpam-819	64	22	=	=	SYM
ejpam-819	64	23	φx	φx	PROPN
ejpam-819	64	24	x	x	X
ejpam-819	64	25	−	−	PROPN
ejpam-819	64	26	2dφx	2dφx	NUM
ejpam-819	64	27	ẋ	ẋ	PROPN
ejpam-819	65	1	+	+	CCONJ
ejpam-819	65	2	d2φ	d2φ	INTJ
ejpam-819	65	3	ẋ	ẋ	PROPN
ejpam-819	65	4	ẋ	ẋ	PUNCT
ejpam-819	66	1	−	−	PROPN
ejpam-819	66	2	d3φ	d3φ	PROPN
ejpam-819	66	3	ẋ	ẋ	PROPN
ejpam-819	66	4	ẍ	ẍ	PROPN
ejpam-819	67	1	and	and	CCONJ
ejpam-819	67	2	p	p	PROPN
ejpam-819	67	3	∈	∈	PROPN
ejpam-819	67	4	c(i	c(i	NOUN
ejpam-819	67	5	,	,	PUNCT
ejpam-819	67	6	rn	rn	PROPN
ejpam-819	67	7	)	)	PUNCT
ejpam-819	67	8	,	,	PUNCT
ejpam-819	67	9	the	the	DET
ejpam-819	67	10	space	space	NOUN
ejpam-819	67	11	of	of	ADP
ejpam-819	67	12	continuous	continuous	ADJ
ejpam-819	67	13	n	n	CCONJ
ejpam-819	67	14	-	-	PUNCT
ejpam-819	67	15	dimensional	dimensional	ADJ
ejpam-819	67	16	continuous	continuous	ADJ
ejpam-819	67	17	vector	vector	NOUN
ejpam-819	67	18	functions	function	NOUN
ejpam-819	67	19	.	.	PUNCT
ejpam-819	68	1	definition	definition	NOUN
ejpam-819	68	2	2	2	NUM
ejpam-819	68	3	(	(	PUNCT
ejpam-819	68	4	second	second	ADJ
ejpam-819	68	5	order	order	NOUN
ejpam-819	68	6	pseudoinvex	pseudoinvex	NOUN
ejpam-819	68	7	)	)	PUNCT
ejpam-819	68	8	.	.	PUNCT
ejpam-819	69	1	if	if	SCONJ
ejpam-819	69	2	the	the	DET
ejpam-819	69	3	functional	functional	ADJ
ejpam-819	69	4	∫	∫	PROPN
ejpam-819	69	5	i	i	PROPN
ejpam-819	69	6	φ(t	φ(t	PROPN
ejpam-819	69	7	,	,	PUNCT
ejpam-819	69	8	x	x	INTJ
ejpam-819	69	9	,	,	PUNCT
ejpam-819	69	10	ẋ)d	ẋ)d	PROPN
ejpam-819	69	11	t	t	PROPN
ejpam-819	69	12	satisfies	satisfy	VERB
ejpam-819	69	13	∫	∫	PROPN
ejpam-819	69	14	i	i	PRON
ejpam-819	69	15	{	{	PUNCT
ejpam-819	69	16	ηtφx+(dη	ηtφx+(dη	X
ejpam-819	69	17	)	)	PUNCT
ejpam-819	69	18	tφ	tφ	PROPN
ejpam-819	69	19	ẋ	ẋ	PUNCT
ejpam-819	70	1	+	+	PROPN
ejpam-819	70	2	η	η	PROPN
ejpam-819	70	3	t	t	PROPN
ejpam-819	70	4	gp(t)}d	gp(t)}d	PROPN
ejpam-819	70	5	t	t	PROPN
ejpam-819	70	6	≥	≥	NOUN
ejpam-819	70	7	0=⇒	0=⇒	NUM
ejpam-819	70	8	∫	∫	PROPN
ejpam-819	70	9	i	i	PROPN
ejpam-819	70	10	φ(t	φ(t	PROPN
ejpam-819	70	11	,	,	PUNCT
ejpam-819	70	12	x	x	INTJ
ejpam-819	70	13	,	,	PUNCT
ejpam-819	70	14	ẋ)d	ẋ)d	PROPN
ejpam-819	70	15	t	t	PROPN
ejpam-819	70	16	≥	≥	PROPN
ejpam-819	70	17	∫	∫	PROPN
ejpam-819	70	18	i	i	PRON
ejpam-819	70	19	{	{	PUNCT
ejpam-819	70	20	φ(t	φ(t	PROPN
ejpam-819	70	21	,	,	PUNCT
ejpam-819	70	22	x̄	x̄	NOUN
ejpam-819	70	23	,	,	PUNCT
ejpam-819	70	24	˙̄x)−	˙̄x)−	PROPN
ejpam-819	70	25	1	1	NUM
ejpam-819	70	26	2	2	NUM
ejpam-819	70	27	p(t)t	p(t)t	NOUN
ejpam-819	70	28	gp(t)}d	gp(t)}d	PROPN
ejpam-819	70	29	t	t	PROPN
ejpam-819	70	30	,	,	PUNCT
ejpam-819	70	31	then	then	ADV
ejpam-819	70	32	∫	∫	PROPN
ejpam-819	70	33	i	i	PROPN
ejpam-819	70	34	φ(t	φ(t	PROPN
ejpam-819	70	35	,	,	PUNCT
ejpam-819	70	36	x	x	PRON
ejpam-819	70	37	,	,	PUNCT
ejpam-819	70	38	ẋ)d	ẋ)d	PROPN
ejpam-819	70	39	t	t	PROPN
ejpam-819	70	40	is	be	AUX
ejpam-819	70	41	said	say	VERB
ejpam-819	70	42	to	to	PART
ejpam-819	70	43	be	be	AUX
ejpam-819	70	44	second	second	ADJ
ejpam-819	70	45	-	-	PUNCT
ejpam-819	70	46	order	order	NOUN
ejpam-819	70	47	pseudoinvex	pseudoinvex	NOUN
ejpam-819	70	48	with	with	ADP
ejpam-819	70	49	respect	respect	NOUN
ejpam-819	70	50	to	to	ADP
ejpam-819	70	51	η	η	PROPN
ejpam-819	70	52	.	.	PROPN
ejpam-819	70	53	definition	definition	NOUN
ejpam-819	70	54	3	3	NUM
ejpam-819	70	55	(	(	PUNCT
ejpam-819	70	56	second	second	ADJ
ejpam-819	70	57	order	order	NOUN
ejpam-819	70	58	quasi	quasi	NOUN
ejpam-819	70	59	-	-	NOUN
ejpam-819	70	60	invex	invex	ADJ
ejpam-819	70	61	)	)	PUNCT
ejpam-819	70	62	.	.	PUNCT
ejpam-819	71	1	if	if	SCONJ
ejpam-819	71	2	the	the	DET
ejpam-819	71	3	functional	functional	ADJ
ejpam-819	71	4	∫	∫	PROPN
ejpam-819	71	5	i	i	PROPN
ejpam-819	71	6	φ(t	φ(t	PROPN
ejpam-819	71	7	,	,	PUNCT
ejpam-819	71	8	x	x	INTJ
ejpam-819	71	9	,	,	PUNCT
ejpam-819	71	10	ẋ)d	ẋ)d	PROPN
ejpam-819	71	11	t	t	PROPN
ejpam-819	71	12	satisfies	satisfy	VERB
ejpam-819	71	13	∫	∫	PROPN
ejpam-819	71	14	i	i	PROPN
ejpam-819	71	15	φ(t	φ(t	PROPN
ejpam-819	71	16	,	,	PUNCT
ejpam-819	71	17	x	x	INTJ
ejpam-819	71	18	,	,	PUNCT
ejpam-819	71	19	ẋ)d	ẋ)d	PROPN
ejpam-819	71	20	t	t	PROPN
ejpam-819	71	21	≤	≤	NUM
ejpam-819	72	1	∫	∫	PROPN
ejpam-819	73	1	i	i	PRON
ejpam-819	73	2	{	{	PUNCT
ejpam-819	73	3	φ(t	φ(t	PROPN
ejpam-819	73	4	,	,	PUNCT
ejpam-819	73	5	x̄	x̄	NOUN
ejpam-819	73	6	,	,	PUNCT
ejpam-819	73	7	˙̄x)−	˙̄x)−	PROPN
ejpam-819	73	8	1	1	NUM
ejpam-819	73	9	2	2	NUM
ejpam-819	73	10	p(t)t	p(t)t	NOUN
ejpam-819	73	11	(	(	PUNCT
ejpam-819	73	12	t)gp(t)}d	t)gp(t)}d	NOUN
ejpam-819	73	13	t	t	NOUN
ejpam-819	73	14	=	=	AUX
ejpam-819	73	15	⇒	⇒	PROPN
ejpam-819	73	16	∫	∫	PROPN
ejpam-819	74	1	i	i	PRON
ejpam-819	74	2	{	{	PUNCT
ejpam-819	74	3	ηtφx	ηtφx	PROPN
ejpam-819	74	4	+	+	PROPN
ejpam-819	74	5	(	(	PUNCT
ejpam-819	74	6	dη	dη	NOUN
ejpam-819	74	7	)	)	PUNCT
ejpam-819	74	8	tφ	tφ	PROPN
ejpam-819	74	9	ẋ	ẋ	PUNCT
ejpam-819	75	1	+	+	PROPN
ejpam-819	75	2	η	η	PROPN
ejpam-819	75	3	t	t	NOUN
ejpam-819	75	4	g(t)p(t)}d	g(t)p(t)}d	NOUN
ejpam-819	75	5	t	t	PROPN
ejpam-819	75	6	≤	≤	NUM
ejpam-819	75	7	0	0	NUM
ejpam-819	75	8	,	,	PUNCT
ejpam-819	75	9	then	then	ADV
ejpam-819	75	10	∫	∫	PROPN
ejpam-819	75	11	i	i	PROPN
ejpam-819	75	12	φ(t	φ(t	PROPN
ejpam-819	75	13	,	,	PUNCT
ejpam-819	75	14	x	x	PRON
ejpam-819	75	15	,	,	PUNCT
ejpam-819	75	16	ẋ)d	ẋ)d	PROPN
ejpam-819	75	17	t	t	PROPN
ejpam-819	75	18	is	be	AUX
ejpam-819	75	19	said	say	VERB
ejpam-819	75	20	to	to	PART
ejpam-819	75	21	be	be	AUX
ejpam-819	75	22	second	second	ADJ
ejpam-819	75	23	-	-	PUNCT
ejpam-819	75	24	order	order	NOUN
ejpam-819	75	25	quasi	quasi	NOUN
ejpam-819	75	26	-	-	NOUN
ejpam-819	75	27	invex	invex	ADJ
ejpam-819	75	28	with	with	ADP
ejpam-819	75	29	respect	respect	NOUN
ejpam-819	75	30	to	to	ADP
ejpam-819	75	31	η	η	PROPN
ejpam-819	75	32	.	.	PROPN
ejpam-819	75	33	remark	remark	PROPN
ejpam-819	75	34	1	1	NUM
ejpam-819	75	35	.	.	PUNCT
ejpam-819	76	1	if	if	SCONJ
ejpam-819	76	2	φ	φ	PROPN
ejpam-819	76	3	does	do	AUX
ejpam-819	76	4	not	not	PART
ejpam-819	76	5	depend	depend	VERB
ejpam-819	76	6	explicitly	explicitly	ADV
ejpam-819	76	7	on	on	ADP
ejpam-819	76	8	t	t	PROPN
ejpam-819	76	9	,	,	PUNCT
ejpam-819	76	10	then	then	ADV
ejpam-819	76	11	the	the	DET
ejpam-819	76	12	above	above	ADJ
ejpam-819	76	13	definitions	definition	NOUN
ejpam-819	76	14	reduce	reduce	VERB
ejpam-819	76	15	to	to	ADP
ejpam-819	76	16	those	those	PRON
ejpam-819	76	17	given	give	VERB
ejpam-819	76	18	in	in	ADP
ejpam-819	76	19	[	[	X
ejpam-819	76	20	6	6	NUM
ejpam-819	76	21	]	]	PUNCT
ejpam-819	76	22	for	for	ADP
ejpam-819	76	23	static	static	ADJ
ejpam-819	76	24	cases	case	NOUN
ejpam-819	76	25	.	.	PUNCT
ejpam-819	77	1	consider	consider	VERB
ejpam-819	77	2	the	the	DET
ejpam-819	77	3	following	follow	VERB
ejpam-819	77	4	class	class	NOUN
ejpam-819	77	5	of	of	ADP
ejpam-819	77	6	non	non	ADJ
ejpam-819	77	7	-	-	ADJ
ejpam-819	77	8	differentiable	differentiable	ADJ
ejpam-819	77	9	continuous	continuous	ADJ
ejpam-819	77	10	programming	programming	NOUN
ejpam-819	77	11	problem	problem	NOUN
ejpam-819	77	12	studied	study	VERB
ejpam-819	77	13	in	in	ADP
ejpam-819	77	14	[	[	X
ejpam-819	77	15	2	2	NUM
ejpam-819	77	16	]	]	NUM
ejpam-819	77	17	:	:	PUNCT
ejpam-819	77	18	(	(	PUNCT
ejpam-819	77	19	p+	p+	NOUN
ejpam-819	77	20	)	)	PUNCT
ejpam-819	77	21	minimize	minimize	VERB
ejpam-819	77	22	∫	∫	PROPN
ejpam-819	77	23	i	i	PRON
ejpam-819	77	24	{	{	PUNCT
ejpam-819	77	25	f	f	PROPN
ejpam-819	77	26	(	(	PUNCT
ejpam-819	77	27	t	t	PROPN
ejpam-819	77	28	,	,	PUNCT
ejpam-819	77	29	x(t	x(t	PROPN
ejpam-819	77	30	)	)	PUNCT
ejpam-819	77	31	,	,	PUNCT
ejpam-819	77	32	ẋ(t	ẋ(t	NOUN
ejpam-819	77	33	)	)	PUNCT
ejpam-819	77	34	)	)	PUNCT
ejpam-819	78	1	+	+	CCONJ
ejpam-819	78	2	(	(	PUNCT
ejpam-819	78	3	x(t)t	x(t)t	PROPN
ejpam-819	78	4	b(t)x(t))1/2}d	b(t)x(t))1/2}d	PROPN
ejpam-819	78	5	t	t	AUX
ejpam-819	78	6	subject	subject	NOUN
ejpam-819	78	7	to	to	ADP
ejpam-819	78	8	x(a	x(a	NOUN
ejpam-819	78	9	)	)	PUNCT
ejpam-819	78	10	=	=	SYM
ejpam-819	78	11	0=	0=	NUM
ejpam-819	79	1	x(b	x(b	PROPN
ejpam-819	79	2	)	)	PUNCT
ejpam-819	79	3	,	,	PUNCT
ejpam-819	79	4	g(t	g(t	PROPN
ejpam-819	79	5	,	,	PUNCT
ejpam-819	79	6	x(t	x(t	PROPN
ejpam-819	79	7	)	)	PUNCT
ejpam-819	79	8	,	,	PUNCT
ejpam-819	79	9	ẋ(t	ẋ(t	NUM
ejpam-819	79	10	)	)	PUNCT
ejpam-819	79	11	)	)	PUNCT
ejpam-819	79	12	≤	≤	ADV
ejpam-819	79	13	0	0	NUM
ejpam-819	79	14	,	,	PUNCT
ejpam-819	79	15	t	t	PROPN
ejpam-819	79	16	∈	∈	PROPN
ejpam-819	80	1	i	i	PRON
ejpam-819	80	2	,	,	PUNCT
ejpam-819	80	3	h(t	h(t	PROPN
ejpam-819	80	4	,	,	PUNCT
ejpam-819	80	5	x(t	x(t	PROPN
ejpam-819	80	6	)	)	PUNCT
ejpam-819	80	7	,	,	PUNCT
ejpam-819	80	8	ẋ(t	ẋ(t	NOUN
ejpam-819	80	9	)	)	PUNCT
ejpam-819	80	10	)	)	PUNCT
ejpam-819	81	1	=	=	SYM
ejpam-819	81	2	0	0	NUM
ejpam-819	81	3	,	,	PUNCT
ejpam-819	81	4	t	t	PROPN
ejpam-819	81	5	∈	∈	PROPN
ejpam-819	82	1	i	i	PRON
ejpam-819	82	2	where	where	SCONJ
ejpam-819	82	3	i.	i.	PROPN
ejpam-819	82	4	husain	husain	PROPN
ejpam-819	82	5	,	,	PUNCT
ejpam-819	82	6	m.	m.	NOUN
ejpam-819	82	7	masoodi	masoodi	PROPN
ejpam-819	82	8	/	/	SYM
ejpam-819	82	9	eur	eur	PROPN
ejpam-819	82	10	.	.	PUNCT
ejpam-819	83	1	j.	j.	PROPN
ejpam-819	83	2	pure	pure	PROPN
ejpam-819	83	3	appl	appl	PROPN
ejpam-819	83	4	.	.	PROPN
ejpam-819	83	5	math	math	PROPN
ejpam-819	83	6	,	,	PUNCT
ejpam-819	83	7	5	5	NUM
ejpam-819	83	8	(	(	PUNCT
ejpam-819	83	9	2012	2012	NUM
ejpam-819	83	10	)	)	PUNCT
ejpam-819	83	11	,	,	PUNCT
ejpam-819	83	12	390	390	NUM
ejpam-819	83	13	-	-	SYM
ejpam-819	83	14	400	400	NUM
ejpam-819	83	15	393	393	NUM
ejpam-819	83	16	(	(	PUNCT
ejpam-819	83	17	i	i	NOUN
ejpam-819	83	18	)	)	PUNCT
ejpam-819	83	19	f	f	PROPN
ejpam-819	83	20	,	,	PUNCT
ejpam-819	83	21	g	g	PROPN
ejpam-819	83	22	and	and	CCONJ
ejpam-819	83	23	h	h	NOUN
ejpam-819	83	24	are	be	AUX
ejpam-819	83	25	twice	twice	ADV
ejpam-819	83	26	differentiable	differentiable	ADJ
ejpam-819	83	27	functions	function	NOUN
ejpam-819	83	28	from	from	ADP
ejpam-819	83	29	i	i	PRON
ejpam-819	83	30	×	×	NOUN
ejpam-819	83	31	rn×	rn×	NOUN
ejpam-819	83	32	rn	rn	PROPN
ejpam-819	83	33	into	into	ADP
ejpam-819	83	34	r	r	PROPN
ejpam-819	83	35	,	,	PUNCT
ejpam-819	83	36	rm	rm	NOUN
ejpam-819	83	37	and	and	CCONJ
ejpam-819	83	38	rk	rk	NOUN
ejpam-819	83	39	respectively	respectively	ADV
ejpam-819	83	40	,	,	PUNCT
ejpam-819	83	41	and	and	CCONJ
ejpam-819	83	42	(	(	PUNCT
ejpam-819	83	43	ii	ii	NOUN
ejpam-819	83	44	)	)	PUNCT
ejpam-819	83	45	b(t	b(t	PROPN
ejpam-819	83	46	)	)	PUNCT
ejpam-819	83	47	is	be	AUX
ejpam-819	83	48	a	a	DET
ejpam-819	83	49	positive	positive	ADJ
ejpam-819	83	50	semidefinite	semidefinite	NOUN
ejpam-819	83	51	n×	n×	PROPN
ejpam-819	83	52	n	n	NOUN
ejpam-819	83	53	matrix	matrix	NOUN
ejpam-819	83	54	with	with	ADP
ejpam-819	83	55	b	b	PROPN
ejpam-819	83	56	(	(	PUNCT
ejpam-819	83	57	.	.	PUNCT
ejpam-819	83	58	)	)	PUNCT
ejpam-819	83	59	continuous	continuous	ADJ
ejpam-819	83	60	on	on	ADP
ejpam-819	83	61	i	i	PRON
ejpam-819	83	62	.	.	PUNCT
ejpam-819	84	1	the	the	DET
ejpam-819	84	2	following	follow	VERB
ejpam-819	84	3	proposition	proposition	NOUN
ejpam-819	84	4	gives	give	VERB
ejpam-819	84	5	the	the	DET
ejpam-819	84	6	fritz	fritz	PROPN
ejpam-819	84	7	john	john	PROPN
ejpam-819	84	8	type	type	NOUN
ejpam-819	84	9	of	of	ADP
ejpam-819	84	10	optimality	optimality	NOUN
ejpam-819	84	11	conditions	condition	NOUN
ejpam-819	84	12	which	which	PRON
ejpam-819	84	13	are	be	AUX
ejpam-819	84	14	derived	derive	VERB
ejpam-819	84	15	by	by	ADP
ejpam-819	84	16	chandra	chandra	PROPN
ejpam-819	84	17	,	,	PUNCT
ejpam-819	84	18	craven	craven	NOUN
ejpam-819	84	19	and	and	CCONJ
ejpam-819	84	20	husain	husain	NOUN
ejpam-819	85	1	[	[	X
ejpam-819	85	2	2	2	NUM
ejpam-819	85	3	]	]	PUNCT
ejpam-819	85	4	:	:	PUNCT
ejpam-819	85	5	proposition	proposition	NOUN
ejpam-819	85	6	1	1	NUM
ejpam-819	85	7	(	(	PUNCT
ejpam-819	85	8	fritz	fritz	PROPN
ejpam-819	85	9	-	-	PUNCT
ejpam-819	85	10	john	john	PROPN
ejpam-819	85	11	conditions	condition	NOUN
ejpam-819	85	12	)	)	PUNCT
ejpam-819	85	13	.	.	PUNCT
ejpam-819	86	1	if	if	SCONJ
ejpam-819	86	2	(	(	PUNCT
ejpam-819	86	3	vp+	vp+	NOUN
ejpam-819	86	4	)	)	PUNCT
ejpam-819	86	5	attains	attain	VERB
ejpam-819	86	6	a	a	DET
ejpam-819	86	7	local	local	ADJ
ejpam-819	86	8	minimum	minimum	NOUN
ejpam-819	86	9	at	at	ADP
ejpam-819	86	10	x̄	x̄	X
ejpam-819	86	11	∈	∈	PROPN
ejpam-819	86	12	x	x	X
ejpam-819	86	13	and	and	CCONJ
ejpam-819	86	14	if	if	SCONJ
ejpam-819	86	15	hx	hx	PROPN
ejpam-819	86	16	(	(	PUNCT
ejpam-819	86	17	·	·	PUNCT
ejpam-819	86	18	,	,	PUNCT
ejpam-819	86	19	x̄	x̄	PROPN
ejpam-819	86	20	(	(	PUNCT
ejpam-819	86	21	·	·	PUNCT
ejpam-819	86	22	)	)	PUNCT
ejpam-819	86	23	,	,	PUNCT
ejpam-819	86	24	˙̄x	˙̄x	PUNCT
ejpam-819	86	25	(	(	PUNCT
ejpam-819	86	26	·	·	PUNCT
ejpam-819	86	27	)	)	PUNCT
ejpam-819	86	28	)	)	PUNCT
ejpam-819	86	29	maps	map	VERB
ejpam-819	86	30	x	x	PUNCT
ejpam-819	86	31	onto	onto	ADP
ejpam-819	86	32	a	a	DET
ejpam-819	86	33	closed	closed	ADJ
ejpam-819	86	34	subspace	subspace	NOUN
ejpam-819	86	35	of	of	ADP
ejpam-819	86	36	c(i	c(i	NOUN
ejpam-819	86	37	,	,	PUNCT
ejpam-819	86	38	rp	rp	NOUN
ejpam-819	86	39	)	)	PUNCT
ejpam-819	86	40	,	,	PUNCT
ejpam-819	86	41	then	then	ADV
ejpam-819	86	42	there	there	PRON
ejpam-819	86	43	exist	exist	VERB
ejpam-819	86	44	lagrange	lagrange	NOUN
ejpam-819	86	45	multipliers	multiplier	NOUN
ejpam-819	86	46	τ	τ	PROPN
ejpam-819	86	47	∈	∈	PROPN
ejpam-819	86	48	r+	r+	NOUN
ejpam-819	86	49	,	,	PUNCT
ejpam-819	87	1	piecewise	piecewise	NOUN
ejpam-819	87	2	smooth	smooth	NOUN
ejpam-819	87	3	ȳ	ȳ	NOUN
ejpam-819	87	4	:	:	PUNCT
ejpam-819	87	5	i	i	PRON
ejpam-819	87	6	→	→	SYM
ejpam-819	87	7	rm	rm	PROPN
ejpam-819	87	8	and	and	CCONJ
ejpam-819	87	9	λ̄	λ̄	PRON
ejpam-819	87	10	:	:	PUNCT
ejpam-819	87	11	i	i	PRON
ejpam-819	87	12	→	→	SYM
ejpam-819	87	13	rk	rk	NOUN
ejpam-819	87	14	,	,	PUNCT
ejpam-819	87	15	not	not	PART
ejpam-819	87	16	all	all	DET
ejpam-819	87	17	zero	zero	NUM
ejpam-819	87	18	,	,	PUNCT
ejpam-819	87	19	and	and	CCONJ
ejpam-819	87	20	also	also	ADV
ejpam-819	87	21	piecewise	piecewise	VERB
ejpam-819	87	22	smooth	smooth	ADJ
ejpam-819	87	23	z̄	z̄	NOUN
ejpam-819	87	24	:	:	PUNCT
ejpam-819	87	25	i	i	PROPN
ejpam-819	87	26	→	→	SYM
ejpam-819	87	27	rn	rn	NOUN
ejpam-819	87	28	satisfying	satisfy	VERB
ejpam-819	87	29	for	for	ADP
ejpam-819	87	30	all	all	DET
ejpam-819	87	31	t	t	NOUN
ejpam-819	87	32	∈	∈	PROPN
ejpam-819	88	1	i	i	PRON
ejpam-819	88	2	,	,	PUNCT
ejpam-819	88	3	τ	τ	PROPN
ejpam-819	88	4	fx	fx	PROPN
ejpam-819	88	5	(	(	PUNCT
ejpam-819	88	6	t	t	PROPN
ejpam-819	88	7	,	,	PUNCT
ejpam-819	88	8	x̄(t	x̄(t	PROPN
ejpam-819	88	9	)	)	PUNCT
ejpam-819	88	10	,	,	PUNCT
ejpam-819	88	11	˙̄x(t	˙̄x(t	NOUN
ejpam-819	88	12	)	)	PUNCT
ejpam-819	88	13	)	)	PUNCT
ejpam-819	89	1	+	+	CCONJ
ejpam-819	89	2	z̄(t)t	z̄(t)t	NUM
ejpam-819	89	3	b(t	b(t	NOUN
ejpam-819	89	4	)	)	PUNCT
ejpam-819	90	1	+	+	NUM
ejpam-819	90	2	ȳ(t)t	ȳ(t)t	NOUN
ejpam-819	90	3	gx(t	gx(t	NOUN
ejpam-819	90	4	,	,	PUNCT
ejpam-819	90	5	x̄(t	x̄(t	NUM
ejpam-819	90	6	)	)	PUNCT
ejpam-819	90	7	,	,	PUNCT
ejpam-819	90	8	˙̄x(t	˙̄x(t	NOUN
ejpam-819	90	9	)	)	PUNCT
ejpam-819	90	10	)	)	PUNCT
ejpam-819	91	1	+	+	CCONJ
ejpam-819	91	2	µ̄(t)t	µ̄(t)t	ADV
ejpam-819	91	3	hx(t	hx(t	NOUN
ejpam-819	91	4	,	,	PUNCT
ejpam-819	91	5	x̄(t	x̄(t	NUM
ejpam-819	91	6	)	)	PUNCT
ejpam-819	91	7	,	,	PUNCT
ejpam-819	91	8	˙̄x(t	˙̄x(t	NOUN
ejpam-819	91	9	)	)	PUNCT
ejpam-819	91	10	)	)	PUNCT
ejpam-819	92	1	=	=	NOUN
ejpam-819	92	2	d[τ	d[τ	NOUN
ejpam-819	92	3	fx(t	fx(t	NOUN
ejpam-819	92	4	,	,	PUNCT
ejpam-819	92	5	x̄(t	x̄(t	NUM
ejpam-819	92	6	)	)	PUNCT
ejpam-819	92	7	,	,	PUNCT
ejpam-819	92	8	˙̄x(t	˙̄x(t	NOUN
ejpam-819	92	9	)	)	PUNCT
ejpam-819	92	10	)	)	PUNCT
ejpam-819	93	1	+	+	CCONJ
ejpam-819	93	2	ȳ(t)t	ȳ(t)t	NOUN
ejpam-819	93	3	g	g	PROPN
ejpam-819	93	4	ẋ(t	ẋ(t	PROPN
ejpam-819	93	5	,	,	PUNCT
ejpam-819	93	6	x̄(t	x̄(t	PROPN
ejpam-819	93	7	)	)	PUNCT
ejpam-819	93	8	,	,	PUNCT
ejpam-819	93	9	˙̄x(t	˙̄x(t	NOUN
ejpam-819	93	10	)	)	PUNCT
ejpam-819	93	11	)	)	PUNCT
ejpam-819	94	1	+	+	CCONJ
ejpam-819	94	2	µ̄(t)t	µ̄(t)t	ADJ
ejpam-819	94	3	h	h	NOUN
ejpam-819	94	4	ẋ(t	ẋ(t	PROPN
ejpam-819	94	5	,	,	PUNCT
ejpam-819	94	6	x̄(t	x̄(t	NUM
ejpam-819	94	7	)	)	PUNCT
ejpam-819	94	8	,	,	PUNCT
ejpam-819	94	9	˙̄x(t	˙̄x(t	NOUN
ejpam-819	94	10	)	)	PUNCT
ejpam-819	94	11	)	)	PUNCT
ejpam-819	94	12	]	]	PUNCT
ejpam-819	95	1	t	t	PROPN
ejpam-819	95	2	∈	∈	PROPN
ejpam-819	95	3	t	t	PROPN
ejpam-819	95	4	,	,	PUNCT
ejpam-819	95	5	ȳ(t)t	ȳ(t)t	PROPN
ejpam-819	95	6	g(t	g(t	PROPN
ejpam-819	95	7	,	,	PUNCT
ejpam-819	95	8	x̄(t	x̄(t	PROPN
ejpam-819	95	9	)	)	PUNCT
ejpam-819	95	10	,	,	PUNCT
ejpam-819	95	11	˙̄x(t	˙̄x(t	NOUN
ejpam-819	95	12	)	)	PUNCT
ejpam-819	95	13	)	)	PUNCT
ejpam-819	96	1	=	=	SYM
ejpam-819	96	2	0	0	NUM
ejpam-819	96	3	,	,	PUNCT
ejpam-819	96	4	t	t	PROPN
ejpam-819	96	5	∈	∈	PROPN
ejpam-819	97	1	i	i	PROPN
ejpam-819	97	2	z̄(t)t	z̄(t)t	PROPN
ejpam-819	97	3	b(t	b(t	PROPN
ejpam-819	97	4	)	)	PUNCT
ejpam-819	97	5	z̄(t	z̄(t	ADJ
ejpam-819	97	6	)	)	PUNCT
ejpam-819	97	7	≤	≤	NUM
ejpam-819	97	8	1	1	NUM
ejpam-819	97	9	,	,	PUNCT
ejpam-819	97	10	t	t	PROPN
ejpam-819	97	11	∈	∈	PROPN
ejpam-819	98	1	i	i	PRON
ejpam-819	98	2	x̄(t)t	x̄(t)t	PROPN
ejpam-819	98	3	b(t	b(t	PROPN
ejpam-819	98	4	)	)	PUNCT
ejpam-819	98	5	z̄(t	z̄(t	PROPN
ejpam-819	98	6	)	)	PUNCT
ejpam-819	98	7	=	=	SYM
ejpam-819	99	1	(	(	PUNCT
ejpam-819	99	2	x̄(t)t	x̄(t)t	PROPN
ejpam-819	99	3	b(t	b(t	PROPN
ejpam-819	99	4	)	)	PUNCT
ejpam-819	99	5	x̄(t))1/2	x̄(t))1/2	PROPN
ejpam-819	99	6	,	,	PUNCT
ejpam-819	99	7	t	t	PROPN
ejpam-819	99	8	∈	∈	PROPN
ejpam-819	100	1	i	i	PRON
ejpam-819	100	2	if	if	SCONJ
ejpam-819	100	3	hx	hx	PROPN
ejpam-819	100	4	(	(	PUNCT
ejpam-819	100	5	·	·	PUNCT
ejpam-819	100	6	,	,	PUNCT
ejpam-819	100	7	x̄	x̄	PROPN
ejpam-819	100	8	(	(	PUNCT
ejpam-819	100	9	·	·	PUNCT
ejpam-819	100	10	)	)	PUNCT
ejpam-819	100	11	,	,	PUNCT
ejpam-819	100	12	˙̄x	˙̄x	PUNCT
ejpam-819	100	13	(	(	PUNCT
ejpam-819	100	14	·	·	PUNCT
ejpam-819	100	15	)	)	PUNCT
ejpam-819	100	16	)	)	PUNCT
ejpam-819	100	17	is	be	AUX
ejpam-819	100	18	subjective	subjective	ADJ
ejpam-819	100	19	,	,	PUNCT
ejpam-819	100	20	then	then	ADV
ejpam-819	100	21	τ	τ	PROPN
ejpam-819	100	22	and	and	CCONJ
ejpam-819	100	23	ȳ	ȳ	PROPN
ejpam-819	100	24	are	be	AUX
ejpam-819	100	25	not	not	PART
ejpam-819	100	26	both	both	DET
ejpam-819	100	27	zero	zero	NUM
ejpam-819	100	28	.	.	PUNCT
ejpam-819	101	1	lemma	lemma	PROPN
ejpam-819	101	2	1	1	PROPN
ejpam-819	101	3	(	(	PUNCT
ejpam-819	101	4	schwartz	schwartz	PROPN
ejpam-819	101	5	inequality	inequality	PROPN
ejpam-819	101	6	)	)	PUNCT
ejpam-819	101	7	.	.	PUNCT
ejpam-819	102	1	it	it	PRON
ejpam-819	102	2	states	state	VERB
ejpam-819	102	3	that	that	SCONJ
ejpam-819	102	4	x(t)t	x(t)t	PROPN
ejpam-819	102	5	b(t)z(t	b(t)z(t	PROPN
ejpam-819	102	6	)	)	PUNCT
ejpam-819	102	7	≤	≤	NOUN
ejpam-819	102	8	(	(	PUNCT
ejpam-819	102	9	x(t)t	x(t)t	PROPN
ejpam-819	102	10	b(t	b(t	PROPN
ejpam-819	102	11	)	)	PUNCT
ejpam-819	102	12	x(t))1/2(z(t)t	x(t))1/2(z(t)t	PROPN
ejpam-819	102	13	b(t	b(t	PROPN
ejpam-819	102	14	)	)	PUNCT
ejpam-819	102	15	z(t))1/2	z(t))1/2	PROPN
ejpam-819	102	16	,	,	PUNCT
ejpam-819	102	17	t	t	PROPN
ejpam-819	102	18	∈	∈	PROPN
ejpam-819	103	1	i	i	PRON
ejpam-819	103	2	(	(	PUNCT
ejpam-819	103	3	1	1	NUM
ejpam-819	103	4	)	)	PUNCT
ejpam-819	103	5	with	with	ADP
ejpam-819	103	6	equality	equality	NOUN
ejpam-819	103	7	in	in	ADP
ejpam-819	103	8	(	(	PUNCT
ejpam-819	103	9	1	1	X
ejpam-819	103	10	)	)	PUNCT
ejpam-819	103	11	if	if	SCONJ
ejpam-819	103	12	(	(	PUNCT
ejpam-819	103	13	and	and	CCONJ
ejpam-819	103	14	only	only	ADV
ejpam-819	103	15	if	if	SCONJ
ejpam-819	103	16	)	)	PUNCT
ejpam-819	103	17	b(t)(x(t)−	b(t)(x(t)−	PROPN
ejpam-819	103	18	q(t)z(t	q(t)z(t	NOUN
ejpam-819	103	19	)	)	PUNCT
ejpam-819	103	20	)	)	PUNCT
ejpam-819	104	1	=	=	SYM
ejpam-819	104	2	0	0	NUM
ejpam-819	104	3	for	for	ADP
ejpam-819	104	4	some	some	DET
ejpam-819	104	5	q(t	q(t	PROPN
ejpam-819	104	6	)	)	PUNCT
ejpam-819	104	7	∈	∈	PROPN
ejpam-819	104	8	r.	r.	PROPN
ejpam-819	104	9	remark	remark	NOUN
ejpam-819	104	10	2	2	NUM
ejpam-819	104	11	.	.	PUNCT
ejpam-819	105	1	the	the	DET
ejpam-819	105	2	fritz	fritz	PROPN
ejpam-819	105	3	john	john	PROPN
ejpam-819	105	4	necessary	necessary	ADJ
ejpam-819	105	5	optimality	optimality	NOUN
ejpam-819	105	6	conditions	condition	NOUN
ejpam-819	105	7	in	in	ADP
ejpam-819	105	8	proposition	proposition	NOUN
ejpam-819	105	9	1	1	NUM
ejpam-819	105	10	for	for	ADP
ejpam-819	105	11	(	(	PUNCT
ejpam-819	105	12	p+	p+	NOUN
ejpam-819	105	13	)	)	PUNCT
ejpam-819	105	14	,	,	PUNCT
ejpam-819	105	15	become	become	VERB
ejpam-819	105	16	the	the	DET
ejpam-819	105	17	karush	karush	PROPN
ejpam-819	105	18	-	-	PUNCT
ejpam-819	105	19	kuhn	kuhn	PROPN
ejpam-819	105	20	-	-	PUNCT
ejpam-819	105	21	tucker	tucker	PROPN
ejpam-819	105	22	type	type	NOUN
ejpam-819	105	23	optimality	optimality	NOUN
ejpam-819	105	24	conditions	condition	NOUN
ejpam-819	105	25	if	if	SCONJ
ejpam-819	105	26	τ	τ	PROPN
ejpam-819	105	27	=	=	SYM
ejpam-819	105	28	1	1	X
ejpam-819	105	29	.	.	PUNCT
ejpam-819	106	1	it	it	PRON
ejpam-819	106	2	suffices	suffice	VERB
ejpam-819	106	3	for	for	ADP
ejpam-819	106	4	τ	τ	PROPN
ejpam-819	106	5	=	=	SYM
ejpam-819	106	6	1	1	NUM
ejpam-819	106	7	,	,	PUNCT
ejpam-819	106	8	that	that	SCONJ
ejpam-819	106	9	the	the	DET
ejpam-819	106	10	following	follow	VERB
ejpam-819	106	11	slater	slater	PROPN
ejpam-819	106	12	’s	’s	PART
ejpam-819	106	13	condition	condition	NOUN
ejpam-819	106	14	holds	hold	VERB
ejpam-819	106	15	:	:	PUNCT
ejpam-819	107	1	g(t	g(t	PROPN
ejpam-819	107	2	,	,	PUNCT
ejpam-819	107	3	x̄(t	x̄(t	NUM
ejpam-819	107	4	)	)	PUNCT
ejpam-819	107	5	,	,	PUNCT
ejpam-819	107	6	˙̄x(t	˙̄x(t	NOUN
ejpam-819	107	7	)	)	PUNCT
ejpam-819	107	8	)	)	PUNCT
ejpam-819	108	1	+	+	CCONJ
ejpam-819	108	2	gx(t	gx(t	NOUN
ejpam-819	108	3	,	,	PUNCT
ejpam-819	108	4	x̄(t	x̄(t	NUM
ejpam-819	108	5	)	)	PUNCT
ejpam-819	108	6	,	,	PUNCT
ejpam-819	108	7	˙̄x(t))ν(t	˙̄x(t))ν(t	X
ejpam-819	108	8	)	)	PUNCT
ejpam-819	109	1	+	+	CCONJ
ejpam-819	109	2	g	g	PROPN
ejpam-819	109	3	ẋ(t	ẋ(t	PROPN
ejpam-819	109	4	,	,	PUNCT
ejpam-819	109	5	x̄(t	x̄(t	PROPN
ejpam-819	109	6	)	)	PUNCT
ejpam-819	109	7	,	,	PUNCT
ejpam-819	109	8	˙̄x(t))ν̇(t	˙̄x(t))ν̇(t	X
ejpam-819	109	9	)	)	PUNCT
ejpam-819	110	1	<	<	X
ejpam-819	110	2	0	0	NUM
ejpam-819	110	3	,	,	PUNCT
ejpam-819	110	4	ν(t	ν(t	NOUN
ejpam-819	110	5	)	)	PUNCT
ejpam-819	110	6	∈	∈	PROPN
ejpam-819	110	7	x	x	X
ejpam-819	110	8	,	,	PUNCT
ejpam-819	111	1	t	t	PROPN
ejpam-819	111	2	∈	∈	PROPN
ejpam-819	112	1	i	i	PRON
ejpam-819	112	2	.	.	PUNCT
ejpam-819	113	1	3	3	X
ejpam-819	113	2	.	.	X
ejpam-819	113	3	second	second	ADJ
ejpam-819	113	4	-	-	PUNCT
ejpam-819	113	5	order	order	NOUN
ejpam-819	113	6	duality	duality	NOUN
ejpam-819	113	7	consider	consider	VERB
ejpam-819	113	8	the	the	DET
ejpam-819	113	9	following	follow	VERB
ejpam-819	113	10	continuous	continuous	ADJ
ejpam-819	113	11	programming	programming	NOUN
ejpam-819	113	12	problem	problem	NOUN
ejpam-819	113	13	(	(	PUNCT
ejpam-819	113	14	cp	cp	NOUN
ejpam-819	113	15	)	)	PUNCT
ejpam-819	113	16	by	by	ADP
ejpam-819	113	17	ignoring	ignore	VERB
ejpam-819	113	18	the	the	DET
ejpam-819	113	19	equality	equality	NOUN
ejpam-819	113	20	constraint	constraint	NOUN
ejpam-819	113	21	h(t	h(t	PROPN
ejpam-819	113	22	,	,	PUNCT
ejpam-819	113	23	x̄(t	x̄(t	NUM
ejpam-819	113	24	)	)	PUNCT
ejpam-819	113	25	,	,	PUNCT
ejpam-819	113	26	˙̄x(t	˙̄x(t	NOUN
ejpam-819	113	27	)	)	PUNCT
ejpam-819	113	28	)	)	PUNCT
ejpam-819	114	1	=	=	SYM
ejpam-819	114	2	0	0	NUM
ejpam-819	114	3	,	,	PUNCT
ejpam-819	114	4	t	t	PROPN
ejpam-819	114	5	∈	∈	PROPN
ejpam-819	114	6	i	i	PRON
ejpam-819	114	7	in	in	ADP
ejpam-819	114	8	the	the	DET
ejpam-819	114	9	problem	problem	NOUN
ejpam-819	114	10	(	(	PUNCT
ejpam-819	114	11	p+	p+	NOUN
ejpam-819	114	12	):	):	PUNCT
ejpam-819	114	13	(	(	PUNCT
ejpam-819	114	14	cp	cp	X
ejpam-819	114	15	)	)	PUNCT
ejpam-819	114	16	minimize	minimize	VERB
ejpam-819	114	17	∫	∫	PROPN
ejpam-819	114	18	i	i	PRON
ejpam-819	114	19	{	{	PUNCT
ejpam-819	114	20	f	f	PROPN
ejpam-819	114	21	(	(	PUNCT
ejpam-819	114	22	t	t	PROPN
ejpam-819	114	23	,	,	PUNCT
ejpam-819	114	24	x(t	x(t	PROPN
ejpam-819	114	25	)	)	PUNCT
ejpam-819	114	26	,	,	PUNCT
ejpam-819	114	27	ẋ(t	ẋ(t	NOUN
ejpam-819	114	28	)	)	PUNCT
ejpam-819	114	29	)	)	PUNCT
ejpam-819	115	1	+	+	CCONJ
ejpam-819	115	2	(	(	PUNCT
ejpam-819	115	3	x(t)t	x(t)t	PROPN
ejpam-819	115	4	b(t)x(t))1/2}d	b(t)x(t))1/2}d	PROPN
ejpam-819	115	5	t	t	AUX
ejpam-819	115	6	subject	subject	NOUN
ejpam-819	115	7	to	to	ADP
ejpam-819	115	8	x(a	x(a	NOUN
ejpam-819	115	9	)	)	PUNCT
ejpam-819	115	10	=	=	SYM
ejpam-819	115	11	0=	0=	NUM
ejpam-819	116	1	x(b	x(b	PROPN
ejpam-819	116	2	)	)	PUNCT
ejpam-819	116	3	,	,	PUNCT
ejpam-819	116	4	(	(	PUNCT
ejpam-819	116	5	2	2	X
ejpam-819	116	6	)	)	PUNCT
ejpam-819	116	7	g(t	g(t	PROPN
ejpam-819	116	8	,	,	PUNCT
ejpam-819	116	9	x(t	x(t	PROPN
ejpam-819	116	10	)	)	PUNCT
ejpam-819	116	11	,	,	PUNCT
ejpam-819	116	12	ẋ(t))≤	ẋ(t))≤	PROPN
ejpam-819	116	13	0	0	NUM
ejpam-819	116	14	,	,	PUNCT
ejpam-819	116	15	t	t	PROPN
ejpam-819	116	16	∈	∈	PROPN
ejpam-819	117	1	i	i	PRON
ejpam-819	117	2	(	(	PUNCT
ejpam-819	117	3	3	3	X
ejpam-819	117	4	)	)	PUNCT
ejpam-819	117	5	i.	i.	NOUN
ejpam-819	117	6	husain	husain	PROPN
ejpam-819	117	7	,	,	PUNCT
ejpam-819	117	8	m.	m.	NOUN
ejpam-819	117	9	masoodi	masoodi	PROPN
ejpam-819	117	10	/	/	SYM
ejpam-819	117	11	eur	eur	PROPN
ejpam-819	117	12	.	.	PUNCT
ejpam-819	118	1	j.	j.	PROPN
ejpam-819	118	2	pure	pure	PROPN
ejpam-819	118	3	appl	appl	PROPN
ejpam-819	118	4	.	.	PROPN
ejpam-819	118	5	math	math	PROPN
ejpam-819	118	6	,	,	PUNCT
ejpam-819	118	7	5	5	NUM
ejpam-819	118	8	(	(	PUNCT
ejpam-819	118	9	2012	2012	NUM
ejpam-819	118	10	)	)	PUNCT
ejpam-819	118	11	,	,	PUNCT
ejpam-819	118	12	390	390	NUM
ejpam-819	118	13	-	-	SYM
ejpam-819	118	14	400	400	NUM
ejpam-819	118	15	394	394	NUM
ejpam-819	118	16	analogously	analogously	ADV
ejpam-819	118	17	to	to	ADP
ejpam-819	118	18	the	the	DET
ejpam-819	118	19	second	second	ADJ
ejpam-819	118	20	-	-	PUNCT
ejpam-819	118	21	order	order	NOUN
ejpam-819	118	22	dual	dual	ADJ
ejpam-819	118	23	problem	problem	NOUN
ejpam-819	118	24	introduced	introduce	VERB
ejpam-819	118	25	by	by	ADP
ejpam-819	118	26	mangasarian	mangasarian	PROPN
ejpam-819	118	27	[	[	X
ejpam-819	118	28	5	5	NUM
ejpam-819	118	29	]	]	PUNCT
ejpam-819	118	30	for	for	ADP
ejpam-819	118	31	a	a	DET
ejpam-819	118	32	nonlinear	nonlinear	ADJ
ejpam-819	118	33	programming	programming	NOUN
ejpam-819	118	34	problem	problem	NOUN
ejpam-819	118	35	,	,	PUNCT
ejpam-819	118	36	we	we	PRON
ejpam-819	118	37	consider	consider	VERB
ejpam-819	118	38	the	the	DET
ejpam-819	118	39	following	follow	VERB
ejpam-819	118	40	second	second	ADJ
ejpam-819	118	41	order	order	NOUN
ejpam-819	118	42	dual	dual	ADJ
ejpam-819	118	43	continuous	continuous	ADJ
ejpam-819	118	44	programming	programming	NOUN
ejpam-819	118	45	problem	problem	NOUN
ejpam-819	118	46	(	(	PUNCT
ejpam-819	118	47	cd	cd	PROPN
ejpam-819	118	48	)	)	PUNCT
ejpam-819	118	49	for	for	ADP
ejpam-819	118	50	(	(	PUNCT
ejpam-819	118	51	cp	cp	NOUN
ejpam-819	118	52	)	)	PUNCT
ejpam-819	118	53	.	.	PUNCT
ejpam-819	119	1	(	(	PUNCT
ejpam-819	119	2	cd	cd	PROPN
ejpam-819	119	3	)	)	PUNCT
ejpam-819	119	4	maximize	maximize	VERB
ejpam-819	119	5	∫	∫	PROPN
ejpam-819	120	1	i	i	PRON
ejpam-819	120	2	{	{	PUNCT
ejpam-819	120	3	f	f	PROPN
ejpam-819	120	4	(	(	PUNCT
ejpam-819	120	5	t	t	PROPN
ejpam-819	120	6	,	,	PUNCT
ejpam-819	120	7	u(t	u(t	PROPN
ejpam-819	120	8	)	)	PUNCT
ejpam-819	120	9	,	,	PUNCT
ejpam-819	120	10	u̇(t	u̇(t	NOUN
ejpam-819	120	11	)	)	PUNCT
ejpam-819	120	12	)	)	PUNCT
ejpam-819	121	1	+	+	CCONJ
ejpam-819	121	2	u(t)t	u(t)t	NOUN
ejpam-819	121	3	b(t)z(t	b(t)z(t	NOUN
ejpam-819	121	4	)	)	PUNCT
ejpam-819	121	5	+	+	NUM
ejpam-819	121	6	y(t)t	y(t)t	PROPN
ejpam-819	121	7	g(t	g(t	PROPN
ejpam-819	121	8	,	,	PUNCT
ejpam-819	121	9	u(t	u(t	NOUN
ejpam-819	121	10	)	)	PUNCT
ejpam-819	121	11	,	,	PUNCT
ejpam-819	121	12	u̇(t))−	u̇(t))−	VERB
ejpam-819	121	13	1	1	NUM
ejpam-819	121	14	2	2	NUM
ejpam-819	121	15	p(t)t	p(t)t	NOUN
ejpam-819	121	16	h	h	NOUN
ejpam-819	121	17	p(t)}d	p(t)}d	PROPN
ejpam-819	121	18	t	t	PROPN
ejpam-819	121	19	subject	subject	NOUN
ejpam-819	121	20	to	to	ADP
ejpam-819	121	21	u(a	u(a	PROPN
ejpam-819	121	22	)	)	PUNCT
ejpam-819	121	23	=	=	SYM
ejpam-819	121	24	0=	0=	PUNCT
ejpam-819	122	1	u(b	u(b	NOUN
ejpam-819	122	2	)	)	PUNCT
ejpam-819	122	3	,	,	PUNCT
ejpam-819	122	4	(	(	PUNCT
ejpam-819	122	5	4	4	X
ejpam-819	122	6	)	)	PUNCT
ejpam-819	122	7	fu(t	fu(t	NOUN
ejpam-819	122	8	,	,	PUNCT
ejpam-819	122	9	u(t	u(t	NOUN
ejpam-819	122	10	)	)	PUNCT
ejpam-819	122	11	,	,	PUNCT
ejpam-819	122	12	u̇(t	u̇(t	NOUN
ejpam-819	122	13	)	)	PUNCT
ejpam-819	122	14	)	)	PUNCT
ejpam-819	123	1	+	+	CCONJ
ejpam-819	123	2	b(t)z(t	b(t)z(t	NOUN
ejpam-819	123	3	)	)	PUNCT
ejpam-819	123	4	+	+	NUM
ejpam-819	123	5	y(t)t	y(t)t	NOUN
ejpam-819	123	6	gu(t	gu(t	PUNCT
ejpam-819	123	7	,	,	PUNCT
ejpam-819	123	8	u(t	u(t	NOUN
ejpam-819	123	9	)	)	PUNCT
ejpam-819	123	10	,	,	PUNCT
ejpam-819	123	11	u̇(t	u̇(t	NOUN
ejpam-819	123	12	)	)	PUNCT
ejpam-819	123	13	)	)	PUNCT
ejpam-819	124	1	−d	−d	PROPN
ejpam-819	124	2	(	(	PUNCT
ejpam-819	124	3	fu̇(t	fu̇(t	PROPN
ejpam-819	124	4	,	,	PUNCT
ejpam-819	124	5	u(t	u(t	NOUN
ejpam-819	124	6	)	)	PUNCT
ejpam-819	124	7	,	,	PUNCT
ejpam-819	124	8	u̇(t	u̇(t	NOUN
ejpam-819	124	9	)	)	PUNCT
ejpam-819	124	10	)	)	PUNCT
ejpam-819	125	1	+	+	CCONJ
ejpam-819	125	2	y(t)t	y(t)t	NOUN
ejpam-819	125	3	(	(	PUNCT
ejpam-819	125	4	5	5	NUM
ejpam-819	125	5	)	)	PUNCT
ejpam-819	125	6	z(t)t	z(t)t	NOUN
ejpam-819	125	7	b(t)z(t	b(t)z(t	NOUN
ejpam-819	125	8	)	)	PUNCT
ejpam-819	125	9	≤	≤	NUM
ejpam-819	125	10	1	1	NUM
ejpam-819	125	11	,	,	PUNCT
ejpam-819	125	12	t	t	PROPN
ejpam-819	125	13	∈	∈	PROPN
ejpam-819	126	1	i	i	PRON
ejpam-819	126	2	(	(	PUNCT
ejpam-819	126	3	6	6	NUM
ejpam-819	126	4	)	)	PUNCT
ejpam-819	126	5	y(t	y(t	NUM
ejpam-819	126	6	)	)	PUNCT
ejpam-819	126	7	≥	≥	NOUN
ejpam-819	126	8	0	0	NUM
ejpam-819	126	9	,	,	PUNCT
ejpam-819	126	10	t	t	PROPN
ejpam-819	126	11	∈	∈	PROPN
ejpam-819	126	12	i	i	PRON
ejpam-819	126	13	(	(	PUNCT
ejpam-819	126	14	7	7	NUM
ejpam-819	126	15	)	)	PUNCT
ejpam-819	126	16	where	where	SCONJ
ejpam-819	126	17	h	h	NOUN
ejpam-819	126	18	=	=	SYM
ejpam-819	126	19	fuu(t	fuu(t	PROPN
ejpam-819	126	20	,	,	PUNCT
ejpam-819	126	21	u	u	NOUN
ejpam-819	126	22	,	,	PUNCT
ejpam-819	126	23	u̇	u̇	PROPN
ejpam-819	126	24	)	)	PUNCT
ejpam-819	127	1	+	+	CCONJ
ejpam-819	127	2	(	(	PUNCT
ejpam-819	127	3	y(t)t	y(t)t	NOUN
ejpam-819	127	4	gu(t	gu(t	PUNCT
ejpam-819	127	5	,	,	PUNCT
ejpam-819	127	6	u	u	NOUN
ejpam-819	127	7	,	,	PUNCT
ejpam-819	127	8	u̇))u−	u̇))u−	PROPN
ejpam-819	127	9	2d	2d	NOUN
ejpam-819	127	10	[	[	PUNCT
ejpam-819	127	11	fuu̇(t	fuu̇(t	NOUN
ejpam-819	127	12	,	,	PUNCT
ejpam-819	127	13	u	u	NOUN
ejpam-819	127	14	,	,	PUNCT
ejpam-819	127	15	u̇	u̇	PROPN
ejpam-819	127	16	)	)	PUNCT
ejpam-819	128	1	+	+	CCONJ
ejpam-819	128	2	(	(	PUNCT
ejpam-819	128	3	y(t)t	y(t)t	NOUN
ejpam-819	128	4	gu(t	gu(t	PUNCT
ejpam-819	128	5	,	,	PUNCT
ejpam-819	128	6	u	u	NOUN
ejpam-819	128	7	,	,	PUNCT
ejpam-819	128	8	u̇))u̇	u̇))u̇	NOUN
ejpam-819	128	9	]	]	X
ejpam-819	128	10	+	+	CCONJ
ejpam-819	128	11	d2	d2	PROPN
ejpam-819	128	12	[	[	PUNCT
ejpam-819	128	13	fu̇u̇(t	fu̇u̇(t	SYM
ejpam-819	128	14	,	,	PUNCT
ejpam-819	128	15	u	u	NOUN
ejpam-819	128	16	,	,	PUNCT
ejpam-819	128	17	u̇	u̇	PROPN
ejpam-819	128	18	)	)	PUNCT
ejpam-819	128	19	+	+	CCONJ
ejpam-819	128	20	(	(	PUNCT
ejpam-819	128	21	y(t)t	y(t)t	NOUN
ejpam-819	128	22	gu̇(t	gu̇(t	PROPN
ejpam-819	128	23	,	,	PUNCT
ejpam-819	128	24	u	u	NOUN
ejpam-819	128	25	,	,	PUNCT
ejpam-819	128	26	u̇))u̇]−	u̇))u̇]−	ADJ
ejpam-819	128	27	d3	d3	PROPN
ejpam-819	128	28	[	[	PUNCT
ejpam-819	128	29	fu̇ü(t	fu̇ü(t	NOUN
ejpam-819	128	30	,	,	PUNCT
ejpam-819	128	31	u	u	NOUN
ejpam-819	128	32	,	,	PUNCT
ejpam-819	128	33	u̇	u̇	PROPN
ejpam-819	128	34	)	)	PUNCT
ejpam-819	128	35	+	+	CCONJ
ejpam-819	128	36	(	(	PUNCT
ejpam-819	128	37	y(t)t	y(t)t	NOUN
ejpam-819	128	38	gu̇(t	gu̇(t	PROPN
ejpam-819	128	39	,	,	PUNCT
ejpam-819	128	40	u	u	NOUN
ejpam-819	128	41	,	,	PUNCT
ejpam-819	128	42	u̇))ü	u̇))ü	ADJ
ejpam-819	128	43	]	]	PUNCT
ejpam-819	128	44	theorem	theorem	ADJ
ejpam-819	128	45	1	1	NUM
ejpam-819	128	46	(	(	PUNCT
ejpam-819	128	47	weak	weak	ADJ
ejpam-819	128	48	duality	duality	NOUN
ejpam-819	128	49	)	)	PUNCT
ejpam-819	128	50	.	.	PUNCT
ejpam-819	129	1	let	let	VERB
ejpam-819	129	2	x(t	x(t	NOUN
ejpam-819	129	3	)	)	PUNCT
ejpam-819	129	4	∈	∈	PROPN
ejpam-819	129	5	x	x	VERB
ejpam-819	129	6	be	be	AUX
ejpam-819	129	7	a	a	DET
ejpam-819	129	8	feasible	feasible	ADJ
ejpam-819	129	9	solution	solution	NOUN
ejpam-819	129	10	of	of	ADP
ejpam-819	129	11	(	(	PUNCT
ejpam-819	129	12	cp	cp	NOUN
ejpam-819	129	13	)	)	PUNCT
ejpam-819	129	14	and	and	CCONJ
ejpam-819	129	15	u(t	u(t	NOUN
ejpam-819	129	16	)	)	PUNCT
ejpam-819	129	17	,	,	PUNCT
ejpam-819	129	18	y(t	y(t	PROPN
ejpam-819	129	19	)	)	PUNCT
ejpam-819	129	20	,	,	PUNCT
ejpam-819	129	21	z(t	z(t	PROPN
ejpam-819	129	22	)	)	PUNCT
ejpam-819	129	23	be	be	VERB
ejpam-819	129	24	a	a	DET
ejpam-819	129	25	feasible	feasible	ADJ
ejpam-819	129	26	solution	solution	NOUN
ejpam-819	129	27	of	of	ADP
ejpam-819	129	28	(	(	PUNCT
ejpam-819	129	29	cd	cd	PROPN
ejpam-819	129	30	)	)	PUNCT
ejpam-819	129	31	.	.	PUNCT
ejpam-819	130	1	if	if	SCONJ
ejpam-819	130	2	∫	∫	PROPN
ejpam-819	130	3	i	i	PRON
ejpam-819	130	4	{	{	PUNCT
ejpam-819	130	5	f	f	PROPN
ejpam-819	130	6	(	(	PUNCT
ejpam-819	130	7	t	t	PROPN
ejpam-819	130	8	,	,	PUNCT
ejpam-819	130	9	.	.	PUNCT
ejpam-819	130	10	,	,	PUNCT
ejpam-819	130	11	.	.	PUNCT
ejpam-819	130	12	)	)	PUNCT
ejpam-819	131	1	+	+	CCONJ
ejpam-819	131	2	(	(	PUNCT
ejpam-819	131	3	·	·	PUNCT
ejpam-819	131	4	)	)	PUNCT
ejpam-819	131	5	t	t	PROPN
ejpam-819	131	6	b(t)z(t	b(t)z(t	NOUN
ejpam-819	131	7	)	)	PUNCT
ejpam-819	131	8	+	+	NUM
ejpam-819	131	9	y(t)t	y(t)t	PROPN
ejpam-819	131	10	g(t	g(t	PROPN
ejpam-819	131	11	,	,	PUNCT
ejpam-819	131	12	.	.	PUNCT
ejpam-819	131	13	,	,	PUNCT
ejpam-819	131	14	.)}d	.)}d	PROPN
ejpam-819	131	15	t	t	PROPN
ejpam-819	131	16	is	be	AUX
ejpam-819	131	17	second	second	ADJ
ejpam-819	131	18	-	-	PUNCT
ejpam-819	131	19	order	order	NOUN
ejpam-819	131	20	pseudo	pseudo	NOUN
ejpam-819	131	21	-	-	NOUN
ejpam-819	131	22	invex	invex	NOUN
ejpam-819	131	23	with	with	ADP
ejpam-819	131	24	respect	respect	NOUN
ejpam-819	131	25	to	to	ADP
ejpam-819	131	26	η	η	PROPN
ejpam-819	131	27	=	=	SYM
ejpam-819	131	28	η(t	η(t	NOUN
ejpam-819	131	29	,	,	PUNCT
ejpam-819	131	30	x	x	X
ejpam-819	131	31	,	,	PUNCT
ejpam-819	131	32	u	u	NOUN
ejpam-819	131	33	)	)	PUNCT
ejpam-819	131	34	,	,	PUNCT
ejpam-819	131	35	then	then	ADV
ejpam-819	131	36	inf(c	inf(c	PROPN
ejpam-819	131	37	p)≥	p)≥	NOUN
ejpam-819	131	38	sup(c	sup(c	NOUN
ejpam-819	131	39	d	d	NOUN
ejpam-819	131	40	)	)	PUNCT
ejpam-819	131	41	.	.	PUNCT
ejpam-819	132	1	proof	proof	NOUN
ejpam-819	132	2	.	.	PUNCT
ejpam-819	133	1	from	from	ADP
ejpam-819	133	2	(	(	PUNCT
ejpam-819	133	3	5	5	NUM
ejpam-819	133	4	)	)	PUNCT
ejpam-819	133	5	,	,	PUNCT
ejpam-819	133	6	we	we	PRON
ejpam-819	133	7	have	have	VERB
ejpam-819	133	8	∫	∫	PROPN
ejpam-819	134	1	i	i	PRON
ejpam-819	134	2	ηt	ηt	ADP
ejpam-819	134	3	{	{	PUNCT
ejpam-819	134	4	fu(t	fu(t	NOUN
ejpam-819	134	5	,	,	PUNCT
ejpam-819	134	6	u(t	u(t	NOUN
ejpam-819	134	7	)	)	PUNCT
ejpam-819	134	8	,	,	PUNCT
ejpam-819	134	9	u̇(t	u̇(t	NOUN
ejpam-819	134	10	)	)	PUNCT
ejpam-819	134	11	)	)	PUNCT
ejpam-819	135	1	+	+	CCONJ
ejpam-819	135	2	b(t)z(t	b(t)z(t	NOUN
ejpam-819	135	3	)	)	PUNCT
ejpam-819	135	4	+	+	NUM
ejpam-819	135	5	y(t)t	y(t)t	NOUN
ejpam-819	135	6	gu(t	gu(t	PUNCT
ejpam-819	135	7	,	,	PUNCT
ejpam-819	135	8	u(t	u(t	NOUN
ejpam-819	135	9	)	)	PUNCT
ejpam-819	135	10	,	,	PUNCT
ejpam-819	135	11	u̇(t	u̇(t	NOUN
ejpam-819	135	12	)	)	PUNCT
ejpam-819	135	13	)	)	PUNCT
ejpam-819	136	1	−	−	PROPN
ejpam-819	136	2	d	d	X
ejpam-819	136	3	(	(	PUNCT
ejpam-819	136	4	fu̇(t	fu̇(t	PROPN
ejpam-819	136	5	,	,	PUNCT
ejpam-819	136	6	u(t	u(t	NOUN
ejpam-819	136	7	)	)	PUNCT
ejpam-819	136	8	,	,	PUNCT
ejpam-819	136	9	u̇(t	u̇(t	NOUN
ejpam-819	136	10	)	)	PUNCT
ejpam-819	136	11	)	)	PUNCT
ejpam-819	136	12	+	+	NUM
ejpam-819	136	13	y(t)t	y(t)t	NOUN
ejpam-819	136	14	gu̇(t	gu̇(t	NOUN
ejpam-819	136	15	,	,	PUNCT
ejpam-819	136	16	u(t	u(t	PROPN
ejpam-819	136	17	)	)	PUNCT
ejpam-819	136	18	,	,	PUNCT
ejpam-819	136	19	u̇(t)))}d	u̇(t)))}d	NOUN
ejpam-819	136	20	t	t	PROPN
ejpam-819	137	1	+	+	CCONJ
ejpam-819	138	1	∫	∫	PROPN
ejpam-819	139	1	i	i	PRON
ejpam-819	139	2	ηt	ηt	ADP
ejpam-819	139	3	h	h	NOUN
ejpam-819	139	4	p(t)d	p(t)d	PROPN
ejpam-819	139	5	t	t	PROPN
ejpam-819	140	1	=	=	SYM
ejpam-819	141	1	∫	∫	PROPN
ejpam-819	142	1	i	i	PRON
ejpam-819	143	1	[	[	X
ejpam-819	143	2	ηt	ηt	ADP
ejpam-819	143	3	{	{	PUNCT
ejpam-819	143	4	fu(t	fu(t	NOUN
ejpam-819	143	5	,	,	PUNCT
ejpam-819	143	6	u(t	u(t	NOUN
ejpam-819	143	7	)	)	PUNCT
ejpam-819	143	8	,	,	PUNCT
ejpam-819	143	9	u̇(t	u̇(t	NOUN
ejpam-819	143	10	)	)	PUNCT
ejpam-819	143	11	)	)	PUNCT
ejpam-819	144	1	+	+	CCONJ
ejpam-819	144	2	b(t)z(t	b(t)z(t	NOUN
ejpam-819	144	3	)	)	PUNCT
ejpam-819	144	4	+	+	NUM
ejpam-819	144	5	y(t)t	y(t)t	NOUN
ejpam-819	144	6	gu(t	gu(t	PUNCT
ejpam-819	144	7	,	,	PUNCT
ejpam-819	144	8	u(t	u(t	NOUN
ejpam-819	144	9	)	)	PUNCT
ejpam-819	144	10	,	,	PUNCT
ejpam-819	144	11	u̇(t	u̇(t	NOUN
ejpam-819	144	12	)	)	PUNCT
ejpam-819	144	13	)	)	PUNCT
ejpam-819	145	1	+	+	CCONJ
ejpam-819	145	2	(	(	PUNCT
ejpam-819	145	3	dη)t	dη)t	PROPN
ejpam-819	145	4	(	(	PUNCT
ejpam-819	145	5	fu̇(t	fu̇(t	PROPN
ejpam-819	145	6	,	,	PUNCT
ejpam-819	145	7	u(t	u(t	NOUN
ejpam-819	145	8	)	)	PUNCT
ejpam-819	145	9	,	,	PUNCT
ejpam-819	145	10	u̇(t	u̇(t	NOUN
ejpam-819	145	11	)	)	PUNCT
ejpam-819	145	12	)	)	PUNCT
ejpam-819	146	1	+	+	NUM
ejpam-819	146	2	y(t)t	y(t)t	NOUN
ejpam-819	146	3	gu̇(t	gu̇(t	NOUN
ejpam-819	146	4	,	,	PUNCT
ejpam-819	146	5	u(t	u(t	PROPN
ejpam-819	146	6	)	)	PUNCT
ejpam-819	146	7	,	,	PUNCT
ejpam-819	146	8	u̇(t	u̇(t	NOUN
ejpam-819	146	9	)	)	PUNCT
ejpam-819	146	10	)	)	PUNCT
ejpam-819	146	11	)	)	PUNCT
ejpam-819	147	1	+	+	ADP
ejpam-819	147	2	η	η	PROPN
ejpam-819	147	3	t	t	PROPN
ejpam-819	147	4	h	h	NOUN
ejpam-819	147	5	p(t)}]d	p(t)}]d	PROPN
ejpam-819	147	6	t	t	PROPN
ejpam-819	147	7	−ηt	−ηt	PROPN
ejpam-819	147	8	(	(	PUNCT
ejpam-819	147	9	fu̇(t	fu̇(t	PROPN
ejpam-819	147	10	,	,	PUNCT
ejpam-819	147	11	u(t	u(t	NOUN
ejpam-819	147	12	)	)	PUNCT
ejpam-819	147	13	,	,	PUNCT
ejpam-819	147	14	u̇(t	u̇(t	NOUN
ejpam-819	147	15	)	)	PUNCT
ejpam-819	147	16	)	)	PUNCT
ejpam-819	148	1	+	+	NUM
ejpam-819	148	2	y(t)t	y(t)t	NOUN
ejpam-819	148	3	gu̇(t	gu̇(t	NOUN
ejpam-819	148	4	,	,	PUNCT
ejpam-819	148	5	u(t	u(t	PROPN
ejpam-819	148	6	)	)	PUNCT
ejpam-819	148	7	,	,	PUNCT
ejpam-819	148	8	u̇(t)))|	u̇(t)))|	PROPN
ejpam-819	148	9	t	t	PROPN
ejpam-819	148	10	=	=	PROPN
ejpam-819	148	11	b	b	PROPN
ejpam-819	148	12	t	t	PROPN
ejpam-819	148	13	=	=	SYM
ejpam-819	148	14	a	a	NOUN
ejpam-819	148	15	,	,	PUNCT
ejpam-819	148	16	by	by	ADP
ejpam-819	148	17	integration	integration	NOUN
ejpam-819	148	18	by	by	ADP
ejpam-819	148	19	parts	part	NOUN
ejpam-819	148	20	.	.	PUNCT
ejpam-819	149	1	using	use	VERB
ejpam-819	149	2	the	the	DET
ejpam-819	149	3	boundary	boundary	ADJ
ejpam-819	149	4	conditions	condition	NOUN
ejpam-819	149	5	(	(	PUNCT
ejpam-819	149	6	2	2	NUM
ejpam-819	149	7	)	)	PUNCT
ejpam-819	149	8	and	and	CCONJ
ejpam-819	149	9	(	(	PUNCT
ejpam-819	149	10	4	4	NUM
ejpam-819	149	11	)	)	PUNCT
ejpam-819	149	12	,	,	PUNCT
ejpam-819	149	13	we	we	PRON
ejpam-819	149	14	have	have	VERB
ejpam-819	149	15	∫	∫	PROPN
ejpam-819	150	1	i	i	PRON
ejpam-819	151	1	[	[	X
ejpam-819	151	2	ηt	ηt	ADP
ejpam-819	151	3	{	{	PUNCT
ejpam-819	151	4	fu(t	fu(t	NOUN
ejpam-819	151	5	,	,	PUNCT
ejpam-819	151	6	u(t	u(t	NOUN
ejpam-819	151	7	)	)	PUNCT
ejpam-819	151	8	,	,	PUNCT
ejpam-819	151	9	u̇(t	u̇(t	NOUN
ejpam-819	151	10	)	)	PUNCT
ejpam-819	151	11	)	)	PUNCT
ejpam-819	152	1	+	+	CCONJ
ejpam-819	152	2	b(t)z(t	b(t)z(t	NOUN
ejpam-819	152	3	)	)	PUNCT
ejpam-819	152	4	+	+	NUM
ejpam-819	152	5	y(t)t	y(t)t	NOUN
ejpam-819	152	6	gu(t	gu(t	PUNCT
ejpam-819	152	7	,	,	PUNCT
ejpam-819	152	8	u(t	u(t	NOUN
ejpam-819	152	9	)	)	PUNCT
ejpam-819	152	10	,	,	PUNCT
ejpam-819	152	11	u̇(t	u̇(t	NOUN
ejpam-819	152	12	)	)	PUNCT
ejpam-819	152	13	)	)	PUNCT
ejpam-819	153	1	+	+	CCONJ
ejpam-819	153	2	(	(	PUNCT
ejpam-819	153	3	dη)t	dη)t	PROPN
ejpam-819	153	4	(	(	PUNCT
ejpam-819	153	5	fu̇(t	fu̇(t	PROPN
ejpam-819	153	6	,	,	PUNCT
ejpam-819	153	7	u(t	u(t	NOUN
ejpam-819	153	8	)	)	PUNCT
ejpam-819	153	9	,	,	PUNCT
ejpam-819	153	10	u̇(t	u̇(t	NOUN
ejpam-819	153	11	)	)	PUNCT
ejpam-819	153	12	)	)	PUNCT
ejpam-819	154	1	+	+	NUM
ejpam-819	154	2	y(t)t	y(t)t	NOUN
ejpam-819	154	3	gu̇(t	gu̇(t	NOUN
ejpam-819	154	4	,	,	PUNCT
ejpam-819	154	5	u(t	u(t	PROPN
ejpam-819	154	6	)	)	PUNCT
ejpam-819	154	7	,	,	PUNCT
ejpam-819	154	8	u̇(t	u̇(t	NOUN
ejpam-819	154	9	)	)	PUNCT
ejpam-819	154	10	)	)	PUNCT
ejpam-819	154	11	)	)	PUNCT
ejpam-819	155	1	+	+	ADP
ejpam-819	155	2	η	η	PROPN
ejpam-819	155	3	t	t	PROPN
ejpam-819	155	4	h	h	NOUN
ejpam-819	155	5	p(t)}]d	p(t)}]d	PROPN
ejpam-819	155	6	t	t	PROPN
ejpam-819	155	7	=	=	SYM
ejpam-819	155	8	0	0	PROPN
ejpam-819	155	9	.	.	PUNCT
ejpam-819	155	10	i.	i.	PROPN
ejpam-819	155	11	husain	husain	PROPN
ejpam-819	155	12	,	,	PUNCT
ejpam-819	155	13	m.	m.	NOUN
ejpam-819	155	14	masoodi	masoodi	PROPN
ejpam-819	155	15	/	/	SYM
ejpam-819	155	16	eur	eur	PROPN
ejpam-819	155	17	.	.	PUNCT
ejpam-819	156	1	j.	j.	PROPN
ejpam-819	156	2	pure	pure	PROPN
ejpam-819	156	3	appl	appl	PROPN
ejpam-819	156	4	.	.	PROPN
ejpam-819	156	5	math	math	PROPN
ejpam-819	156	6	,	,	PUNCT
ejpam-819	156	7	5	5	NUM
ejpam-819	156	8	(	(	PUNCT
ejpam-819	156	9	2012	2012	NUM
ejpam-819	156	10	)	)	PUNCT
ejpam-819	156	11	,	,	PUNCT
ejpam-819	156	12	390	390	NUM
ejpam-819	156	13	-	-	SYM
ejpam-819	156	14	400	400	NUM
ejpam-819	156	15	395	395	NUM
ejpam-819	156	16	this	this	PRON
ejpam-819	156	17	,	,	PUNCT
ejpam-819	156	18	in	in	ADP
ejpam-819	156	19	view	view	NOUN
ejpam-819	156	20	of	of	ADP
ejpam-819	156	21	second	second	ADJ
ejpam-819	156	22	-	-	PUNCT
ejpam-819	156	23	order	order	NOUN
ejpam-819	156	24	pseudo	pseudo	NOUN
ejpam-819	156	25	-	-	NOUN
ejpam-819	156	26	invexity	invexity	NOUN
ejpam-819	156	27	of	of	ADP
ejpam-819	156	28	∫	∫	PROPN
ejpam-819	157	1	i	i	INTJ
ejpam-819	157	2	{	{	PUNCT
ejpam-819	157	3	f	f	PROPN
ejpam-819	157	4	(	(	PUNCT
ejpam-819	157	5	t	t	PROPN
ejpam-819	157	6	,	,	PUNCT
ejpam-819	157	7	.	.	PUNCT
ejpam-819	157	8	,	,	PUNCT
ejpam-819	157	9	.)+(·)t	.)+(·)t	PUNCT
ejpam-819	157	10	b(t)z(t)+	b(t)z(t)+	NOUN
ejpam-819	157	11	y(t)t	y(t)t	PROPN
ejpam-819	157	12	g(t	g(t	PROPN
ejpam-819	157	13	,	,	PUNCT
ejpam-819	157	14	.	.	PUNCT
ejpam-819	157	15	,	,	PUNCT
ejpam-819	157	16	.)}d	.)}d	PROPN
ejpam-819	157	17	t	t	PROPN
ejpam-819	157	18	yields	yield	NOUN
ejpam-819	157	19	∫	∫	PROPN
ejpam-819	158	1	i	i	PRON
ejpam-819	158	2	{	{	PUNCT
ejpam-819	158	3	f	f	PROPN
ejpam-819	158	4	(	(	PUNCT
ejpam-819	158	5	t	t	PROPN
ejpam-819	158	6	,	,	PUNCT
ejpam-819	158	7	x	x	X
ejpam-819	158	8	,	,	PUNCT
ejpam-819	158	9	ẋ	ẋ	PROPN
ejpam-819	158	10	)	)	PUNCT
ejpam-819	158	11	+	+	CCONJ
ejpam-819	158	12	x(t)t	x(t)t	PROPN
ejpam-819	158	13	b(t)z(t	b(t)z(t	NOUN
ejpam-819	158	14	)	)	PUNCT
ejpam-819	158	15	+	+	NUM
ejpam-819	158	16	y(t)t	y(t)t	PROPN
ejpam-819	158	17	g(t	g(t	PROPN
ejpam-819	158	18	,	,	PUNCT
ejpam-819	158	19	x	x	X
ejpam-819	158	20	,	,	PUNCT
ejpam-819	158	21	ẋ)}d	ẋ)}d	PROPN
ejpam-819	158	22	t	t	PROPN
ejpam-819	158	23	≥	≥	X
ejpam-819	158	24	∫	∫	PROPN
ejpam-819	159	1	i	i	PRON
ejpam-819	159	2	{	{	PUNCT
ejpam-819	159	3	f	f	PROPN
ejpam-819	159	4	(	(	PUNCT
ejpam-819	159	5	t	t	PROPN
ejpam-819	159	6	,	,	PUNCT
ejpam-819	159	7	u	u	NOUN
ejpam-819	159	8	,	,	PUNCT
ejpam-819	159	9	u̇	u̇	PROPN
ejpam-819	159	10	)	)	PUNCT
ejpam-819	159	11	+	+	CCONJ
ejpam-819	159	12	u(t)t	u(t)t	NOUN
ejpam-819	159	13	b(t)z(t	b(t)z(t	NOUN
ejpam-819	159	14	)	)	PUNCT
ejpam-819	159	15	+	+	NUM
ejpam-819	159	16	y(t)t	y(t)t	PROPN
ejpam-819	159	17	g(t	g(t	PROPN
ejpam-819	159	18	,	,	PUNCT
ejpam-819	159	19	u	u	NOUN
ejpam-819	159	20	,	,	PUNCT
ejpam-819	159	21	u̇)−	u̇)−	PROPN
ejpam-819	159	22	1	1	NUM
ejpam-819	159	23	2	2	NUM
ejpam-819	159	24	p(t)t	p(t)t	NOUN
ejpam-819	159	25	h	h	NOUN
ejpam-819	159	26	p(t)}d	p(t)}d	PROPN
ejpam-819	159	27	t	t	PROPN
ejpam-819	159	28	because	because	SCONJ
ejpam-819	159	29	of	of	ADP
ejpam-819	159	30	schwartz	schwartz	PROPN
ejpam-819	159	31	’s	’s	PART
ejpam-819	159	32	inequality	inequality	NOUN
ejpam-819	159	33	(	(	PUNCT
ejpam-819	159	34	1	1	NUM
ejpam-819	159	35	)	)	PUNCT
ejpam-819	159	36	along	along	ADP
ejpam-819	159	37	with	with	ADP
ejpam-819	159	38	(	(	PUNCT
ejpam-819	159	39	5	5	NUM
ejpam-819	159	40	)	)	PUNCT
ejpam-819	159	41	,	,	PUNCT
ejpam-819	159	42	(	(	PUNCT
ejpam-819	159	43	6	6	NUM
ejpam-819	159	44	)	)	PUNCT
ejpam-819	159	45	and	and	CCONJ
ejpam-819	159	46	(	(	PUNCT
ejpam-819	159	47	2	2	NUM
ejpam-819	159	48	)	)	PUNCT
ejpam-819	159	49	,	,	PUNCT
ejpam-819	159	50	this	this	PRON
ejpam-819	159	51	implies	imply	VERB
ejpam-819	159	52	∫	∫	PROPN
ejpam-819	159	53	i	i	PRON
ejpam-819	159	54	{	{	PUNCT
ejpam-819	159	55	f	f	PROPN
ejpam-819	159	56	(	(	PUNCT
ejpam-819	159	57	t	t	PROPN
ejpam-819	159	58	,	,	PUNCT
ejpam-819	159	59	x(t	x(t	PROPN
ejpam-819	159	60	)	)	PUNCT
ejpam-819	159	61	,	,	PUNCT
ejpam-819	159	62	ẋ(t	ẋ(t	NOUN
ejpam-819	159	63	)	)	PUNCT
ejpam-819	159	64	)	)	PUNCT
ejpam-819	160	1	+	+	CCONJ
ejpam-819	160	2	(	(	PUNCT
ejpam-819	160	3	x(t)t	x(t)t	PROPN
ejpam-819	160	4	b(t)x(t))1/2}d	b(t)x(t))1/2}d	PROPN
ejpam-819	160	5	t	t	PROPN
ejpam-819	160	6	≥	≥	X
ejpam-819	160	7	∫	∫	PROPN
ejpam-819	161	1	i	i	PRON
ejpam-819	161	2	{	{	PUNCT
ejpam-819	161	3	f	f	PROPN
ejpam-819	161	4	(	(	PUNCT
ejpam-819	161	5	t	t	PROPN
ejpam-819	161	6	,	,	PUNCT
ejpam-819	161	7	u	u	NOUN
ejpam-819	161	8	,	,	PUNCT
ejpam-819	161	9	u̇	u̇	PROPN
ejpam-819	161	10	)	)	PUNCT
ejpam-819	161	11	+	+	CCONJ
ejpam-819	161	12	u(t)t	u(t)t	NOUN
ejpam-819	161	13	b(t)z(t	b(t)z(t	NOUN
ejpam-819	161	14	)	)	PUNCT
ejpam-819	161	15	+	+	NUM
ejpam-819	161	16	y(t)t	y(t)t	PROPN
ejpam-819	161	17	g(t	g(t	PROPN
ejpam-819	161	18	,	,	PUNCT
ejpam-819	161	19	u	u	NOUN
ejpam-819	161	20	,	,	PUNCT
ejpam-819	161	21	u̇)−	u̇)−	PROPN
ejpam-819	161	22	1	1	NUM
ejpam-819	161	23	2	2	NUM
ejpam-819	161	24	p(t)t	p(t)t	NOUN
ejpam-819	161	25	h	h	NOUN
ejpam-819	161	26	p(t)}d	p(t)}d	PROPN
ejpam-819	161	27	t	t	PROPN
ejpam-819	161	28	yielding	yielding	PROPN
ejpam-819	161	29	,	,	PUNCT
ejpam-819	161	30	inf(c	inf(c	PROPN
ejpam-819	161	31	p)≥	p)≥	NOUN
ejpam-819	161	32	sup(c	sup(c	NOUN
ejpam-819	161	33	d	d	NOUN
ejpam-819	161	34	)	)	PUNCT
ejpam-819	161	35	.	.	PUNCT
ejpam-819	162	1	theorem	theorem	ADJ
ejpam-819	162	2	2	2	NUM
ejpam-819	162	3	(	(	PUNCT
ejpam-819	162	4	strong	strong	ADJ
ejpam-819	162	5	duality	duality	NOUN
ejpam-819	162	6	)	)	PUNCT
ejpam-819	162	7	.	.	PUNCT
ejpam-819	163	1	if	if	SCONJ
ejpam-819	163	2	x̄(t	x̄(t	NOUN
ejpam-819	163	3	)	)	PUNCT
ejpam-819	163	4	∈	∈	PROPN
ejpam-819	163	5	x	x	X
ejpam-819	163	6	is	be	AUX
ejpam-819	163	7	an	an	DET
ejpam-819	163	8	optimal	optimal	ADJ
ejpam-819	163	9	solution	solution	NOUN
ejpam-819	163	10	of	of	ADP
ejpam-819	163	11	(	(	PUNCT
ejpam-819	163	12	cp	cp	NOUN
ejpam-819	163	13	)	)	PUNCT
ejpam-819	163	14	and	and	CCONJ
ejpam-819	163	15	is	be	AUX
ejpam-819	163	16	also	also	ADV
ejpam-819	163	17	normal	normal	ADJ
ejpam-819	163	18	,	,	PUNCT
ejpam-819	163	19	then	then	ADV
ejpam-819	163	20	there	there	PRON
ejpam-819	163	21	exist	exist	VERB
ejpam-819	163	22	piecewise	piecewise	NOUN
ejpam-819	163	23	smooth	smooth	ADJ
ejpam-819	163	24	functions	function	NOUN
ejpam-819	163	25	y	y	PROPN
ejpam-819	163	26	→	→	SYM
ejpam-819	163	27	rm	rm	PROPN
ejpam-819	163	28	and	and	CCONJ
ejpam-819	163	29	z→	z→	PROPN
ejpam-819	163	30	rn	rn	PROPN
ejpam-819	163	31	such	such	ADJ
ejpam-819	163	32	that	that	PRON
ejpam-819	163	33	(	(	PUNCT
ejpam-819	163	34	x̄(t	x̄(t	PROPN
ejpam-819	163	35	)	)	PUNCT
ejpam-819	163	36	,	,	PUNCT
ejpam-819	163	37	ȳ(t	ȳ(t	PROPN
ejpam-819	163	38	)	)	PUNCT
ejpam-819	163	39	,	,	PUNCT
ejpam-819	163	40	z̄(t	z̄(t	ADJ
ejpam-819	163	41	)	)	PUNCT
ejpam-819	163	42	,	,	PUNCT
ejpam-819	163	43	p(t	p(t	NOUN
ejpam-819	163	44	)	)	PUNCT
ejpam-819	163	45	=	=	SYM
ejpam-819	164	1	0	0	X
ejpam-819	164	2	)	)	PUNCT
ejpam-819	164	3	is	be	AUX
ejpam-819	164	4	a	a	DET
ejpam-819	164	5	feasible	feasible	ADJ
ejpam-819	164	6	solution	solution	NOUN
ejpam-819	164	7	of	of	ADP
ejpam-819	164	8	(	(	PUNCT
ejpam-819	164	9	cd	cd	PROPN
ejpam-819	164	10	)	)	PUNCT
ejpam-819	164	11	and	and	CCONJ
ejpam-819	164	12	the	the	DET
ejpam-819	164	13	two	two	NUM
ejpam-819	164	14	objective	objective	ADJ
ejpam-819	164	15	values	value	NOUN
ejpam-819	164	16	are	be	AUX
ejpam-819	164	17	equal	equal	ADJ
ejpam-819	164	18	.	.	PUNCT
ejpam-819	165	1	furthermore	furthermore	ADV
ejpam-819	165	2	,	,	PUNCT
ejpam-819	165	3	if	if	SCONJ
ejpam-819	165	4	the	the	DET
ejpam-819	165	5	hypotheses	hypothesis	NOUN
ejpam-819	165	6	of	of	ADP
ejpam-819	165	7	theorem	theorem	ADJ
ejpam-819	165	8	1	1	NUM
ejpam-819	165	9	hold	hold	NOUN
ejpam-819	165	10	,	,	PUNCT
ejpam-819	165	11	then	then	ADV
ejpam-819	165	12	(	(	PUNCT
ejpam-819	165	13	x̄(t	x̄(t	PROPN
ejpam-819	165	14	)	)	PUNCT
ejpam-819	165	15	,	,	PUNCT
ejpam-819	165	16	ȳ(t	ȳ(t	PROPN
ejpam-819	165	17	)	)	PUNCT
ejpam-819	165	18	,	,	PUNCT
ejpam-819	165	19	z̄(t	z̄(t	ADJ
ejpam-819	165	20	)	)	PUNCT
ejpam-819	165	21	,	,	PUNCT
ejpam-819	165	22	p(t	p(t	NOUN
ejpam-819	165	23	)	)	PUNCT
ejpam-819	165	24	)	)	PUNCT
ejpam-819	165	25	is	be	AUX
ejpam-819	165	26	an	an	DET
ejpam-819	165	27	optimal	optimal	ADJ
ejpam-819	165	28	of	of	ADP
ejpam-819	165	29	(	(	PUNCT
ejpam-819	165	30	cd	cd	PROPN
ejpam-819	165	31	)	)	PUNCT
ejpam-819	165	32	.	.	PUNCT
ejpam-819	166	1	proof	proof	NOUN
ejpam-819	166	2	.	.	PUNCT
ejpam-819	167	1	from	from	ADP
ejpam-819	167	2	proposition	proposition	NOUN
ejpam-819	167	3	1	1	NUM
ejpam-819	167	4	,	,	PUNCT
ejpam-819	167	5	there	there	PRON
ejpam-819	167	6	exist	exist	VERB
ejpam-819	167	7	piecewise	piecewise	NOUN
ejpam-819	167	8	smooth	smooth	ADJ
ejpam-819	167	9	functions	function	NOUN
ejpam-819	167	10	ȳ	ȳ	NOUN
ejpam-819	167	11	:	:	PUNCT
ejpam-819	168	1	i	i	PROPN
ejpam-819	168	2	→	→	SYM
ejpam-819	168	3	rm	rm	PROPN
ejpam-819	168	4	and	and	CCONJ
ejpam-819	168	5	z̄	z̄	PROPN
ejpam-819	168	6	:	:	PUNCT
ejpam-819	168	7	i	i	PROPN
ejpam-819	168	8	→	→	SYM
ejpam-819	168	9	rn	rn	PROPN
ejpam-819	168	10	such	such	ADJ
ejpam-819	168	11	that	that	PRON
ejpam-819	168	12	(	(	PUNCT
ejpam-819	168	13	for	for	ADP
ejpam-819	168	14	t	t	PROPN
ejpam-819	168	15	∈	∈	PROPN
ejpam-819	168	16	i	i	PROPN
ejpam-819	168	17	)	)	PUNCT
ejpam-819	168	18	(	(	PUNCT
ejpam-819	168	19	fx(t	fx(t	PROPN
ejpam-819	168	20	,	,	PUNCT
ejpam-819	168	21	x̄	x̄	PROPN
ejpam-819	168	22	,	,	PUNCT
ejpam-819	168	23	˙̄x)+	˙̄x)+	NOUN
ejpam-819	168	24	b(t)z̄(t	b(t)z̄(t	NOUN
ejpam-819	168	25	)	)	PUNCT
ejpam-819	169	1	+	+	NUM
ejpam-819	169	2	ȳ(t)t	ȳ(t)t	PROPN
ejpam-819	169	3	g(t	g(t	PROPN
ejpam-819	169	4	,	,	PUNCT
ejpam-819	169	5	x̄	x̄	NOUN
ejpam-819	169	6	,	,	PUNCT
ejpam-819	169	7	˙̄x))−	˙̄x))−	PROPN
ejpam-819	170	1	d	d	X
ejpam-819	170	2	(	(	PUNCT
ejpam-819	170	3	f	f	PROPN
ejpam-819	170	4	ẋ	ẋ	PROPN
ejpam-819	170	5	(	(	PUNCT
ejpam-819	170	6	t	t	PROPN
ejpam-819	170	7	,	,	PUNCT
ejpam-819	170	8	x̄	x̄	NOUN
ejpam-819	170	9	,	,	PUNCT
ejpam-819	170	10	˙̄x	˙̄x	PUNCT
ejpam-819	170	11	)	)	PUNCT
ejpam-819	171	1	+	+	CCONJ
ejpam-819	171	2	ȳ(t)t	ȳ(t)t	NOUN
ejpam-819	171	3	g	g	PROPN
ejpam-819	171	4	ẋ(t	ẋ(t	PROPN
ejpam-819	171	5	,	,	PUNCT
ejpam-819	171	6	x̄	x̄	NOUN
ejpam-819	171	7	,	,	PUNCT
ejpam-819	171	8	˙̄x	˙̄x	NOUN
ejpam-819	171	9	)	)	PUNCT
ejpam-819	171	10	)	)	PUNCT
ejpam-819	172	1	=	=	SYM
ejpam-819	172	2	0	0	NUM
ejpam-819	172	3	,	,	PUNCT
ejpam-819	172	4	(	(	PUNCT
ejpam-819	172	5	8)	8)	NUM
ejpam-819	172	6	ȳ(t)t	ȳ(t)t	NOUN
ejpam-819	172	7	g(t	g(t	PROPN
ejpam-819	172	8	,	,	PUNCT
ejpam-819	172	9	x̄	x̄	NOUN
ejpam-819	172	10	,	,	PUNCT
ejpam-819	172	11	˙̄x	˙̄x	PRON
ejpam-819	172	12	)	)	PUNCT
ejpam-819	172	13	=	=	SYM
ejpam-819	172	14	0	0	NUM
ejpam-819	172	15	,	,	PUNCT
ejpam-819	172	16	(	(	PUNCT
ejpam-819	172	17	9	9	X
ejpam-819	172	18	)	)	PUNCT
ejpam-819	172	19	x̄(t)t	x̄(t)t	NOUN
ejpam-819	172	20	b(t)z̄(t	b(t)z̄(t	NOUN
ejpam-819	172	21	)	)	PUNCT
ejpam-819	172	22	=	=	PUNCT
ejpam-819	173	1	(	(	PUNCT
ejpam-819	173	2	x̄(t)t	x̄(t)t	NOUN
ejpam-819	173	3	b(t)x(t))1/2	b(t)x(t))1/2	PROPN
ejpam-819	173	4	,	,	PUNCT
ejpam-819	173	5	(	(	PUNCT
ejpam-819	173	6	10	10	NUM
ejpam-819	173	7	)	)	PUNCT
ejpam-819	173	8	z̄(t)t	z̄(t)t	NOUN
ejpam-819	173	9	b(t)z̄(t	b(t)z̄(t	NOUN
ejpam-819	173	10	)	)	PUNCT
ejpam-819	173	11	≤	≤	NUM
ejpam-819	173	12	1	1	NUM
ejpam-819	173	13	,	,	PUNCT
ejpam-819	173	14	(	(	PUNCT
ejpam-819	173	15	11	11	NUM
ejpam-819	173	16	)	)	PUNCT
ejpam-819	173	17	y(t	y(t	NUM
ejpam-819	173	18	)	)	PUNCT
ejpam-819	173	19	≥	≥	NOUN
ejpam-819	173	20	1	1	NUM
ejpam-819	173	21	.	.	PUNCT
ejpam-819	174	1	(	(	PUNCT
ejpam-819	174	2	12	12	NUM
ejpam-819	174	3	)	)	PUNCT
ejpam-819	174	4	hence	hence	ADV
ejpam-819	174	5	(	(	PUNCT
ejpam-819	174	6	x̄(t	x̄(t	PROPN
ejpam-819	174	7	)	)	PUNCT
ejpam-819	174	8	,	,	PUNCT
ejpam-819	174	9	ȳ(t	ȳ(t	PROPN
ejpam-819	174	10	)	)	PUNCT
ejpam-819	174	11	,	,	PUNCT
ejpam-819	174	12	z̄(t	z̄(t	ADJ
ejpam-819	174	13	)	)	PUNCT
ejpam-819	174	14	,	,	PUNCT
ejpam-819	174	15	p̄(t	p̄(t	PROPN
ejpam-819	174	16	)	)	PUNCT
ejpam-819	174	17	=	=	SYM
ejpam-819	174	18	0	0	X
ejpam-819	174	19	)	)	PUNCT
ejpam-819	174	20	satisfies	satisfy	VERB
ejpam-819	174	21	the	the	DET
ejpam-819	174	22	constraints	constraint	NOUN
ejpam-819	174	23	of	of	ADP
ejpam-819	174	24	(	(	PUNCT
ejpam-819	174	25	cd	cd	PROPN
ejpam-819	174	26	)	)	PUNCT
ejpam-819	174	27	and	and	CCONJ
ejpam-819	174	28	the	the	DET
ejpam-819	174	29	objective	objective	ADJ
ejpam-819	174	30	values	value	NOUN
ejpam-819	174	31	are	be	AUX
ejpam-819	174	32	equal	equal	ADJ
ejpam-819	174	33	.	.	PUNCT
ejpam-819	175	1	furthermore	furthermore	ADV
ejpam-819	175	2	,	,	PUNCT
ejpam-819	175	3	for	for	ADP
ejpam-819	175	4	every	every	DET
ejpam-819	175	5	feasible	feasible	ADJ
ejpam-819	175	6	solution	solution	NOUN
ejpam-819	175	7	(	(	PUNCT
ejpam-819	175	8	u(t	u(t	PROPN
ejpam-819	175	9	)	)	PUNCT
ejpam-819	175	10	,	,	PUNCT
ejpam-819	175	11	y(t	y(t	PROPN
ejpam-819	175	12	)	)	PUNCT
ejpam-819	175	13	,	,	PUNCT
ejpam-819	175	14	z(t	z(t	PROPN
ejpam-819	175	15	)	)	PUNCT
ejpam-819	175	16	,	,	PUNCT
ejpam-819	175	17	p(t	p(t	NOUN
ejpam-819	175	18	)	)	PUNCT
ejpam-819	175	19	=	=	SYM
ejpam-819	175	20	0	0	NUM
ejpam-819	175	21	)	)	PUNCT
ejpam-819	175	22	,	,	PUNCT
ejpam-819	175	23	from	from	ADP
ejpam-819	175	24	the	the	DET
ejpam-819	175	25	above	above	ADJ
ejpam-819	175	26	conditions	condition	NOUN
ejpam-819	175	27	and	and	CCONJ
ejpam-819	175	28	using	use	VERB
ejpam-819	175	29	(	(	PUNCT
ejpam-819	175	30	9	9	NUM
ejpam-819	175	31	)	)	PUNCT
ejpam-819	175	32	,	,	PUNCT
ejpam-819	175	33	(	(	PUNCT
ejpam-819	175	34	10	10	NUM
ejpam-819	175	35	)	)	PUNCT
ejpam-819	175	36	and	and	CCONJ
ejpam-819	175	37	p̄(t	p̄(t	ADJ
ejpam-819	175	38	)	)	PUNCT
ejpam-819	175	39	=	=	SYM
ejpam-819	175	40	0	0	NUM
ejpam-819	175	41	we	we	PRON
ejpam-819	175	42	have	have	VERB
ejpam-819	175	43	∫	∫	PROPN
ejpam-819	176	1	i	i	PRON
ejpam-819	176	2	{	{	PUNCT
ejpam-819	176	3	f	f	PROPN
ejpam-819	176	4	(	(	PUNCT
ejpam-819	176	5	t	t	PROPN
ejpam-819	176	6	,	,	PUNCT
ejpam-819	176	7	x̄	x̄	NOUN
ejpam-819	176	8	,	,	PUNCT
ejpam-819	176	9	˙̄x)+	˙̄x)+	NOUN
ejpam-819	176	10	x̄(t)t	x̄(t)t	PROPN
ejpam-819	176	11	b(t)z̄(t)+	b(t)z̄(t)+	PROPN
ejpam-819	176	12	ȳ(t)t	ȳ(t)t	PROPN
ejpam-819	176	13	g(t	g(t	PROPN
ejpam-819	176	14	,	,	PUNCT
ejpam-819	176	15	x̄(t	x̄(t	PROPN
ejpam-819	176	16	)	)	PUNCT
ejpam-819	176	17	,	,	PUNCT
ejpam-819	176	18	˙̄x(t))−	˙̄x(t))−	NOUN
ejpam-819	176	19	1	1	NUM
ejpam-819	176	20	2	2	NUM
ejpam-819	176	21	p̄(t)t	p̄(t)t	NOUN
ejpam-819	176	22	h	h	NOUN
ejpam-819	176	23	p̄(t)}d	p̄(t)}d	NOUN
ejpam-819	176	24	t	t	PROPN
ejpam-819	176	25	=	=	SYM
ejpam-819	176	26	∫	∫	PROPN
ejpam-819	177	1	i	i	PRON
ejpam-819	177	2	{	{	PUNCT
ejpam-819	177	3	f	f	PROPN
ejpam-819	177	4	(	(	PUNCT
ejpam-819	177	5	t	t	PROPN
ejpam-819	177	6	,	,	PUNCT
ejpam-819	177	7	x̄	x̄	NOUN
ejpam-819	177	8	,	,	PUNCT
ejpam-819	177	9	˙̄x)+	˙̄x)+	NOUN
ejpam-819	177	10	(	(	PUNCT
ejpam-819	177	11	x̄(t)t	x̄(t)t	PROPN
ejpam-819	177	12	b(t	b(t	PROPN
ejpam-819	177	13	)	)	PUNCT
ejpam-819	178	1	x̄(t))1/2}d	x̄(t))1/2}d	PROPN
ejpam-819	178	2	t	t	PROPN
ejpam-819	178	3	i.	i.	PROPN
ejpam-819	178	4	husain	husain	PROPN
ejpam-819	178	5	,	,	PUNCT
ejpam-819	178	6	m.	m.	NOUN
ejpam-819	178	7	masoodi	masoodi	PROPN
ejpam-819	178	8	/	/	SYM
ejpam-819	178	9	eur	eur	PROPN
ejpam-819	178	10	.	.	PUNCT
ejpam-819	179	1	j.	j.	PROPN
ejpam-819	179	2	pure	pure	PROPN
ejpam-819	179	3	appl	appl	PROPN
ejpam-819	179	4	.	.	PROPN
ejpam-819	179	5	math	math	PROPN
ejpam-819	179	6	,	,	PUNCT
ejpam-819	179	7	5	5	NUM
ejpam-819	179	8	(	(	PUNCT
ejpam-819	179	9	2012	2012	NUM
ejpam-819	179	10	)	)	PUNCT
ejpam-819	179	11	,	,	PUNCT
ejpam-819	179	12	390	390	NUM
ejpam-819	179	13	-	-	SYM
ejpam-819	179	14	400	400	NUM
ejpam-819	179	15	396	396	NUM
ejpam-819	179	16	≥	≥	NOUN
ejpam-819	179	17	∫	∫	NOUN
ejpam-819	180	1	i	i	PRON
ejpam-819	180	2	{	{	PUNCT
ejpam-819	180	3	f	f	PROPN
ejpam-819	180	4	(	(	PUNCT
ejpam-819	180	5	t	t	PROPN
ejpam-819	180	6	,	,	PUNCT
ejpam-819	180	7	u	u	NOUN
ejpam-819	180	8	,	,	PUNCT
ejpam-819	180	9	u̇	u̇	PROPN
ejpam-819	180	10	)	)	PUNCT
ejpam-819	180	11	+	+	CCONJ
ejpam-819	180	12	u(t)t	u(t)t	NOUN
ejpam-819	180	13	b(t)z(t	b(t)z(t	NOUN
ejpam-819	180	14	)	)	PUNCT
ejpam-819	180	15	+	+	NUM
ejpam-819	180	16	y(t)t	y(t)t	PROPN
ejpam-819	180	17	g(t	g(t	PROPN
ejpam-819	180	18	,	,	PUNCT
ejpam-819	180	19	u	u	NOUN
ejpam-819	180	20	,	,	PUNCT
ejpam-819	180	21	u̇)−	u̇)−	PROPN
ejpam-819	180	22	1	1	NUM
ejpam-819	180	23	2	2	NUM
ejpam-819	180	24	p(t)t	p(t)t	NOUN
ejpam-819	180	25	h	h	NOUN
ejpam-819	180	26	p(t)}d	p(t)}d	PROPN
ejpam-819	180	27	t	t	PROPN
ejpam-819	181	1	so	so	ADV
ejpam-819	181	2	,	,	PUNCT
ejpam-819	181	3	(	(	PUNCT
ejpam-819	181	4	x̄(t	x̄(t	PROPN
ejpam-819	181	5	)	)	PUNCT
ejpam-819	181	6	,	,	PUNCT
ejpam-819	181	7	ȳ(t	ȳ(t	PROPN
ejpam-819	181	8	)	)	PUNCT
ejpam-819	181	9	,	,	PUNCT
ejpam-819	181	10	z̄(t	z̄(t	ADJ
ejpam-819	181	11	)	)	PUNCT
ejpam-819	181	12	,	,	PUNCT
ejpam-819	181	13	p̄(t	p̄(t	PROPN
ejpam-819	181	14	)	)	PUNCT
ejpam-819	181	15	)	)	PUNCT
ejpam-819	181	16	is	be	AUX
ejpam-819	181	17	an	an	DET
ejpam-819	181	18	optimal	optimal	ADJ
ejpam-819	181	19	solution	solution	NOUN
ejpam-819	181	20	of	of	ADP
ejpam-819	181	21	(	(	PUNCT
ejpam-819	181	22	cd	cd	PROPN
ejpam-819	181	23	)	)	PUNCT
ejpam-819	181	24	.	.	PUNCT
ejpam-819	182	1	theorem	theorem	ADJ
ejpam-819	182	2	3	3	NUM
ejpam-819	182	3	(	(	PUNCT
ejpam-819	182	4	converse	converse	NOUN
ejpam-819	182	5	duality	duality	NOUN
ejpam-819	182	6	)	)	PUNCT
ejpam-819	182	7	.	.	PUNCT
ejpam-819	183	1	assume	assume	VERB
ejpam-819	183	2	that	that	SCONJ
ejpam-819	183	3	f	f	PROPN
ejpam-819	183	4	and	and	CCONJ
ejpam-819	183	5	g	g	PROPN
ejpam-819	183	6	are	be	AUX
ejpam-819	183	7	thrice	thrice	NOUN
ejpam-819	183	8	continuously	continuously	ADV
ejpam-819	183	9	differentiable	differentiable	VERB
ejpam-819	183	10	and	and	CCONJ
ejpam-819	183	11	(	(	PUNCT
ejpam-819	183	12	x̄(t	x̄(t	PROPN
ejpam-819	183	13	)	)	PUNCT
ejpam-819	183	14	,	,	PUNCT
ejpam-819	183	15	ȳ(t	ȳ(t	PROPN
ejpam-819	183	16	)	)	PUNCT
ejpam-819	183	17	,	,	PUNCT
ejpam-819	183	18	z̄(t	z̄(t	ADJ
ejpam-819	183	19	)	)	PUNCT
ejpam-819	183	20	,	,	PUNCT
ejpam-819	183	21	p̄(t	p̄(t	PROPN
ejpam-819	183	22	)	)	PUNCT
ejpam-819	183	23	)	)	PUNCT
ejpam-819	183	24	be	be	AUX
ejpam-819	183	25	an	an	DET
ejpam-819	183	26	optimal	optimal	ADJ
ejpam-819	183	27	solution	solution	NOUN
ejpam-819	183	28	of	of	ADP
ejpam-819	183	29	(	(	PUNCT
ejpam-819	183	30	cd	cd	PROPN
ejpam-819	183	31	)	)	PUNCT
ejpam-819	183	32	.	.	PUNCT
ejpam-819	184	1	let	let	VERB
ejpam-819	184	2	the	the	DET
ejpam-819	184	3	following	follow	VERB
ejpam-819	184	4	conditions	condition	NOUN
ejpam-819	184	5	hold	hold	VERB
ejpam-819	184	6	:	:	PUNCT
ejpam-819	184	7	(	(	PUNCT
ejpam-819	184	8	i	i	NOUN
ejpam-819	184	9	)	)	PUNCT
ejpam-819	184	10	the	the	DET
ejpam-819	184	11	hessian	hessian	ADJ
ejpam-819	184	12	matrix	matrix	NOUN
ejpam-819	184	13	h	h	NOUN
ejpam-819	184	14	is	be	AUX
ejpam-819	184	15	non	non	ADJ
ejpam-819	184	16	-	-	ADJ
ejpam-819	184	17	singular	singular	ADJ
ejpam-819	184	18	,	,	PUNCT
ejpam-819	184	19	and	and	CCONJ
ejpam-819	184	20	(	(	PUNCT
ejpam-819	184	21	ii	ii	NOUN
ejpam-819	184	22	)	)	PUNCT
ejpam-819	184	23	(	(	PUNCT
ejpam-819	184	24	ψ(t)t	ψ(t)t	X
ejpam-819	184	25	hψ(t))x	hψ(t))x	X
ejpam-819	185	1	+	+	CCONJ
ejpam-819	185	2	2(d(ψ(t)t	2(d(ψ(t)t	NUM
ejpam-819	185	3	hψ(t	hψ(t	NUM
ejpam-819	185	4	)	)	PUNCT
ejpam-819	185	5	)	)	PUNCT
ejpam-819	185	6	ẋ	ẋ	PROPN
ejpam-819	186	1	−ψ(t	−ψ(t	PROPN
ejpam-819	186	2	)	)	PUNCT
ejpam-819	186	3	t	t	PROPN
ejpam-819	186	4	d(hψ(t	d(hψ(t	PROPN
ejpam-819	186	5	)	)	PUNCT
ejpam-819	186	6	)	)	PUNCT
ejpam-819	187	1	ẋ	ẋ	PROPN
ejpam-819	187	2	)	)	PUNCT
ejpam-819	188	1	−	−	PROPN
ejpam-819	189	1	(	(	PUNCT
ejpam-819	189	2	d2(ψ(t)t	d2(ψ(t)t	X
ejpam-819	189	3	hψ(t	hψ(t	NUM
ejpam-819	189	4	)	)	PUNCT
ejpam-819	189	5	)	)	PUNCT
ejpam-819	189	6	ẍ	ẍ	PUNCT
ejpam-819	190	1	−ψ(t	−ψ(t	PROPN
ejpam-819	190	2	)	)	PUNCT
ejpam-819	190	3	t	t	NOUN
ejpam-819	190	4	d2(hψ(t	d2(hψ(t	NOUN
ejpam-819	190	5	)	)	PUNCT
ejpam-819	190	6	)	)	PUNCT
ejpam-819	191	1	ẍ	ẍ	X
ejpam-819	191	2	)	)	PUNCT
ejpam-819	192	1	+	+	CCONJ
ejpam-819	192	2	(	(	PUNCT
ejpam-819	192	3	d3(ψ(t)t	d3(ψ(t)t	NOUN
ejpam-819	192	4	hψ(t))	hψ(t))	PROPN
ejpam-819	192	5	...	...	PUNCT
ejpam-819	192	6	x	x	SYM
ejpam-819	192	7	−ψ(t	−ψ(t	PROPN
ejpam-819	192	8	)	)	PUNCT
ejpam-819	192	9	t	t	NOUN
ejpam-819	192	10	d3(hψ(t))	d3(hψ(t))	VERB
ejpam-819	192	11	...	...	PUNCT
ejpam-819	192	12	x	x	X
ejpam-819	192	13	)	)	PUNCT
ejpam-819	192	14	−	−	PROPN
ejpam-819	192	15	(	(	PUNCT
ejpam-819	192	16	d4(ψ(t)t	d4(ψ(t)t	X
ejpam-819	192	17	hψ(t))	hψ(t))	PROPN
ejpam-819	192	18	....	....	SYM
ejpam-819	192	19	x	x	SYM
ejpam-819	192	20	−ψ(t	−ψ(t	PROPN
ejpam-819	192	21	)	)	PUNCT
ejpam-819	192	22	t	t	PROPN
ejpam-819	192	23	d4(hψ(t))	d4(hψ(t))	VERB
ejpam-819	192	24	....	....	PUNCT
ejpam-819	192	25	x	x	X
ejpam-819	192	26	)	)	PUNCT
ejpam-819	192	27	=	=	SYM
ejpam-819	192	28	0	0	NUM
ejpam-819	192	29	,	,	PUNCT
ejpam-819	192	30	t	t	PROPN
ejpam-819	192	31	∈	∈	PROPN
ejpam-819	192	32	i	i	PRON
ejpam-819	192	33	=	=	AUX
ejpam-819	192	34	⇒ψ(t	⇒ψ(t	X
ejpam-819	192	35	)	)	PUNCT
ejpam-819	192	36	=	=	SYM
ejpam-819	192	37	0	0	NUM
ejpam-819	192	38	,	,	PUNCT
ejpam-819	192	39	t	t	PROPN
ejpam-819	192	40	∈	∈	PROPN
ejpam-819	192	41	i	i	PRON
ejpam-819	192	42	then	then	ADV
ejpam-819	192	43	x(t	x(t	PROPN
ejpam-819	192	44	)	)	PUNCT
ejpam-819	192	45	is	be	AUX
ejpam-819	192	46	feasible	feasible	ADJ
ejpam-819	192	47	for	for	ADP
ejpam-819	192	48	(	(	PUNCT
ejpam-819	192	49	cp	cp	NOUN
ejpam-819	192	50	)	)	PUNCT
ejpam-819	192	51	,	,	PUNCT
ejpam-819	192	52	ȳ(t)t	ȳ(t)t	PROPN
ejpam-819	192	53	g(t	g(t	PROPN
ejpam-819	192	54	,	,	PUNCT
ejpam-819	192	55	x̄	x̄	NOUN
ejpam-819	192	56	,	,	PUNCT
ejpam-819	192	57	˙̄x	˙̄x	PRON
ejpam-819	192	58	)	)	PUNCT
ejpam-819	192	59	=	=	SYM
ejpam-819	193	1	0	0	NUM
ejpam-819	193	2	,	,	PUNCT
ejpam-819	193	3	t	t	PROPN
ejpam-819	193	4	∈	∈	PROPN
ejpam-819	194	1	i	i	PRON
ejpam-819	194	2	.	.	PUNCT
ejpam-819	195	1	in	in	ADP
ejpam-819	195	2	addition	addition	NOUN
ejpam-819	195	3	,	,	PUNCT
ejpam-819	195	4	if	if	SCONJ
ejpam-819	195	5	the	the	DET
ejpam-819	195	6	hypotheses	hypothesis	NOUN
ejpam-819	195	7	in	in	ADP
ejpam-819	195	8	theorem	theorem	ADJ
ejpam-819	195	9	1	1	NUM
ejpam-819	195	10	hold	hold	NOUN
ejpam-819	195	11	,	,	PUNCT
ejpam-819	195	12	then	then	ADV
ejpam-819	195	13	x̄(t	x̄(t	NUM
ejpam-819	195	14	)	)	PUNCT
ejpam-819	195	15	is	be	AUX
ejpam-819	195	16	an	an	DET
ejpam-819	195	17	optimal	optimal	ADJ
ejpam-819	195	18	solution	solution	NOUN
ejpam-819	195	19	.	.	PUNCT
ejpam-819	196	1	proof	proof	NOUN
ejpam-819	196	2	.	.	PUNCT
ejpam-819	197	1	since	since	SCONJ
ejpam-819	197	2	(	(	PUNCT
ejpam-819	197	3	x̄(t	x̄(t	PROPN
ejpam-819	197	4	)	)	PUNCT
ejpam-819	197	5	,	,	PUNCT
ejpam-819	197	6	ȳ(t	ȳ(t	PROPN
ejpam-819	197	7	)	)	PUNCT
ejpam-819	197	8	,	,	PUNCT
ejpam-819	197	9	z̄(t	z̄(t	ADJ
ejpam-819	197	10	)	)	PUNCT
ejpam-819	197	11	,	,	PUNCT
ejpam-819	197	12	p̄(t	p̄(t	PROPN
ejpam-819	197	13	)	)	PUNCT
ejpam-819	197	14	)	)	PUNCT
ejpam-819	197	15	is	be	AUX
ejpam-819	197	16	an	an	DET
ejpam-819	197	17	optimal	optimal	ADJ
ejpam-819	197	18	solution	solution	NOUN
ejpam-819	197	19	for	for	ADP
ejpam-819	197	20	(	(	PUNCT
ejpam-819	197	21	cd	cd	PROPN
ejpam-819	197	22	)	)	PUNCT
ejpam-819	197	23	,	,	PUNCT
ejpam-819	197	24	by	by	ADP
ejpam-819	197	25	proposition	proposition	NOUN
ejpam-819	197	26	1	1	NUM
ejpam-819	197	27	,	,	PUNCT
ejpam-819	197	28	there	there	PRON
ejpam-819	197	29	exist	exist	VERB
ejpam-819	197	30	lagrange	lagrange	NOUN
ejpam-819	197	31	multiplier	multiplier	ADV
ejpam-819	197	32	τ	τ	PROPN
ejpam-819	197	33	∈	∈	PROPN
ejpam-819	197	34	r	r	NOUN
ejpam-819	197	35	,	,	PUNCT
ejpam-819	197	36	and	and	CCONJ
ejpam-819	197	37	piecewise	piecewise	VERB
ejpam-819	197	38	smooth	smooth	ADJ
ejpam-819	197	39	θ	θ	PROPN
ejpam-819	197	40	:	:	PUNCT
ejpam-819	198	1	i	i	PRON
ejpam-819	198	2	→	→	SYM
ejpam-819	198	3	rn	rn	PROPN
ejpam-819	198	4	,	,	PUNCT
ejpam-819	198	5	µ	µ	X
ejpam-819	198	6	:	:	PUNCT
ejpam-819	198	7	i	i	PROPN
ejpam-819	198	8	→	→	SYM
ejpam-819	198	9	rm	rm	PROPN
ejpam-819	198	10	and	and	CCONJ
ejpam-819	198	11	α	α	NOUN
ejpam-819	198	12	:	:	PUNCT
ejpam-819	199	1	i	i	PRON
ejpam-819	199	2	→	→	SYM
ejpam-819	199	3	rn	rn	PROPN
ejpam-819	199	4	such	such	ADJ
ejpam-819	199	5	that	that	SCONJ
ejpam-819	199	6	following	follow	VERB
ejpam-819	199	7	conditions	condition	NOUN
ejpam-819	199	8	hold	hold	VERB
ejpam-819	199	9	at	at	ADP
ejpam-819	199	10	the	the	DET
ejpam-819	199	11	feasible	feasible	ADJ
ejpam-819	199	12	point	point	NOUN
ejpam-819	199	13	of	of	ADP
ejpam-819	199	14	(	(	PUNCT
ejpam-819	199	15	cd	cd	PROPN
ejpam-819	199	16	)	)	PUNCT
ejpam-819	199	17	.	.	PUNCT
ejpam-819	200	1	τ	τ	X
ejpam-819	201	1	[	[	X
ejpam-819	201	2	(	(	PUNCT
ejpam-819	201	3	fx	fx	PROPN
ejpam-819	201	4	+	+	NUM
ejpam-819	201	5	b(t)z(t	b(t)z(t	NOUN
ejpam-819	201	6	)	)	PUNCT
ejpam-819	201	7	+	+	NUM
ejpam-819	201	8	y(t)t	y(t)t	NOUN
ejpam-819	201	9	gx)−	gx)−	NOUN
ejpam-819	202	1	d	d	NOUN
ejpam-819	202	2	(	(	PUNCT
ejpam-819	202	3	f	f	PROPN
ejpam-819	202	4	ẋ	ẋ	PROPN
ejpam-819	203	1	+	+	NUM
ejpam-819	203	2	y(t)t	y(t)t	PROPN
ejpam-819	203	3	g	g	NOUN
ejpam-819	203	4	ẋ)−	ẋ)−	PROPN
ejpam-819	203	5	1	1	NUM
ejpam-819	203	6	2	2	NUM
ejpam-819	203	7	(	(	PUNCT
ejpam-819	203	8	p(t)t	p(t)t	NOUN
ejpam-819	203	9	h	h	NOUN
ejpam-819	203	10	p(t))x	p(t))x	NOUN
ejpam-819	204	1	+	+	CCONJ
ejpam-819	204	2	d(p(t)t	d(p(t)t	NOUN
ejpam-819	204	3	h	h	NOUN
ejpam-819	204	4	p(t	p(t	NOUN
ejpam-819	204	5	)	)	PUNCT
ejpam-819	204	6	)	)	PUNCT
ejpam-819	205	1	ẋ	ẋ	PROPN
ejpam-819	206	1	−	−	NOUN
ejpam-819	206	2	1	1	NUM
ejpam-819	206	3	2	2	NUM
ejpam-819	206	4	d2(p(t)t	d2(p(t)t	NOUN
ejpam-819	206	5	h	h	NOUN
ejpam-819	206	6	p(t	p(t	NOUN
ejpam-819	206	7	)	)	PUNCT
ejpam-819	206	8	)	)	PUNCT
ejpam-819	206	9	ẍ	ẍ	PUNCT
ejpam-819	207	1	+	+	CCONJ
ejpam-819	207	2	1	1	NUM
ejpam-819	207	3	2	2	NUM
ejpam-819	207	4	d3(p(t)t	d3(p(t)t	NOUN
ejpam-819	207	5	h	h	PROPN
ejpam-819	207	6	p(t))	p(t))	VERB
ejpam-819	207	7	...	...	PUNCT
ejpam-819	207	8	x	x	X
ejpam-819	208	1	−	−	NOUN
ejpam-819	208	2	1	1	NUM
ejpam-819	208	3	2	2	NUM
ejpam-819	208	4	d4(p(t)t	d4(p(t)t	ADP
ejpam-819	208	5	h	h	PROPN
ejpam-819	208	6	p(t))	p(t))	NOUN
ejpam-819	208	7	....	....	PUNCT
ejpam-819	208	8	x	x	X
ejpam-819	208	9	]	]	X
ejpam-819	209	1	+	+	ADJ
ejpam-819	209	2	θ(t)t	θ(t)t	NOUN
ejpam-819	209	3	[	[	PUNCT
ejpam-819	209	4	fx	fx	NOUN
ejpam-819	209	5	x	x	PUNCT
ejpam-819	209	6	−	−	PROPN
ejpam-819	209	7	(	(	PUNCT
ejpam-819	209	8	y(t	y(t	PROPN
ejpam-819	209	9	)	)	PUNCT
ejpam-819	209	10	t	t	NOUN
ejpam-819	209	11	gx)x	gx)x	NOUN
ejpam-819	209	12	−	−	PROPN
ejpam-819	209	13	2d	2d	NOUN
ejpam-819	209	14	(	(	PUNCT
ejpam-819	209	15	f	f	PROPN
ejpam-819	209	16	ẋ	ẋ	PROPN
ejpam-819	210	1	x	x	PUNCT
ejpam-819	211	1	+	+	PUNCT
ejpam-819	211	2	(	(	PUNCT
ejpam-819	211	3	y(t	y(t	PROPN
ejpam-819	211	4	)	)	PUNCT
ejpam-819	211	5	t	t	PROPN
ejpam-819	211	6	gx	gx	PROPN
ejpam-819	211	7	)	)	PUNCT
ejpam-819	211	8	ẋ)−	ẋ)−	PROPN
ejpam-819	211	9	d2	d2	PROPN
ejpam-819	211	10	(	(	PUNCT
ejpam-819	212	1	f	f	PROPN
ejpam-819	212	2	ẋ	ẋ	PROPN
ejpam-819	212	3	ẋ	ẋ	PROPN
ejpam-819	213	1	+	+	NUM
ejpam-819	213	2	y(t)t	y(t)t	PROPN
ejpam-819	213	3	g	g	PROPN
ejpam-819	213	4	ẋ	ẋ	PROPN
ejpam-819	213	5	ẋ	ẋ	PROPN
ejpam-819	213	6	)	)	PUNCT
ejpam-819	214	1	+	+	CCONJ
ejpam-819	214	2	d3	d3	PROPN
ejpam-819	214	3	(	(	PUNCT
ejpam-819	214	4	f	f	PROPN
ejpam-819	214	5	ẋ	ẋ	PROPN
ejpam-819	214	6	ẍ	ẍ	X
ejpam-819	215	1	+	+	CCONJ
ejpam-819	215	2	(	(	PUNCT
ejpam-819	215	3	y(t	y(t	PROPN
ejpam-819	215	4	)	)	PUNCT
ejpam-819	215	5	t	t	PROPN
ejpam-819	215	6	g	g	PROPN
ejpam-819	215	7	ẋ	ẋ	PROPN
ejpam-819	215	8	)	)	PUNCT
ejpam-819	215	9	ẍ	ẍ	X
ejpam-819	216	1	+	+	CCONJ
ejpam-819	216	2	(	(	PUNCT
ejpam-819	216	3	h	h	NOUN
ejpam-819	216	4	p(t))x	p(t))x	NOUN
ejpam-819	216	5	−	−	PROPN
ejpam-819	216	6	d(h	d(h	PROPN
ejpam-819	216	7	p(t	p(t	PROPN
ejpam-819	216	8	)	)	PUNCT
ejpam-819	216	9	)	)	PUNCT
ejpam-819	216	10	ẋ	ẋ	PROPN
ejpam-819	217	1	+	+	CCONJ
ejpam-819	217	2	d2(h	d2(h	PROPN
ejpam-819	217	3	p(t	p(t	NOUN
ejpam-819	217	4	)	)	PUNCT
ejpam-819	217	5	)	)	PUNCT
ejpam-819	217	6	ẍ	ẍ	X
ejpam-819	218	1	−	−	PROPN
ejpam-819	218	2	d3(h	d3(h	ADV
ejpam-819	218	3	p(t))	p(t))	ADJ
ejpam-819	218	4	...	...	PUNCT
ejpam-819	218	5	x	x	X
ejpam-819	219	1	+	+	CCONJ
ejpam-819	219	2	d4(h	d4(h	NUM
ejpam-819	219	3	p(t))	p(t))	INTJ
ejpam-819	219	4	....	....	PUNCT
ejpam-819	219	5	x	x	X
ejpam-819	219	6	]	]	X
ejpam-819	219	7	(	(	PUNCT
ejpam-819	219	8	13	13	NUM
ejpam-819	219	9	)	)	PUNCT
ejpam-819	219	10	τ	τ	PROPN
ejpam-819	220	1	(	(	PUNCT
ejpam-819	220	2	f	f	PROPN
ejpam-819	220	3	j	j	PROPN
ejpam-819	220	4	−	−	NOUN
ejpam-819	220	5	1	1	NUM
ejpam-819	220	6	2	2	NUM
ejpam-819	220	7	p(t)t	p(t)t	NOUN
ejpam-819	220	8	g	g	PROPN
ejpam-819	220	9	j	j	PROPN
ejpam-819	220	10	x	x	X
ejpam-819	220	11	x	x	SYM
ejpam-819	220	12	p(t	p(t	NOUN
ejpam-819	220	13	)	)	PUNCT
ejpam-819	220	14	)	)	PUNCT
ejpam-819	221	1	+	+	CCONJ
ejpam-819	221	2	θ(t)t	θ(t)t	X
ejpam-819	221	3	(	(	PUNCT
ejpam-819	221	4	g	g	PROPN
ejpam-819	221	5	j	j	PROPN
ejpam-819	221	6	x	x	X
ejpam-819	221	7	x	x	PUNCT
ejpam-819	222	1	−	−	NUM
ejpam-819	222	2	2dg	2dg	NOUN
ejpam-819	222	3	j	j	PROPN
ejpam-819	222	4	x	x	SYM
ejpam-819	222	5	ẋ	ẋ	PROPN
ejpam-819	223	1	+	+	NUM
ejpam-819	223	2	d2	d2	PROPN
ejpam-819	223	3	g	g	PROPN
ejpam-819	223	4	j	j	PROPN
ejpam-819	223	5	ẋ	ẋ	PROPN
ejpam-819	223	6	ẋ	ẋ	PROPN
ejpam-819	223	7	)	)	PUNCT
ejpam-819	223	8	p(t	p(t	NOUN
ejpam-819	223	9	)	)	PUNCT
ejpam-819	224	1	+	+	NOUN
ejpam-819	224	2	µ	µ	X
ejpam-819	224	3	j(t	j(t	PROPN
ejpam-819	224	4	)	)	PUNCT
ejpam-819	224	5	=	=	SYM
ejpam-819	224	6	0	0	NUM
ejpam-819	224	7	,	,	PUNCT
ejpam-819	224	8	j	j	X
ejpam-819	224	9	=	=	SYM
ejpam-819	224	10	1,2	1,2	NUM
ejpam-819	224	11	,	,	PUNCT
ejpam-819	224	12	.	.	PUNCT
ejpam-819	224	13	.	.	PUNCT
ejpam-819	224	14	.	.	PUNCT
ejpam-819	225	1	,	,	PUNCT
ejpam-819	225	2	m.	m.	NOUN
ejpam-819	225	3	(	(	PUNCT
ejpam-819	225	4	14	14	NUM
ejpam-819	225	5	)	)	PUNCT
ejpam-819	225	6	τ	τ	PROPN
ejpam-819	225	7	x̄(t)t	x̄(t)t	PROPN
ejpam-819	225	8	b(t	b(t	PROPN
ejpam-819	225	9	)	)	PUNCT
ejpam-819	226	1	+	+	CCONJ
ejpam-819	226	2	θ(t)t	θ(t)t	PROPN
ejpam-819	226	3	b(t)−	b(t)−	PROPN
ejpam-819	226	4	2α(t)b(t)z(t	2α(t)b(t)z(t	PROPN
ejpam-819	226	5	)	)	PUNCT
ejpam-819	227	1	=	=	SYM
ejpam-819	227	2	0	0	NUM
ejpam-819	227	3	,	,	PUNCT
ejpam-819	227	4	(	(	PUNCT
ejpam-819	227	5	15	15	NUM
ejpam-819	227	6	)	)	PUNCT
ejpam-819	227	7	(	(	PUNCT
ejpam-819	227	8	θ(t)−τp(t))h	θ(t)−τp(t))h	NOUN
ejpam-819	227	9	=	=	SYM
ejpam-819	227	10	0	0	NUM
ejpam-819	227	11	,	,	PUNCT
ejpam-819	227	12	(	(	PUNCT
ejpam-819	227	13	16	16	NUM
ejpam-819	227	14	)	)	PUNCT
ejpam-819	227	15	fx	fx	NOUN
ejpam-819	227	16	+	+	NUM
ejpam-819	227	17	b(t)z(t	b(t)z(t	NOUN
ejpam-819	227	18	)	)	PUNCT
ejpam-819	227	19	+	+	NUM
ejpam-819	227	20	ȳ(t)t	ȳ(t)t	NOUN
ejpam-819	227	21	gx	gx	PROPN
ejpam-819	227	22	−	−	PROPN
ejpam-819	228	1	d	d	PROPN
ejpam-819	228	2	(	(	PUNCT
ejpam-819	228	3	f	f	PROPN
ejpam-819	228	4	ẋ	ẋ	PROPN
ejpam-819	229	1	+	+	CCONJ
ejpam-819	229	2	ȳ(t)g	ȳ(t)g	ADJ
ejpam-819	229	3	ẋ	ẋ	PROPN
ejpam-819	229	4	)	)	PUNCT
ejpam-819	230	1	+	+	NOUN
ejpam-819	230	2	h	h	NOUN
ejpam-819	230	3	p(t	p(t	NOUN
ejpam-819	230	4	)	)	PUNCT
ejpam-819	231	1	=	=	SYM
ejpam-819	231	2	0	0	NUM
ejpam-819	231	3	,	,	PUNCT
ejpam-819	231	4	(	(	PUNCT
ejpam-819	231	5	17	17	NUM
ejpam-819	231	6	)	)	PUNCT
ejpam-819	231	7	α(t)(1−	α(t)(1−	NUM
ejpam-819	231	8	z̄(t)t	z̄(t)t	NOUN
ejpam-819	231	9	b(t)z̄(t	b(t)z̄(t	NOUN
ejpam-819	231	10	)	)	PUNCT
ejpam-819	231	11	)	)	PUNCT
ejpam-819	232	1	=	=	SYM
ejpam-819	232	2	0	0	NUM
ejpam-819	232	3	,	,	PUNCT
ejpam-819	232	4	(	(	PUNCT
ejpam-819	232	5	18	18	NUM
ejpam-819	232	6	)	)	PUNCT
ejpam-819	232	7	µ̄(t)t	µ̄(t)t	ADJ
ejpam-819	232	8	ȳ(t	ȳ(t	NOUN
ejpam-819	232	9	)	)	PUNCT
ejpam-819	232	10	=	=	SYM
ejpam-819	232	11	0	0	NUM
ejpam-819	232	12	,	,	PUNCT
ejpam-819	232	13	(	(	PUNCT
ejpam-819	232	14	19	19	NUM
ejpam-819	232	15	)	)	PUNCT
ejpam-819	232	16	i.	i.	NOUN
ejpam-819	232	17	husain	husain	PROPN
ejpam-819	232	18	,	,	PUNCT
ejpam-819	232	19	m.	m.	NOUN
ejpam-819	232	20	masoodi	masoodi	PROPN
ejpam-819	232	21	/	/	SYM
ejpam-819	232	22	eur	eur	PROPN
ejpam-819	232	23	.	.	PUNCT
ejpam-819	233	1	j.	j.	PROPN
ejpam-819	233	2	pure	pure	PROPN
ejpam-819	233	3	appl	appl	PROPN
ejpam-819	233	4	.	.	PROPN
ejpam-819	233	5	math	math	PROPN
ejpam-819	233	6	,	,	PUNCT
ejpam-819	233	7	5	5	NUM
ejpam-819	233	8	(	(	PUNCT
ejpam-819	233	9	2012	2012	NUM
ejpam-819	233	10	)	)	PUNCT
ejpam-819	233	11	,	,	PUNCT
ejpam-819	233	12	390	390	NUM
ejpam-819	233	13	-	-	SYM
ejpam-819	233	14	400	400	NUM
ejpam-819	233	15	397	397	NUM
ejpam-819	233	16	(	(	PUNCT
ejpam-819	233	17	τ	τ	PROPN
ejpam-819	233	18	,	,	PUNCT
ejpam-819	233	19	α(t),µ(t	α(t),µ(t	PROPN
ejpam-819	233	20	)	)	PUNCT
ejpam-819	233	21	)	)	PUNCT
ejpam-819	233	22	≥	≥	NOUN
ejpam-819	233	23	0	0	NUM
ejpam-819	233	24	,	,	PUNCT
ejpam-819	233	25	(	(	PUNCT
ejpam-819	233	26	20	20	NUM
ejpam-819	233	27	)	)	PUNCT
ejpam-819	233	28	(	(	PUNCT
ejpam-819	233	29	τ	τ	PROPN
ejpam-819	233	30	,	,	PUNCT
ejpam-819	233	31	α(t),µ(t),θ(t	α(t),µ(t),θ(t	NUM
ejpam-819	233	32	)	)	PUNCT
ejpam-819	233	33	)	)	PUNCT
ejpam-819	234	1	6=	6=	ADP
ejpam-819	234	2	0	0	NUM
ejpam-819	234	3	,	,	PUNCT
ejpam-819	234	4	(	(	PUNCT
ejpam-819	234	5	21	21	NUM
ejpam-819	234	6	)	)	PUNCT
ejpam-819	234	7	where	where	SCONJ
ejpam-819	234	8	t	t	PROPN
ejpam-819	234	9	∈	∈	PROPN
ejpam-819	235	1	i	i	PRON
ejpam-819	235	2	.	.	PUNCT
ejpam-819	236	1	by	by	ADP
ejpam-819	236	2	the	the	DET
ejpam-819	236	3	nonsingularity	nonsingularity	NOUN
ejpam-819	236	4	of	of	ADP
ejpam-819	236	5	h	h	NOUN
ejpam-819	236	6	,	,	PUNCT
ejpam-819	236	7	eqref11	eqref11	NOUN
ejpam-819	236	8	yields	yield	NOUN
ejpam-819	236	9	,	,	PUNCT
ejpam-819	236	10	θ(t	θ(t	PROPN
ejpam-819	236	11	)	)	PUNCT
ejpam-819	236	12	+	+	NOUN
ejpam-819	236	13	τp̄(t	τp̄(t	NUM
ejpam-819	236	14	)	)	PUNCT
ejpam-819	236	15	=	=	SYM
ejpam-819	236	16	0	0	NUM
ejpam-819	236	17	,	,	PUNCT
ejpam-819	236	18	t	t	PROPN
ejpam-819	236	19	∈	∈	PROPN
ejpam-819	236	20	i	i	PRON
ejpam-819	236	21	(	(	PUNCT
ejpam-819	236	22	22	22	NUM
ejpam-819	236	23	)	)	PUNCT
ejpam-819	236	24	if	if	SCONJ
ejpam-819	236	25	τ	τ	PROPN
ejpam-819	236	26	=	=	SYM
ejpam-819	236	27	0	0	NUM
ejpam-819	236	28	,	,	PUNCT
ejpam-819	236	29	(	(	PUNCT
ejpam-819	236	30	22	22	NUM
ejpam-819	236	31	)	)	PUNCT
ejpam-819	236	32	implies	imply	VERB
ejpam-819	236	33	θ(t	θ(t	NOUN
ejpam-819	236	34	)	)	PUNCT
ejpam-819	236	35	=	=	SYM
ejpam-819	237	1	0	0	NUM
ejpam-819	237	2	t	t	X
ejpam-819	237	3	∈	∈	PROPN
ejpam-819	238	1	i	i	PRON
ejpam-819	238	2	.	.	PUNCT
ejpam-819	239	1	from	from	ADP
ejpam-819	239	2	(	(	PUNCT
ejpam-819	239	3	14	14	NUM
ejpam-819	239	4	)	)	PUNCT
ejpam-819	239	5	,	,	PUNCT
ejpam-819	239	6	we	we	PRON
ejpam-819	239	7	have	have	AUX
ejpam-819	239	8	µ(t	µ(t	ADJ
ejpam-819	239	9	)	)	PUNCT
ejpam-819	240	1	=	=	SYM
ejpam-819	240	2	0	0	NUM
ejpam-819	240	3	,	,	PUNCT
ejpam-819	240	4	t	t	PROPN
ejpam-819	240	5	∈	∈	PROPN
ejpam-819	241	1	i	i	PRON
ejpam-819	241	2	.	.	PUNCT
ejpam-819	242	1	the	the	DET
ejpam-819	242	2	relation	relation	NOUN
ejpam-819	242	3	(	(	PUNCT
ejpam-819	242	4	15	15	NUM
ejpam-819	242	5	)	)	PUNCT
ejpam-819	242	6	together	together	ADV
ejpam-819	242	7	with	with	ADP
ejpam-819	242	8	(	(	PUNCT
ejpam-819	242	9	18	18	NUM
ejpam-819	242	10	)	)	PUNCT
ejpam-819	242	11	gives	give	VERB
ejpam-819	242	12	α(t	α(t	NOUN
ejpam-819	242	13	)	)	PUNCT
ejpam-819	242	14	=	=	SYM
ejpam-819	243	1	0	0	X
ejpam-819	243	2	.	.	PUNCT
ejpam-819	244	1	hence	hence	ADV
ejpam-819	244	2	(	(	PUNCT
ejpam-819	244	3	τ	τ	X
ejpam-819	244	4	,	,	PUNCT
ejpam-819	244	5	α(t),θ(t),µ(t	α(t),θ(t),µ(t	NOUN
ejpam-819	244	6	)	)	PUNCT
ejpam-819	244	7	)	)	PUNCT
ejpam-819	245	1	=	=	SYM
ejpam-819	245	2	0	0	NUM
ejpam-819	245	3	,	,	PUNCT
ejpam-819	245	4	t	t	PROPN
ejpam-819	245	5	∈	∈	PROPN
ejpam-819	246	1	i	i	PRON
ejpam-819	246	2	,	,	PUNCT
ejpam-819	246	3	contradicting	contradict	VERB
ejpam-819	246	4	(	(	PUNCT
ejpam-819	246	5	21	21	NUM
ejpam-819	246	6	)	)	PUNCT
ejpam-819	246	7	.	.	PUNCT
ejpam-819	247	1	consequently	consequently	ADV
ejpam-819	247	2	τ	τ	X
ejpam-819	247	3	>	>	X
ejpam-819	247	4	0	0	PROPN
ejpam-819	247	5	.	.	PUNCT
ejpam-819	247	6	from	from	ADP
ejpam-819	247	7	(	(	PUNCT
ejpam-819	247	8	22	22	NUM
ejpam-819	247	9	)	)	PUNCT
ejpam-819	247	10	and	and	CCONJ
ejpam-819	247	11	τ	τ	X
ejpam-819	247	12	>	>	X
ejpam-819	247	13	0	0	NUM
ejpam-819	247	14	,	,	PUNCT
ejpam-819	247	15	(	(	PUNCT
ejpam-819	247	16	13	13	NUM
ejpam-819	247	17	)	)	PUNCT
ejpam-819	247	18	becomes	become	VERB
ejpam-819	247	19	,	,	PUNCT
ejpam-819	247	20	[	[	X
ejpam-819	247	21	(	(	PUNCT
ejpam-819	247	22	fx	fx	NOUN
ejpam-819	247	23	+	+	NUM
ejpam-819	247	24	b(t)z(t	b(t)z(t	NOUN
ejpam-819	247	25	)	)	PUNCT
ejpam-819	247	26	+	+	NUM
ejpam-819	247	27	y(t)t	y(t)t	NOUN
ejpam-819	247	28	gx)−	gx)−	NOUN
ejpam-819	248	1	d	d	PROPN
ejpam-819	248	2	(	(	PUNCT
ejpam-819	248	3	f	f	PROPN
ejpam-819	248	4	ẋ+y(t)t	ẋ+y(t)t	PROPN
ejpam-819	248	5	g	g	PROPN
ejpam-819	248	6	ẋ	ẋ	PROPN
ejpam-819	248	7	)	)	PUNCT
ejpam-819	248	8	−	−	PROPN
ejpam-819	249	1	1	1	NUM
ejpam-819	249	2	2	2	NUM
ejpam-819	249	3	(	(	PUNCT
ejpam-819	249	4	p(t)t	p(t)t	NOUN
ejpam-819	249	5	h	h	NOUN
ejpam-819	249	6	p(t))x	p(t))x	NOUN
ejpam-819	249	7	+	+	CCONJ
ejpam-819	249	8	d(p(t)t	d(p(t)t	NOUN
ejpam-819	249	9	h	h	NOUN
ejpam-819	249	10	p(t	p(t	NOUN
ejpam-819	249	11	)	)	PUNCT
ejpam-819	249	12	)	)	PUNCT
ejpam-819	250	1	ẋ	ẋ	PROPN
ejpam-819	251	1	−	−	NOUN
ejpam-819	251	2	1	1	NUM
ejpam-819	251	3	2	2	NUM
ejpam-819	251	4	d2(p(t)t	d2(p(t)t	NOUN
ejpam-819	251	5	h	h	NOUN
ejpam-819	251	6	p(t	p(t	NOUN
ejpam-819	251	7	)	)	PUNCT
ejpam-819	251	8	)	)	PUNCT
ejpam-819	251	9	ẍ	ẍ	PUNCT
ejpam-819	252	1	+	+	CCONJ
ejpam-819	252	2	1	1	NUM
ejpam-819	252	3	2	2	NUM
ejpam-819	252	4	d3(p(t)t	d3(p(t)t	NOUN
ejpam-819	252	5	h	h	PROPN
ejpam-819	252	6	p(t))	p(t))	VERB
ejpam-819	252	7	...	...	PUNCT
ejpam-819	252	8	x	x	X
ejpam-819	253	1	−	−	NOUN
ejpam-819	253	2	1	1	NUM
ejpam-819	253	3	2	2	NUM
ejpam-819	253	4	d4(p(t)t	d4(p(t)t	ADP
ejpam-819	253	5	h	h	PROPN
ejpam-819	253	6	p(t))	p(t))	NOUN
ejpam-819	253	7	....	....	PUNCT
ejpam-819	253	8	x	x	X
ejpam-819	253	9	]	]	PUNCT
ejpam-819	254	1	+	+	CCONJ
ejpam-819	254	2	p(t)t	p(t)t	NOUN
ejpam-819	254	3	[	[	X
ejpam-819	254	4	(	(	PUNCT
ejpam-819	254	5	fx	fx	INTJ
ejpam-819	254	6	x	x	SYM
ejpam-819	254	7	−	−	PROPN
ejpam-819	254	8	(	(	PUNCT
ejpam-819	254	9	y(t	y(t	PROPN
ejpam-819	254	10	)	)	PUNCT
ejpam-819	254	11	t	t	PROPN
ejpam-819	254	12	gx)x)−	gx)x)−	PROPN
ejpam-819	255	1	d	d	PROPN
ejpam-819	255	2	(	(	PUNCT
ejpam-819	255	3	f	f	PROPN
ejpam-819	255	4	ẋ	ẋ	PROPN
ejpam-819	255	5	x	x	PUNCT
ejpam-819	256	1	+	+	PUNCT
ejpam-819	256	2	(	(	PUNCT
ejpam-819	256	3	y(t	y(t	PROPN
ejpam-819	256	4	)	)	PUNCT
ejpam-819	256	5	t	t	PROPN
ejpam-819	256	6	gx	gx	PROPN
ejpam-819	256	7	)	)	PUNCT
ejpam-819	256	8	ẋ)−	ẋ)−	PROPN
ejpam-819	257	1	d	d	PROPN
ejpam-819	257	2	(	(	PUNCT
ejpam-819	257	3	f	f	PROPN
ejpam-819	257	4	ẋ	ẋ	PROPN
ejpam-819	257	5	x	x	PUNCT
ejpam-819	258	1	+	+	PUNCT
ejpam-819	258	2	(	(	PUNCT
ejpam-819	258	3	y(t	y(t	PROPN
ejpam-819	258	4	)	)	PUNCT
ejpam-819	258	5	t	t	PROPN
ejpam-819	258	6	g	g	PROPN
ejpam-819	258	7	ẋ)x	ẋ)x	NOUN
ejpam-819	258	8	)	)	PUNCT
ejpam-819	259	1	−	−	PROPN
ejpam-819	259	2	d	d	NOUN
ejpam-819	259	3	(	(	PUNCT
ejpam-819	259	4	d	d	X
ejpam-819	259	5	(	(	PUNCT
ejpam-819	259	6	f	f	PROPN
ejpam-819	259	7	ẋ	ẋ	PROPN
ejpam-819	259	8	ẋ	ẋ	PROPN
ejpam-819	260	1	+	+	NUM
ejpam-819	260	2	y(t)t	y(t)t	PROPN
ejpam-819	260	3	g	g	PROPN
ejpam-819	260	4	ẋ	ẋ	PROPN
ejpam-819	260	5	ẋ))+	ẋ))+	PROPN
ejpam-819	260	6	d2	d2	PROPN
ejpam-819	260	7	(	(	PUNCT
ejpam-819	260	8	d	d	X
ejpam-819	260	9	(	(	PUNCT
ejpam-819	260	10	f	f	PROPN
ejpam-819	260	11	ẋ	ẋ	PROPN
ejpam-819	260	12	ẍ	ẍ	X
ejpam-819	261	1	+	+	CCONJ
ejpam-819	261	2	(	(	PUNCT
ejpam-819	261	3	y(t	y(t	PROPN
ejpam-819	261	4	)	)	PUNCT
ejpam-819	261	5	t	t	PROPN
ejpam-819	261	6	g	g	PROPN
ejpam-819	261	7	ẋ)x	ẋ)x	NOUN
ejpam-819	261	8	)	)	PUNCT
ejpam-819	261	9	)	)	PUNCT
ejpam-819	262	1	+	+	CCONJ
ejpam-819	262	2	(	(	PUNCT
ejpam-819	262	3	h	h	NOUN
ejpam-819	262	4	p(t))x	p(t))x	NOUN
ejpam-819	262	5	−	−	PROPN
ejpam-819	262	6	d(h	d(h	PROPN
ejpam-819	262	7	p(t	p(t	PROPN
ejpam-819	262	8	)	)	PUNCT
ejpam-819	262	9	)	)	PUNCT
ejpam-819	262	10	ẋ	ẋ	PROPN
ejpam-819	263	1	+	+	CCONJ
ejpam-819	263	2	d2(h	d2(h	PROPN
ejpam-819	263	3	p(t	p(t	NOUN
ejpam-819	263	4	)	)	PUNCT
ejpam-819	263	5	)	)	PUNCT
ejpam-819	263	6	ẍ	ẍ	X
ejpam-819	264	1	−	−	PROPN
ejpam-819	264	2	d3(h	d3(h	ADV
ejpam-819	264	3	p(t))	p(t))	ADJ
ejpam-819	264	4	...	...	PUNCT
ejpam-819	264	5	x	x	X
ejpam-819	265	1	+	+	CCONJ
ejpam-819	265	2	d4(h	d4(h	NUM
ejpam-819	265	3	p(t))	p(t))	NOUN
ejpam-819	265	4	....	....	PUNCT
ejpam-819	265	5	x	x	X
ejpam-819	265	6	]	]	PUNCT
ejpam-819	265	7	=	=	PUNCT
ejpam-819	266	1	0	0	X
ejpam-819	266	2	.	.	PUNCT
ejpam-819	267	1	using	use	VERB
ejpam-819	267	2	the	the	DET
ejpam-819	267	3	expression	expression	NOUN
ejpam-819	267	4	for	for	ADP
ejpam-819	267	5	h	h	NOUN
ejpam-819	267	6	,	,	PUNCT
ejpam-819	267	7	this	this	PRON
ejpam-819	267	8	gives	give	VERB
ejpam-819	267	9	[	[	PUNCT
ejpam-819	267	10	(	(	PUNCT
ejpam-819	267	11	fx	fx	PROPN
ejpam-819	267	12	+	+	NUM
ejpam-819	267	13	b(t)z(t	b(t)z(t	NOUN
ejpam-819	267	14	)	)	PUNCT
ejpam-819	267	15	+	+	NUM
ejpam-819	267	16	y(t)t	y(t)t	NOUN
ejpam-819	267	17	gx)−	gx)−	NOUN
ejpam-819	268	1	d	d	PROPN
ejpam-819	268	2	(	(	PUNCT
ejpam-819	268	3	f	f	PROPN
ejpam-819	268	4	ẋ+y(t)t	ẋ+y(t)t	PROPN
ejpam-819	268	5	g	g	PROPN
ejpam-819	268	6	ẋ	ẋ	PROPN
ejpam-819	268	7	)	)	PUNCT
ejpam-819	269	1	+	+	PUNCT
ejpam-819	269	2	h	h	PROPN
ejpam-819	269	3	p(t)−	p(t)−	PROPN
ejpam-819	269	4	1	1	NUM
ejpam-819	269	5	2	2	NUM
ejpam-819	269	6	(	(	PUNCT
ejpam-819	269	7	p(t)t	p(t)t	NOUN
ejpam-819	269	8	h	h	NOUN
ejpam-819	269	9	p(t))x	p(t))x	NOUN
ejpam-819	269	10	+	+	CCONJ
ejpam-819	269	11	d(p(t)t	d(p(t)t	NOUN
ejpam-819	269	12	h	h	NOUN
ejpam-819	269	13	p(t	p(t	NOUN
ejpam-819	269	14	)	)	PUNCT
ejpam-819	269	15	)	)	PUNCT
ejpam-819	270	1	ẋ	ẋ	PROPN
ejpam-819	271	1	−	−	NOUN
ejpam-819	271	2	1	1	NUM
ejpam-819	271	3	2	2	NUM
ejpam-819	271	4	d2(p(t)t	d2(p(t)t	NOUN
ejpam-819	271	5	h	h	NOUN
ejpam-819	271	6	p(t	p(t	NOUN
ejpam-819	271	7	)	)	PUNCT
ejpam-819	271	8	)	)	PUNCT
ejpam-819	271	9	ẍ	ẍ	PUNCT
ejpam-819	272	1	+	+	CCONJ
ejpam-819	272	2	1	1	NUM
ejpam-819	272	3	2	2	NUM
ejpam-819	272	4	d3(p(t)t	d3(p(t)t	NOUN
ejpam-819	272	5	h	h	PROPN
ejpam-819	272	6	p(t))	p(t))	VERB
ejpam-819	272	7	...	...	PUNCT
ejpam-819	272	8	x	x	X
ejpam-819	273	1	−	−	NOUN
ejpam-819	273	2	1	1	NUM
ejpam-819	273	3	2	2	NUM
ejpam-819	273	4	d4(p(t)t	d4(p(t)t	ADP
ejpam-819	273	5	h	h	PROPN
ejpam-819	273	6	p(t))	p(t))	NOUN
ejpam-819	273	7	....	....	PUNCT
ejpam-819	273	8	x	x	X
ejpam-819	273	9	]	]	PUNCT
ejpam-819	274	1	+	+	CCONJ
ejpam-819	274	2	p(t)t	p(t)t	NOUN
ejpam-819	274	3	[	[	X
ejpam-819	274	4	(	(	PUNCT
ejpam-819	274	5	h	h	NOUN
ejpam-819	274	6	p(t))x	p(t))x	NOUN
ejpam-819	274	7	−	−	PROPN
ejpam-819	274	8	d(h	d(h	PROPN
ejpam-819	274	9	p(t	p(t	PROPN
ejpam-819	274	10	)	)	PUNCT
ejpam-819	274	11	)	)	PUNCT
ejpam-819	274	12	ẋ	ẋ	PROPN
ejpam-819	275	1	+	+	CCONJ
ejpam-819	275	2	d2(h	d2(h	PROPN
ejpam-819	275	3	p(t	p(t	NOUN
ejpam-819	275	4	)	)	PUNCT
ejpam-819	275	5	)	)	PUNCT
ejpam-819	275	6	ẍ	ẍ	X
ejpam-819	276	1	−	−	PROPN
ejpam-819	276	2	d3(h	d3(h	ADV
ejpam-819	276	3	p(t))	p(t))	ADJ
ejpam-819	276	4	...	...	PUNCT
ejpam-819	276	5	x	x	X
ejpam-819	277	1	+	+	CCONJ
ejpam-819	277	2	d4(h	d4(h	NUM
ejpam-819	277	3	p(t))	p(t))	NOUN
ejpam-819	277	4	....	....	PUNCT
ejpam-819	277	5	x	x	X
ejpam-819	277	6	]	]	X
ejpam-819	277	7	=	=	PUNCT
ejpam-819	278	1	0	0	X
ejpam-819	278	2	.	.	PUNCT
ejpam-819	279	1	this	this	PRON
ejpam-819	279	2	,	,	PUNCT
ejpam-819	279	3	by	by	ADP
ejpam-819	279	4	using	use	VERB
ejpam-819	279	5	(	(	PUNCT
ejpam-819	279	6	17	17	NUM
ejpam-819	279	7	)	)	PUNCT
ejpam-819	279	8	,	,	PUNCT
ejpam-819	279	9	reduces	reduce	VERB
ejpam-819	279	10	to	to	ADP
ejpam-819	279	11	(	(	PUNCT
ejpam-819	279	12	p(t)t	p(t)t	NOUN
ejpam-819	279	13	h	h	NOUN
ejpam-819	279	14	p(t))x	p(t))x	NOUN
ejpam-819	279	15	+	+	CCONJ
ejpam-819	279	16	2(d(p(t)t	2(d(p(t)t	NUM
ejpam-819	279	17	h	h	NOUN
ejpam-819	279	18	p(t	p(t	NOUN
ejpam-819	279	19	)	)	PUNCT
ejpam-819	279	20	)	)	PUNCT
ejpam-819	280	1	ẋ	ẋ	PROPN
ejpam-819	281	1	−	−	NOUN
ejpam-819	281	2	p(t)t	p(t)t	NOUN
ejpam-819	281	3	d(h	d(h	PROPN
ejpam-819	281	4	p(t	p(t	PROPN
ejpam-819	281	5	)	)	PUNCT
ejpam-819	281	6	)	)	PUNCT
ejpam-819	281	7	ẋ	ẋ	PROPN
ejpam-819	281	8	)	)	PUNCT
ejpam-819	282	1	−	−	PROPN
ejpam-819	283	1	(	(	PUNCT
ejpam-819	283	2	d	d	PROPN
ejpam-819	283	3	2(p(t)t	2(p(t)t	NUM
ejpam-819	283	4	h	h	NOUN
ejpam-819	283	5	p(t	p(t	NOUN
ejpam-819	283	6	)	)	PUNCT
ejpam-819	283	7	)	)	PUNCT
ejpam-819	283	8	ẍ	ẍ	PUNCT
ejpam-819	284	1	−	−	PROPN
ejpam-819	284	2	2p(t)t	2p(t)t	NUM
ejpam-819	284	3	d2(h	d2(h	PROPN
ejpam-819	284	4	p(t	p(t	NOUN
ejpam-819	284	5	)	)	PUNCT
ejpam-819	284	6	)	)	PUNCT
ejpam-819	284	7	ẍ	ẍ	X
ejpam-819	284	8	)	)	PUNCT
ejpam-819	285	1	+	+	CCONJ
ejpam-819	285	2	(	(	PUNCT
ejpam-819	285	3	d	d	PROPN
ejpam-819	285	4	3(p(t)t	3(p(t)t	NUM
ejpam-819	285	5	h	h	NOUN
ejpam-819	285	6	p(t))	p(t))	VERB
ejpam-819	285	7	...	...	PUNCT
ejpam-819	285	8	x	x	X
ejpam-819	285	9	−	−	PROPN
ejpam-819	285	10	2p(t)t	2p(t)t	NUM
ejpam-819	285	11	d3(h	d3(h	NOUN
ejpam-819	285	12	p(t))	p(t))	ADJ
ejpam-819	285	13	...	...	PUNCT
ejpam-819	285	14	x	x	X
ejpam-819	285	15	)	)	PUNCT
ejpam-819	285	16	−	−	PROPN
ejpam-819	285	17	(	(	PUNCT
ejpam-819	285	18	d4(p(t)t	d4(p(t)t	VERB
ejpam-819	285	19	h	h	PROPN
ejpam-819	285	20	p(t))	p(t))	NOUN
ejpam-819	285	21	....	....	PUNCT
ejpam-819	286	1	x	x	X
ejpam-819	287	1	−	−	PROPN
ejpam-819	287	2	2p(t)t	2p(t)t	NUM
ejpam-819	288	1	d4(h	d4(h	PRON
ejpam-819	288	2	p(t))	p(t))	NOUN
ejpam-819	288	3	....	....	PUNCT
ejpam-819	288	4	x	x	X
ejpam-819	288	5	)	)	PUNCT
ejpam-819	289	1	=	=	SYM
ejpam-819	289	2	0	0	NUM
ejpam-819	289	3	,	,	PUNCT
ejpam-819	289	4	t	t	PROPN
ejpam-819	289	5	∈	∈	PROPN
ejpam-819	290	1	i	i	PRON
ejpam-819	290	2	,	,	PUNCT
ejpam-819	290	3	which	which	PRON
ejpam-819	290	4	,	,	PUNCT
ejpam-819	290	5	because	because	SCONJ
ejpam-819	290	6	of	of	ADP
ejpam-819	290	7	the	the	DET
ejpam-819	290	8	hypothesis	hypothesis	NOUN
ejpam-819	290	9	(	(	PUNCT
ejpam-819	290	10	ii	ii	NOUN
ejpam-819	290	11	)	)	PUNCT
ejpam-819	290	12	implies	imply	VERB
ejpam-819	290	13	p̄(t	p̄(t	PROPN
ejpam-819	290	14	)	)	PUNCT
ejpam-819	290	15	=	=	SYM
ejpam-819	290	16	0	0	NUM
ejpam-819	291	1	t	t	X
ejpam-819	291	2	∈	∈	PROPN
ejpam-819	292	1	i	i	PRON
ejpam-819	292	2	.	.	PUNCT
ejpam-819	293	1	from	from	ADP
ejpam-819	293	2	(	(	PUNCT
ejpam-819	293	3	14	14	NUM
ejpam-819	293	4	)	)	PUNCT
ejpam-819	293	5	,	,	PUNCT
ejpam-819	293	6	we	we	PRON
ejpam-819	293	7	have	have	VERB
ejpam-819	293	8	τg	τg	NUM
ejpam-819	293	9	j	j	PROPN
ejpam-819	293	10	+	+	PROPN
ejpam-819	293	11	µ	µ	X
ejpam-819	293	12	j(t	j(t	PROPN
ejpam-819	293	13	)	)	PUNCT
ejpam-819	293	14	=	=	SYM
ejpam-819	294	1	0	0	NUM
ejpam-819	294	2	,	,	PUNCT
ejpam-819	294	3	t	t	PROPN
ejpam-819	294	4	∈	∈	PROPN
ejpam-819	295	1	i	i	PRON
ejpam-819	295	2	,	,	PUNCT
ejpam-819	295	3	j	j	PROPN
ejpam-819	295	4	=	=	SYM
ejpam-819	295	5	1,2	1,2	NUM
ejpam-819	295	6	,	,	PUNCT
ejpam-819	295	7	.	.	PUNCT
ejpam-819	295	8	.	.	PUNCT
ejpam-819	295	9	.	.	PUNCT
ejpam-819	296	1	,	,	PUNCT
ejpam-819	296	2	m	m	VERB
ejpam-819	296	3	(	(	PUNCT
ejpam-819	296	4	23	23	NUM
ejpam-819	296	5	)	)	PUNCT
ejpam-819	296	6	this	this	PRON
ejpam-819	296	7	because	because	SCONJ
ejpam-819	296	8	of	of	ADP
ejpam-819	296	9	τ	τ	PROPN
ejpam-819	296	10	>	>	X
ejpam-819	296	11	0	0	PROPN
ejpam-819	296	12	,	,	PUNCT
ejpam-819	296	13	yields	yield	VERB
ejpam-819	296	14	g	g	PROPN
ejpam-819	296	15	j(t	j(t	PROPN
ejpam-819	296	16	,	,	PUNCT
ejpam-819	296	17	x̄	x̄	NOUN
ejpam-819	296	18	,	,	PUNCT
ejpam-819	296	19	˙̄x)≤	˙̄x)≤	PROPN
ejpam-819	296	20	0	0	NUM
ejpam-819	296	21	,	,	PUNCT
ejpam-819	296	22	t	t	PROPN
ejpam-819	296	23	∈	∈	PROPN
ejpam-819	296	24	i	i	PRON
ejpam-819	296	25	the	the	DET
ejpam-819	296	26	relation	relation	NOUN
ejpam-819	296	27	(	(	PUNCT
ejpam-819	296	28	23	23	NUM
ejpam-819	296	29	)	)	PUNCT
ejpam-819	296	30	along	along	ADP
ejpam-819	296	31	with	with	ADP
ejpam-819	296	32	(	(	PUNCT
ejpam-819	296	33	19	19	NUM
ejpam-819	296	34	)	)	PUNCT
ejpam-819	296	35	and	and	CCONJ
ejpam-819	296	36	τ	τ	X
ejpam-819	296	37	>	>	X
ejpam-819	296	38	0	0	PUNCT
ejpam-819	296	39	gives	give	VERB
ejpam-819	296	40	ȳ(t)t	ȳ(t)t	PROPN
ejpam-819	296	41	g(t	g(t	PROPN
ejpam-819	296	42	,	,	PUNCT
ejpam-819	296	43	x̄	x̄	NOUN
ejpam-819	296	44	,	,	PUNCT
ejpam-819	296	45	˙̄x	˙̄x	PRON
ejpam-819	296	46	)	)	PUNCT
ejpam-819	296	47	=	=	SYM
ejpam-819	296	48	0	0	NUM
ejpam-819	296	49	,	,	PUNCT
ejpam-819	296	50	t	t	PROPN
ejpam-819	296	51	∈	∈	PROPN
ejpam-819	297	1	i	i	PRON
ejpam-819	297	2	(	(	PUNCT
ejpam-819	297	3	24	24	NUM
ejpam-819	297	4	)	)	PUNCT
ejpam-819	297	5	using	use	VERB
ejpam-819	297	6	θ(t	θ(t	NOUN
ejpam-819	297	7	)	)	PUNCT
ejpam-819	297	8	=	=	SYM
ejpam-819	297	9	0	0	NUM
ejpam-819	297	10	,	,	PUNCT
ejpam-819	297	11	t	t	PROPN
ejpam-819	297	12	∈	∈	PROPN
ejpam-819	298	1	i	i	PRON
ejpam-819	298	2	and	and	CCONJ
ejpam-819	298	3	τ	τ	X
ejpam-819	298	4	>	>	X
ejpam-819	298	5	0	0	NUM
ejpam-819	298	6	,	,	PUNCT
ejpam-819	298	7	(	(	PUNCT
ejpam-819	298	8	15	15	NUM
ejpam-819	298	9	)	)	PUNCT
ejpam-819	298	10	yields	yield	NOUN
ejpam-819	298	11	b(t	b(t	PROPN
ejpam-819	298	12	)	)	PUNCT
ejpam-819	298	13	x̄(t)t	x̄(t)t	NOUN
ejpam-819	298	14	=	=	SYM
ejpam-819	298	15	2	2	NUM
ejpam-819	298	16	(	(	PUNCT
ejpam-819	298	17	α(t	α(t	PROPN
ejpam-819	298	18	)	)	PUNCT
ejpam-819	298	19	τ	τ	PROPN
ejpam-819	298	20	)	)	PUNCT
ejpam-819	298	21	b(t)z̄(t	b(t)z̄(t	NOUN
ejpam-819	298	22	)	)	PUNCT
ejpam-819	298	23	,	,	PUNCT
ejpam-819	298	24	t	t	PROPN
ejpam-819	298	25	∈	∈	PROPN
ejpam-819	299	1	i	i	PRON
ejpam-819	299	2	(	(	PUNCT
ejpam-819	299	3	25	25	NUM
ejpam-819	299	4	)	)	PUNCT
ejpam-819	299	5	i.	i.	NOUN
ejpam-819	299	6	husain	husain	PROPN
ejpam-819	299	7	,	,	PUNCT
ejpam-819	299	8	m.	m.	NOUN
ejpam-819	299	9	masoodi	masoodi	PROPN
ejpam-819	299	10	/	/	SYM
ejpam-819	299	11	eur	eur	PROPN
ejpam-819	299	12	.	.	PUNCT
ejpam-819	300	1	j.	j.	PROPN
ejpam-819	300	2	pure	pure	PROPN
ejpam-819	300	3	appl	appl	PROPN
ejpam-819	300	4	.	.	PROPN
ejpam-819	300	5	math	math	PROPN
ejpam-819	300	6	,	,	PUNCT
ejpam-819	300	7	5	5	NUM
ejpam-819	300	8	(	(	PUNCT
ejpam-819	300	9	2012	2012	NUM
ejpam-819	300	10	)	)	PUNCT
ejpam-819	300	11	,	,	PUNCT
ejpam-819	300	12	390	390	NUM
ejpam-819	300	13	-	-	SYM
ejpam-819	300	14	400	400	NUM
ejpam-819	300	15	398	398	NUM
ejpam-819	300	16	which	which	PRON
ejpam-819	300	17	is	be	AUX
ejpam-819	300	18	the	the	DET
ejpam-819	300	19	required	require	VERB
ejpam-819	300	20	condition	condition	NOUN
ejpam-819	300	21	for	for	ADP
ejpam-819	300	22	the	the	DET
ejpam-819	300	23	equality	equality	NOUN
ejpam-819	300	24	in	in	ADP
ejpam-819	300	25	schwartz	schwartz	PROPN
ejpam-819	300	26	inequality	inequality	PROPN
ejpam-819	300	27	,	,	PUNCT
ejpam-819	300	28	i.e.	i.e.	X
ejpam-819	300	29	,	,	PUNCT
ejpam-819	300	30	x̄(t)t	x̄(t)t	PROPN
ejpam-819	300	31	b(t)z̄(t	b(t)z̄(t	NOUN
ejpam-819	300	32	)	)	PUNCT
ejpam-819	300	33	=	=	SYM
ejpam-819	301	1	(	(	PUNCT
ejpam-819	301	2	x̄(t)t	x̄(t)t	PROPN
ejpam-819	301	3	b(t	b(t	PROPN
ejpam-819	301	4	)	)	PUNCT
ejpam-819	301	5	x̄(t))1/2(z̄(t)t	x̄(t))1/2(z̄(t)t	PROPN
ejpam-819	301	6	b(t)z̄(t))1/2	b(t)z̄(t))1/2	NOUN
ejpam-819	301	7	,	,	PUNCT
ejpam-819	301	8	t	t	PROPN
ejpam-819	301	9	∈	∈	PROPN
ejpam-819	302	1	i	i	PRON
ejpam-819	302	2	(	(	PUNCT
ejpam-819	302	3	26	26	NUM
ejpam-819	302	4	)	)	PUNCT
ejpam-819	302	5	if	if	SCONJ
ejpam-819	302	6	α(t	α(t	NOUN
ejpam-819	302	7	)	)	PUNCT
ejpam-819	302	8	>	>	X
ejpam-819	302	9	0	0	NUM
ejpam-819	302	10	,	,	PUNCT
ejpam-819	302	11	t	t	PROPN
ejpam-819	302	12	∈	∈	PROPN
ejpam-819	303	1	i	i	PRON
ejpam-819	303	2	(	(	PUNCT
ejpam-819	303	3	18	18	NUM
ejpam-819	303	4	)	)	PUNCT
ejpam-819	303	5	gives	give	VERB
ejpam-819	303	6	z̄(t)t	z̄(t)t	NOUN
ejpam-819	303	7	b(t)z̄(t	b(t)z̄(t	NOUN
ejpam-819	303	8	)	)	PUNCT
ejpam-819	303	9	=	=	SYM
ejpam-819	303	10	1	1	NUM
ejpam-819	303	11	,	,	PUNCT
ejpam-819	303	12	and	and	CCONJ
ejpam-819	303	13	so	so	ADV
ejpam-819	303	14	(	(	PUNCT
ejpam-819	303	15	25	25	NUM
ejpam-819	303	16	)	)	PUNCT
ejpam-819	303	17	implies	imply	VERB
ejpam-819	303	18	x̄(t)t	x̄(t)t	PROPN
ejpam-819	303	19	b(t)z̄(t	b(t)z̄(t	ADJ
ejpam-819	303	20	)	)	PUNCT
ejpam-819	304	1	=	=	PUNCT
ejpam-819	304	2	(	(	PUNCT
ejpam-819	304	3	x̄(t)t	x̄(t)t	PROPN
ejpam-819	304	4	b(t	b(t	PROPN
ejpam-819	304	5	)	)	PUNCT
ejpam-819	304	6	x̄(t))1/2	x̄(t))1/2	PROPN
ejpam-819	304	7	,	,	PUNCT
ejpam-819	304	8	t	t	PROPN
ejpam-819	304	9	∈	∈	PROPN
ejpam-819	305	1	i	i	PRON
ejpam-819	305	2	if	if	SCONJ
ejpam-819	305	3	α(t	α(t	NOUN
ejpam-819	305	4	)	)	PUNCT
ejpam-819	305	5	=	=	SYM
ejpam-819	305	6	0	0	NUM
ejpam-819	305	7	,	,	PUNCT
ejpam-819	305	8	t	t	PROPN
ejpam-819	305	9	∈	∈	PROPN
ejpam-819	305	10	i	i	PRON
ejpam-819	305	11	,	,	PUNCT
ejpam-819	305	12	(	(	PUNCT
ejpam-819	305	13	25	25	NUM
ejpam-819	305	14	)	)	PUNCT
ejpam-819	305	15	implies	imply	VERB
ejpam-819	305	16	b(t	b(t	PROPN
ejpam-819	305	17	)	)	PUNCT
ejpam-819	305	18	x̄(t	x̄(t	NUM
ejpam-819	305	19	)	)	PUNCT
ejpam-819	305	20	,	,	PUNCT
ejpam-819	305	21	t	t	PROPN
ejpam-819	305	22	∈	∈	PROPN
ejpam-819	306	1	i	i	PRON
ejpam-819	306	2	.	.	PUNCT
ejpam-819	307	1	so	so	ADV
ejpam-819	307	2	we	we	PRON
ejpam-819	307	3	still	still	ADV
ejpam-819	307	4	get	get	VERB
ejpam-819	307	5	x̄(t)t	x̄(t)t	PROPN
ejpam-819	307	6	b(t)z̄(t	b(t)z̄(t	ADJ
ejpam-819	307	7	)	)	PUNCT
ejpam-819	308	1	=	=	PUNCT
ejpam-819	308	2	(	(	PUNCT
ejpam-819	308	3	x̄(t)t	x̄(t)t	PROPN
ejpam-819	308	4	b(t	b(t	PROPN
ejpam-819	308	5	)	)	PUNCT
ejpam-819	308	6	x̄(t))1/2	x̄(t))1/2	PROPN
ejpam-819	308	7	,	,	PUNCT
ejpam-819	308	8	t	t	PROPN
ejpam-819	308	9	∈	∈	PROPN
ejpam-819	309	1	i	i	PRON
ejpam-819	309	2	(	(	PUNCT
ejpam-819	309	3	27	27	NUM
ejpam-819	309	4	)	)	PUNCT
ejpam-819	309	5	therefore	therefore	ADV
ejpam-819	309	6	from	from	ADP
ejpam-819	309	7	(	(	PUNCT
ejpam-819	309	8	24	24	NUM
ejpam-819	309	9	)	)	PUNCT
ejpam-819	309	10	,	,	PUNCT
ejpam-819	309	11	(	(	PUNCT
ejpam-819	309	12	27	27	NUM
ejpam-819	309	13	)	)	PUNCT
ejpam-819	309	14	and	and	CCONJ
ejpam-819	309	15	p̄(t	p̄(t	ADJ
ejpam-819	309	16	)	)	PUNCT
ejpam-819	309	17	=	=	SYM
ejpam-819	309	18	0	0	NUM
ejpam-819	309	19	,	,	PUNCT
ejpam-819	309	20	t	t	PROPN
ejpam-819	309	21	∈	∈	PROPN
ejpam-819	310	1	i	i	PRON
ejpam-819	310	2	,	,	PUNCT
ejpam-819	310	3	we	we	PRON
ejpam-819	310	4	have	have	VERB
ejpam-819	310	5	∫	∫	PROPN
ejpam-819	310	6	t	t	PROPN
ejpam-819	310	7	{	{	PUNCT
ejpam-819	310	8	f	f	PROPN
ejpam-819	310	9	(	(	PUNCT
ejpam-819	310	10	t	t	PROPN
ejpam-819	310	11	,	,	PUNCT
ejpam-819	310	12	x̄	x̄	NOUN
ejpam-819	310	13	,	,	PUNCT
ejpam-819	310	14	˙̄x	˙̄x	PUNCT
ejpam-819	310	15	)	)	PUNCT
ejpam-819	311	1	+	+	CCONJ
ejpam-819	311	2	(	(	PUNCT
ejpam-819	311	3	x̄(t)t	x̄(t)t	PROPN
ejpam-819	311	4	b(t	b(t	PROPN
ejpam-819	311	5	)	)	PUNCT
ejpam-819	311	6	x̄(t))1/2}d	x̄(t))1/2}d	PROPN
ejpam-819	311	7	t	t	PROPN
ejpam-819	311	8	=	=	SYM
ejpam-819	311	9	∫	∫	PROPN
ejpam-819	311	10	t	t	PROPN
ejpam-819	311	11	{	{	PUNCT
ejpam-819	311	12	f	f	PROPN
ejpam-819	311	13	(	(	PUNCT
ejpam-819	311	14	t	t	PROPN
ejpam-819	311	15	,	,	PUNCT
ejpam-819	311	16	x̄	x̄	NOUN
ejpam-819	311	17	,	,	PUNCT
ejpam-819	311	18	˙̄x)+	˙̄x)+	NOUN
ejpam-819	311	19	x̄(t)t	x̄(t)t	PROPN
ejpam-819	311	20	b(t)z̄(t	b(t)z̄(t	PROPN
ejpam-819	311	21	)	)	PUNCT
ejpam-819	312	1	+	+	NUM
ejpam-819	312	2	ȳ(t)t	ȳ(t)t	PROPN
ejpam-819	312	3	g(t	g(t	PROPN
ejpam-819	312	4	,	,	PUNCT
ejpam-819	312	5	x̄	x̄	NOUN
ejpam-819	312	6	,	,	PUNCT
ejpam-819	312	7	˙̄x)−	˙̄x)−	PROPN
ejpam-819	312	8	1	1	NUM
ejpam-819	312	9	2	2	NUM
ejpam-819	312	10	p̄(t)t	p̄(t)t	NOUN
ejpam-819	312	11	h	h	NOUN
ejpam-819	312	12	p̄(t)}d	p̄(t)}d	NOUN
ejpam-819	312	13	t	t	PROPN
ejpam-819	312	14	thus	thus	ADV
ejpam-819	312	15	,	,	PUNCT
ejpam-819	312	16	by	by	ADP
ejpam-819	312	17	the	the	DET
ejpam-819	312	18	application	application	NOUN
ejpam-819	312	19	of	of	ADP
ejpam-819	312	20	theorem	theorem	NOUN
ejpam-819	312	21	1	1	NUM
ejpam-819	312	22	the	the	DET
ejpam-819	312	23	optimality	optimality	NOUN
ejpam-819	312	24	of	of	ADP
ejpam-819	312	25	x̄(t	x̄(t	PROPN
ejpam-819	312	26	)	)	PUNCT
ejpam-819	312	27	for	for	ADP
ejpam-819	312	28	(	(	PUNCT
ejpam-819	312	29	cp	cp	NOUN
ejpam-819	312	30	)	)	PUNCT
ejpam-819	312	31	follows	follow	VERB
ejpam-819	312	32	.	.	PUNCT
ejpam-819	313	1	4	4	X
ejpam-819	313	2	.	.	NOUN
ejpam-819	313	3	natural	natural	ADJ
ejpam-819	313	4	boundary	boundary	ADJ
ejpam-819	313	5	values	value	NOUN
ejpam-819	313	6	in	in	ADP
ejpam-819	313	7	this	this	DET
ejpam-819	313	8	section	section	NOUN
ejpam-819	313	9	,	,	PUNCT
ejpam-819	313	10	we	we	PRON
ejpam-819	313	11	formulate	formulate	VERB
ejpam-819	313	12	a	a	DET
ejpam-819	313	13	pair	pair	NOUN
ejpam-819	313	14	of	of	ADP
ejpam-819	313	15	non	non	ADJ
ejpam-819	313	16	differentiable	differentiable	ADJ
ejpam-819	313	17	dual	dual	ADJ
ejpam-819	313	18	variational	variational	ADJ
ejpam-819	313	19	problems	problem	NOUN
ejpam-819	313	20	with	with	ADP
ejpam-819	313	21	natural	natural	ADJ
ejpam-819	313	22	boundary	boundary	ADJ
ejpam-819	313	23	values	value	NOUN
ejpam-819	313	24	rather	rather	ADV
ejpam-819	313	25	than	than	ADP
ejpam-819	313	26	fixed	fix	VERB
ejpam-819	313	27	end	end	NOUN
ejpam-819	313	28	points	point	NOUN
ejpam-819	313	29	.	.	PUNCT
ejpam-819	314	1	(	(	PUNCT
ejpam-819	314	2	cp0	cp0	X
ejpam-819	314	3	)	)	PUNCT
ejpam-819	314	4	minimize	minimize	VERB
ejpam-819	314	5	∫	∫	PROPN
ejpam-819	314	6	i	i	PRON
ejpam-819	314	7	{	{	PUNCT
ejpam-819	314	8	f	f	PROPN
ejpam-819	314	9	(	(	PUNCT
ejpam-819	314	10	t	t	PROPN
ejpam-819	314	11	,	,	PUNCT
ejpam-819	314	12	x(t	x(t	PROPN
ejpam-819	314	13	)	)	PUNCT
ejpam-819	314	14	,	,	PUNCT
ejpam-819	314	15	ẋ(t	ẋ(t	NOUN
ejpam-819	314	16	)	)	PUNCT
ejpam-819	314	17	)	)	PUNCT
ejpam-819	315	1	+	+	CCONJ
ejpam-819	315	2	(	(	PUNCT
ejpam-819	315	3	x̄(t)t	x̄(t)t	PROPN
ejpam-819	315	4	b(t	b(t	PROPN
ejpam-819	315	5	)	)	PUNCT
ejpam-819	315	6	x̄(t))1/2}d	x̄(t))1/2}d	PROPN
ejpam-819	315	7	t	t	PROPN
ejpam-819	315	8	subject	subject	VERB
ejpam-819	315	9	to	to	ADP
ejpam-819	315	10	g(t	g(t	PROPN
ejpam-819	315	11	,	,	PUNCT
ejpam-819	315	12	x	x	INTJ
ejpam-819	315	13	,	,	PUNCT
ejpam-819	315	14	ẋ)≤	ẋ)≤	PROPN
ejpam-819	315	15	0	0	NUM
ejpam-819	315	16	,	,	PUNCT
ejpam-819	315	17	t	t	PROPN
ejpam-819	315	18	∈	∈	PROPN
ejpam-819	315	19	i	i	PRON
ejpam-819	315	20	(	(	PUNCT
ejpam-819	315	21	cd0	cd0	NOUN
ejpam-819	315	22	)	)	PUNCT
ejpam-819	315	23	maximize	maximize	NOUN
ejpam-819	315	24	∫	∫	PROPN
ejpam-819	316	1	i	i	PRON
ejpam-819	316	2	{	{	PUNCT
ejpam-819	316	3	f	f	PROPN
ejpam-819	316	4	(	(	PUNCT
ejpam-819	316	5	t	t	PROPN
ejpam-819	316	6	,	,	PUNCT
ejpam-819	316	7	x(t	x(t	PROPN
ejpam-819	316	8	)	)	PUNCT
ejpam-819	316	9	,	,	PUNCT
ejpam-819	316	10	ẋ(t	ẋ(t	NOUN
ejpam-819	316	11	)	)	PUNCT
ejpam-819	316	12	)	)	PUNCT
ejpam-819	317	1	+	+	CCONJ
ejpam-819	317	2	x(t)t	x(t)t	PROPN
ejpam-819	317	3	b(t)z(t	b(t)z(t	NOUN
ejpam-819	317	4	)	)	PUNCT
ejpam-819	317	5	+	+	NUM
ejpam-819	317	6	y(t)t	y(t)t	PROPN
ejpam-819	317	7	g(t	g(t	PROPN
ejpam-819	317	8	,	,	PUNCT
ejpam-819	317	9	x	x	SYM
ejpam-819	317	10	,	,	PUNCT
ejpam-819	317	11	ẋ)−	ẋ)−	PROPN
ejpam-819	317	12	1	1	NUM
ejpam-819	317	13	2	2	NUM
ejpam-819	317	14	p(t)t	p(t)t	NOUN
ejpam-819	317	15	h	h	NOUN
ejpam-819	317	16	p(t)}d	p(t)}d	PROPN
ejpam-819	317	17	t	t	PROPN
ejpam-819	317	18	subject	subject	NOUN
ejpam-819	317	19	to	to	ADP
ejpam-819	317	20	(	(	PUNCT
ejpam-819	317	21	fx	fx	PROPN
ejpam-819	317	22	(	(	PUNCT
ejpam-819	317	23	t	t	PROPN
ejpam-819	317	24	,	,	PUNCT
ejpam-819	317	25	x	x	X
ejpam-819	317	26	,	,	PUNCT
ejpam-819	317	27	ẋ	ẋ	PROPN
ejpam-819	317	28	)	)	PUNCT
ejpam-819	318	1	+	+	CCONJ
ejpam-819	318	2	b(t)z̄(t	b(t)z̄(t	NOUN
ejpam-819	318	3	)	)	PUNCT
ejpam-819	319	1	+	+	NUM
ejpam-819	319	2	ȳ(t)t	ȳ(t)t	NOUN
ejpam-819	319	3	gx(t	gx(t	NOUN
ejpam-819	319	4	,	,	PUNCT
ejpam-819	319	5	x	x	X
ejpam-819	319	6	,	,	PUNCT
ejpam-819	319	7	ẋ	ẋ	PROPN
ejpam-819	319	8	)	)	PUNCT
ejpam-819	319	9	)	)	PUNCT
ejpam-819	320	1	−d	−d	PROPN
ejpam-819	320	2	(	(	PUNCT
ejpam-819	320	3	f	f	PROPN
ejpam-819	320	4	ẋ	ẋ	PROPN
ejpam-819	320	5	(	(	PUNCT
ejpam-819	320	6	t	t	PROPN
ejpam-819	320	7	,	,	PUNCT
ejpam-819	320	8	x	x	X
ejpam-819	320	9	,	,	PUNCT
ejpam-819	320	10	ẋ	ẋ	PROPN
ejpam-819	320	11	)	)	PUNCT
ejpam-819	321	1	+	+	CCONJ
ejpam-819	321	2	ȳ(t)t	ȳ(t)t	NOUN
ejpam-819	321	3	g	g	PROPN
ejpam-819	321	4	ẋ(t	ẋ(t	PROPN
ejpam-819	321	5	,	,	PUNCT
ejpam-819	321	6	x	x	INTJ
ejpam-819	321	7	,	,	PUNCT
ejpam-819	321	8	ẋ	ẋ	PROPN
ejpam-819	321	9	)	)	PUNCT
ejpam-819	321	10	)	)	PUNCT
ejpam-819	322	1	+	+	ADP
ejpam-819	322	2	h	h	NOUN
ejpam-819	322	3	p(t	p(t	NOUN
ejpam-819	322	4	)	)	PUNCT
ejpam-819	322	5	=	=	SYM
ejpam-819	322	6	0	0	NUM
ejpam-819	322	7	,	,	PUNCT
ejpam-819	322	8	t	t	PROPN
ejpam-819	322	9	∈	∈	PROPN
ejpam-819	323	1	i	i	PROPN
ejpam-819	323	2	z(t)t	z(t)t	NOUN
ejpam-819	323	3	b(t)z(t	b(t)z(t	PROPN
ejpam-819	323	4	)	)	PUNCT
ejpam-819	323	5	≤	≤	NUM
ejpam-819	323	6	1	1	NUM
ejpam-819	323	7	,	,	PUNCT
ejpam-819	323	8	t	t	PROPN
ejpam-819	323	9	∈	∈	PROPN
ejpam-819	324	1	i	i	PRON
ejpam-819	324	2	y(t	y(t	PROPN
ejpam-819	324	3	)	)	PUNCT
ejpam-819	324	4	≥	≥	NOUN
ejpam-819	324	5	0	0	NUM
ejpam-819	324	6	,	,	PUNCT
ejpam-819	324	7	t	t	PROPN
ejpam-819	324	8	∈	∈	PROPN
ejpam-819	325	1	i	i	PRON
ejpam-819	325	2	f	f	PROPN
ejpam-819	325	3	ẋ	ẋ	PROPN
ejpam-819	325	4	(	(	PUNCT
ejpam-819	325	5	t	t	PROPN
ejpam-819	325	6	,	,	PUNCT
ejpam-819	325	7	x	x	X
ejpam-819	325	8	,	,	PUNCT
ejpam-819	325	9	ẋ	ẋ	PROPN
ejpam-819	325	10	)	)	PUNCT
ejpam-819	326	1	+	+	CCONJ
ejpam-819	326	2	ȳ(t)t	ȳ(t)t	NOUN
ejpam-819	326	3	g	g	PROPN
ejpam-819	326	4	ẋ(t	ẋ(t	PROPN
ejpam-819	326	5	,	,	PUNCT
ejpam-819	326	6	x	x	PRON
ejpam-819	326	7	,	,	PUNCT
ejpam-819	326	8	ẋ)|t	ẋ)|t	PROPN
ejpam-819	326	9	=	=	PROPN
ejpam-819	326	10	a	a	X
ejpam-819	326	11	=	=	SYM
ejpam-819	326	12	0	0	PUNCT
ejpam-819	326	13	f	f	PROPN
ejpam-819	326	14	ẋ	ẋ	PROPN
ejpam-819	326	15	(	(	PUNCT
ejpam-819	326	16	t	t	PROPN
ejpam-819	326	17	,	,	PUNCT
ejpam-819	326	18	x	x	X
ejpam-819	326	19	,	,	PUNCT
ejpam-819	326	20	ẋ	ẋ	PROPN
ejpam-819	326	21	)	)	PUNCT
ejpam-819	327	1	+	+	CCONJ
ejpam-819	327	2	ȳ(t)t	ȳ(t)t	NOUN
ejpam-819	327	3	g	g	PROPN
ejpam-819	327	4	ẋ(t	ẋ(t	PROPN
ejpam-819	327	5	,	,	PUNCT
ejpam-819	327	6	x	x	X
ejpam-819	327	7	,	,	PUNCT
ejpam-819	327	8	ẋ)|t	ẋ)|t	PROPN
ejpam-819	327	9	=	=	SYM
ejpam-819	327	10	b	b	X
ejpam-819	327	11	=	=	SYM
ejpam-819	327	12	0	0	NUM
ejpam-819	327	13	we	we	PRON
ejpam-819	327	14	shall	shall	AUX
ejpam-819	327	15	not	not	PART
ejpam-819	327	16	repeat	repeat	VERB
ejpam-819	327	17	the	the	DET
ejpam-819	327	18	proofs	proof	NOUN
ejpam-819	327	19	of	of	ADP
ejpam-819	327	20	theorems	theorem	NOUN
ejpam-819	327	21	1	1	NUM
ejpam-819	327	22	-	-	SYM
ejpam-819	327	23	3	3	NUM
ejpam-819	327	24	,	,	PUNCT
ejpam-819	327	25	as	as	SCONJ
ejpam-819	327	26	these	these	PRON
ejpam-819	327	27	follow	follow	VERB
ejpam-819	327	28	on	on	ADP
ejpam-819	327	29	the	the	DET
ejpam-819	327	30	lines	line	NOUN
ejpam-819	327	31	of	of	ADP
ejpam-819	327	32	the	the	DET
ejpam-819	327	33	analysis	analysis	NOUN
ejpam-819	327	34	of	of	ADP
ejpam-819	327	35	the	the	DET
ejpam-819	327	36	preceding	precede	VERB
ejpam-819	327	37	section	section	NOUN
ejpam-819	327	38	with	with	ADP
ejpam-819	327	39	slight	slight	ADJ
ejpam-819	327	40	modifications	modification	NOUN
ejpam-819	327	41	.	.	PUNCT
ejpam-819	328	1	references	reference	NOUN
ejpam-819	328	2	399	399	NUM
ejpam-819	328	3	5	5	NUM
ejpam-819	328	4	.	.	PUNCT
ejpam-819	329	1	non	non	ADJ
ejpam-819	329	2	-	-	ADJ
ejpam-819	329	3	differentiable	differentiable	ADJ
ejpam-819	329	4	nonlinear	nonlinear	ADJ
ejpam-819	329	5	programming	programming	NOUN
ejpam-819	329	6	problems	problem	NOUN
ejpam-819	329	7	if	if	SCONJ
ejpam-819	329	8	all	all	DET
ejpam-819	329	9	functions	function	NOUN
ejpam-819	329	10	in	in	ADP
ejpam-819	329	11	the	the	DET
ejpam-819	329	12	problems	problem	NOUN
ejpam-819	329	13	(	(	PUNCT
ejpam-819	329	14	cp0	cp0	X
ejpam-819	329	15	)	)	PUNCT
ejpam-819	329	16	and	and	CCONJ
ejpam-819	329	17	(	(	PUNCT
ejpam-819	329	18	cd0	cd0	NOUN
ejpam-819	329	19	)	)	PUNCT
ejpam-819	329	20	are	be	AUX
ejpam-819	329	21	independent	independent	ADJ
ejpam-819	329	22	of	of	ADP
ejpam-819	329	23	t	t	PROPN
ejpam-819	329	24	and	and	CCONJ
ejpam-819	329	25	b−	b−	PROPN
ejpam-819	329	26	a	a	DET
ejpam-819	329	27	=	=	SYM
ejpam-819	329	28	1	1	NUM
ejpam-819	329	29	,	,	PUNCT
ejpam-819	329	30	then	then	ADV
ejpam-819	329	31	these	these	DET
ejpam-819	329	32	problems	problem	NOUN
ejpam-819	329	33	will	will	AUX
ejpam-819	329	34	reduce	reduce	VERB
ejpam-819	329	35	to	to	ADP
ejpam-819	329	36	following	follow	VERB
ejpam-819	329	37	nondifferentiable	nondifferentiable	ADJ
ejpam-819	329	38	dual	dual	ADJ
ejpam-819	329	39	variational	variational	ADJ
ejpam-819	329	40	problems	problem	NOUN
ejpam-819	329	41	,	,	PUNCT
ejpam-819	329	42	treated	treat	VERB
ejpam-819	329	43	by	by	ADP
ejpam-819	329	44	zhang	zhang	PROPN
ejpam-819	329	45	and	and	CCONJ
ejpam-819	329	46	mond	mond	VERB
ejpam-819	329	47	[	[	X
ejpam-819	329	48	10	10	NUM
ejpam-819	329	49	]	]	PUNCT
ejpam-819	329	50	.	.	PUNCT
ejpam-819	330	1	(	(	PUNCT
ejpam-819	330	2	np	np	X
ejpam-819	330	3	)	)	PUNCT
ejpam-819	330	4	minimize	minimize	VERB
ejpam-819	330	5	f	f	PROPN
ejpam-819	330	6	(	(	PUNCT
ejpam-819	330	7	x)+	x)+	NUM
ejpam-819	331	1	(	(	PUNCT
ejpam-819	331	2	x	x	SYM
ejpam-819	331	3	t	t	PROPN
ejpam-819	331	4	bx)1/2	bx)1/2	PROPN
ejpam-819	331	5	subject	subject	NOUN
ejpam-819	331	6	to	to	ADP
ejpam-819	331	7	g(x)≤	g(x)≤	PROPN
ejpam-819	331	8	0	0	PROPN
ejpam-819	331	9	,	,	PUNCT
ejpam-819	331	10	(	(	PUNCT
ejpam-819	331	11	nd	nd	NOUN
ejpam-819	331	12	)	)	PUNCT
ejpam-819	331	13	maximize	maximize	VERB
ejpam-819	331	14	f	f	PROPN
ejpam-819	331	15	(	(	PUNCT
ejpam-819	331	16	x)+	x)+	NUM
ejpam-819	331	17	x	x	SYM
ejpam-819	331	18	t	t	PROPN
ejpam-819	331	19	bz	bz	PROPN
ejpam-819	332	1	+	+	CCONJ
ejpam-819	332	2	yt	yt	PROPN
ejpam-819	332	3	g(x)−	g(x)−	PROPN
ejpam-819	332	4	1	1	NUM
ejpam-819	332	5	2	2	NUM
ejpam-819	332	6	pt∇2	pt∇2	NOUN
ejpam-819	332	7	(	(	PUNCT
ejpam-819	332	8	f	f	PROPN
ejpam-819	332	9	(	(	PUNCT
ejpam-819	332	10	x)+	x)+	NUM
ejpam-819	332	11	yt	yt	VERB
ejpam-819	332	12	g(x))p	g(x))p	PROPN
ejpam-819	332	13	subject	subject	ADJ
ejpam-819	332	14	to	to	ADP
ejpam-819	332	15	∇	∇	PROPN
ejpam-819	332	16	(	(	PUNCT
ejpam-819	332	17	f	f	X
ejpam-819	332	18	(	(	PUNCT
ejpam-819	332	19	x)+	x)+	NUM
ejpam-819	332	20	x	x	SYM
ejpam-819	332	21	t	t	PROPN
ejpam-819	332	22	bz	bz	X
ejpam-819	333	1	+	+	CCONJ
ejpam-819	333	2	yt	yt	PRON
ejpam-819	333	3	g(x))+∇2	g(x))+∇2	PROPN
ejpam-819	333	4	(	(	PUNCT
ejpam-819	333	5	f	f	PROPN
ejpam-819	333	6	(	(	PUNCT
ejpam-819	333	7	x)+	x)+	NUM
ejpam-819	333	8	yt	yt	VERB
ejpam-819	333	9	g(x))p	g(x))p	NOUN
ejpam-819	333	10	=	=	SYM
ejpam-819	333	11	0	0	PROPN
ejpam-819	333	12	,	,	PUNCT
ejpam-819	333	13	zt	zt	PROPN
ejpam-819	333	14	bz	bz	PROPN
ejpam-819	333	15	≤	≤	ADV
ejpam-819	333	16	1	1	NUM
ejpam-819	333	17	,	,	PUNCT
ejpam-819	333	18	y	y	PROPN
ejpam-819	333	19	≥	≥	NOUN
ejpam-819	333	20	0	0	NUM
ejpam-819	334	1	where	where	SCONJ
ejpam-819	334	2	∇	∇	X
ejpam-819	334	3	(	(	PUNCT
ejpam-819	334	4	f	f	PROPN
ejpam-819	334	5	(	(	PUNCT
ejpam-819	334	6	x)+	x)+	NUM
ejpam-819	334	7	x	x	SYM
ejpam-819	334	8	t	t	PROPN
ejpam-819	334	9	bz	bz	X
ejpam-819	334	10	+	+	CCONJ
ejpam-819	334	11	yt	yt	X
ejpam-819	334	12	g(x	g(x	NOUN
ejpam-819	334	13	)	)	PUNCT
ejpam-819	334	14	)	)	PUNCT
ejpam-819	334	15	=	=	PUNCT
ejpam-819	334	16	fx(x)+	fx(x)+	PUNCT
ejpam-819	334	17	bz	bz	X
ejpam-819	334	18	+	+	CCONJ
ejpam-819	334	19	yt	yt	PROPN
ejpam-819	334	20	gx(x	gx(x	NOUN
ejpam-819	334	21	)	)	PUNCT
ejpam-819	334	22	and	and	CCONJ
ejpam-819	334	23	∇2	∇2	PROPN
ejpam-819	334	24	(	(	PUNCT
ejpam-819	334	25	f	f	X
ejpam-819	334	26	(	(	PUNCT
ejpam-819	334	27	x)+	x)+	PROPN
ejpam-819	334	28	yt	yt	PROPN
ejpam-819	334	29	g(x	g(x	NOUN
ejpam-819	334	30	)	)	PUNCT
ejpam-819	334	31	)	)	PUNCT
ejpam-819	335	1	=	=	SYM
ejpam-819	335	2	fx	fx	NOUN
ejpam-819	335	3	x	x	SYM
ejpam-819	335	4	(	(	PUNCT
ejpam-819	335	5	x)+	x)+	NUM
ejpam-819	335	6	(	(	PUNCT
ejpam-819	335	7	y	y	PROPN
ejpam-819	335	8	t	t	PROPN
ejpam-819	335	9	gx(x	gx(x	NOUN
ejpam-819	335	10	)	)	PUNCT
ejpam-819	335	11	)	)	PUNCT
ejpam-819	335	12	ẋ	ẋ	PROPN
ejpam-819	336	1	6	6	X
ejpam-819	336	2	.	.	X
ejpam-819	336	3	conclusion	conclusion	NOUN
ejpam-819	336	4	in	in	ADP
ejpam-819	336	5	this	this	DET
ejpam-819	336	6	exposition	exposition	NOUN
ejpam-819	336	7	,	,	PUNCT
ejpam-819	336	8	we	we	PRON
ejpam-819	336	9	have	have	AUX
ejpam-819	336	10	discussed	discuss	VERB
ejpam-819	336	11	a	a	DET
ejpam-819	336	12	class	class	NOUN
ejpam-819	336	13	of	of	ADP
ejpam-819	336	14	nondifferentiable	nondifferentiable	ADJ
ejpam-819	336	15	continuous	continuous	ADJ
ejpam-819	336	16	programming	programming	NOUN
ejpam-819	336	17	problems	problem	NOUN
ejpam-819	336	18	treated	treat	VERB
ejpam-819	336	19	in	in	ADP
ejpam-819	336	20	[	[	X
ejpam-819	336	21	2	2	NUM
ejpam-819	336	22	]	]	PUNCT
ejpam-819	336	23	and	and	CCONJ
ejpam-819	336	24	formulated	formulate	VERB
ejpam-819	336	25	wolfe	wolfe	PROPN
ejpam-819	336	26	type	type	NOUN
ejpam-819	336	27	second	second	ADJ
ejpam-819	336	28	-	-	PUNCT
ejpam-819	336	29	order	order	NOUN
ejpam-819	336	30	dual	dual	ADJ
ejpam-819	336	31	variation	variation	NOUN
ejpam-819	336	32	problem	problem	NOUN
ejpam-819	336	33	which	which	PRON
ejpam-819	336	34	is	be	AUX
ejpam-819	336	35	analogous	analogous	ADJ
ejpam-819	336	36	to	to	ADP
ejpam-819	336	37	the	the	DET
ejpam-819	336	38	second	second	ADJ
ejpam-819	336	39	-	-	PUNCT
ejpam-819	336	40	order	order	NOUN
ejpam-819	336	41	dual	dual	ADJ
ejpam-819	336	42	problem	problem	NOUN
ejpam-819	336	43	constructed	construct	VERB
ejpam-819	336	44	by	by	ADP
ejpam-819	336	45	zhang	zhang	PROPN
ejpam-819	336	46	and	and	CCONJ
ejpam-819	336	47	mond	mond	PROPN
ejpam-819	337	1	[	[	X
ejpam-819	337	2	10	10	NUM
ejpam-819	337	3	]	]	PUNCT
ejpam-819	337	4	for	for	ADP
ejpam-819	337	5	a	a	DET
ejpam-819	337	6	nondifferentiable	nondifferentiable	ADJ
ejpam-819	337	7	nonlinear	nonlinear	ADJ
ejpam-819	337	8	programming	programming	NOUN
ejpam-819	337	9	problem	problem	NOUN
ejpam-819	337	10	.	.	PUNCT
ejpam-819	338	1	under	under	ADP
ejpam-819	338	2	second	second	ADJ
ejpam-819	338	3	-	-	PUNCT
ejpam-819	338	4	order	order	NOUN
ejpam-819	338	5	pseudoinvexity	pseudoinvexity	NOUN
ejpam-819	338	6	we	we	PRON
ejpam-819	338	7	established	establish	VERB
ejpam-819	338	8	weak	weak	ADJ
ejpam-819	338	9	,	,	PUNCT
ejpam-819	338	10	strong	strong	ADJ
ejpam-819	338	11	and	and	CCONJ
ejpam-819	338	12	converse	converse	NOUN
ejpam-819	338	13	duality	duality	NOUN
ejpam-819	338	14	theorems	theorem	NOUN
ejpam-819	338	15	.	.	PUNCT
ejpam-819	339	1	when	when	SCONJ
ejpam-819	339	2	functions	function	NOUN
ejpam-819	339	3	,	,	PUNCT
ejpam-819	339	4	occurring	occur	VERB
ejpam-819	339	5	in	in	ADP
ejpam-819	339	6	the	the	DET
ejpam-819	339	7	formulations	formulation	NOUN
ejpam-819	339	8	of	of	ADP
ejpam-819	339	9	the	the	DET
ejpam-819	339	10	problems	problem	NOUN
ejpam-819	339	11	,	,	PUNCT
ejpam-819	339	12	do	do	AUX
ejpam-819	339	13	not	not	PART
ejpam-819	339	14	depend	depend	VERB
ejpam-819	339	15	explicitly	explicitly	ADV
ejpam-819	339	16	on	on	ADP
ejpam-819	339	17	t	t	PROPN
ejpam-819	339	18	,	,	PUNCT
ejpam-819	339	19	our	our	PRON
ejpam-819	339	20	results	result	NOUN
ejpam-819	339	21	reduce	reduce	VERB
ejpam-819	339	22	to	to	ADP
ejpam-819	339	23	those	those	PRON
ejpam-819	339	24	of	of	ADP
ejpam-819	339	25	[	[	X
ejpam-819	339	26	10	10	NUM
ejpam-819	339	27	]	]	PUNCT
ejpam-819	339	28	.	.	PUNCT
ejpam-819	340	1	thus	thus	ADV
ejpam-819	340	2	our	our	PRON
ejpam-819	340	3	results	result	NOUN
ejpam-819	340	4	become	become	VERB
ejpam-819	340	5	dynamic	dynamic	ADJ
ejpam-819	340	6	generalizations	generalization	NOUN
ejpam-819	340	7	of	of	ADP
ejpam-819	340	8	the	the	DET
ejpam-819	340	9	results	result	NOUN
ejpam-819	340	10	in	in	ADP
ejpam-819	340	11	[	[	X
ejpam-819	340	12	10	10	NUM
ejpam-819	340	13	]	]	PUNCT
ejpam-819	340	14	.	.	PUNCT
ejpam-819	341	1	the	the	DET
ejpam-819	341	2	problems	problem	NOUN
ejpam-819	341	3	of	of	ADP
ejpam-819	341	4	this	this	DET
ejpam-819	341	5	research	research	NOUN
ejpam-819	341	6	can	can	AUX
ejpam-819	341	7	be	be	AUX
ejpam-819	341	8	revisited	revisit	VERB
ejpam-819	341	9	in	in	ADP
ejpam-819	341	10	multiobjective	multiobjective	ADJ
ejpam-819	341	11	setting	setting	NOUN
ejpam-819	341	12	.	.	PUNCT
ejpam-819	342	1	references	reference	NOUN
ejpam-819	342	2	[	[	X
ejpam-819	342	3	1	1	NUM
ejpam-819	342	4	]	]	X
ejpam-819	342	5	c.r	c.r	PROPN
ejpam-819	342	6	.	.	PROPN
ejpam-819	342	7	bector	bector	PROPN
ejpam-819	342	8	,	,	PUNCT
ejpam-819	342	9	s.	s.	PROPN
ejpam-819	342	10	chandra	chandra	PROPN
ejpam-819	342	11	,	,	PUNCT
ejpam-819	342	12	and	and	CCONJ
ejpam-819	342	13	i.	i.	PROPN
ejpam-819	342	14	husain	husain	PROPN
ejpam-819	342	15	.	.	PUNCT
ejpam-819	343	1	generalized	generalized	ADJ
ejpam-819	343	2	concavity	concavity	NOUN
ejpam-819	343	3	and	and	CCONJ
ejpam-819	343	4	duality	duality	NOUN
ejpam-819	343	5	in	in	ADP
ejpam-819	343	6	continuous	continuous	ADJ
ejpam-819	343	7	programming	programming	NOUN
ejpam-819	343	8	.	.	PUNCT
ejpam-819	344	1	utilitas	utilitas	PROPN
ejpam-819	344	2	,	,	PUNCT
ejpam-819	344	3	mathematica	mathematica	PROPN
ejpam-819	344	4	,	,	PUNCT
ejpam-819	344	5	25:171–190	25:171–190	NUM
ejpam-819	344	6	,	,	PUNCT
ejpam-819	344	7	1984	1984	NUM
ejpam-819	344	8	.	.	PUNCT
ejpam-819	345	1	[	[	X
ejpam-819	345	2	2	2	X
ejpam-819	345	3	]	]	PUNCT
ejpam-819	345	4	s.	s.	PROPN
ejpam-819	345	5	chandra	chandra	PROPN
ejpam-819	345	6	,	,	PUNCT
ejpam-819	345	7	b.d	b.d	PROPN
ejpam-819	345	8	.	.	PROPN
ejpam-819	345	9	craven	craven	NOUN
ejpam-819	345	10	,	,	PUNCT
ejpam-819	345	11	and	and	CCONJ
ejpam-819	345	12	i.	i.	PROPN
ejpam-819	345	13	husain	husain	PROPN
ejpam-819	345	14	.	.	PUNCT
ejpam-819	346	1	a	a	DET
ejpam-819	346	2	class	class	NOUN
ejpam-819	346	3	of	of	ADP
ejpam-819	346	4	nondifferentiable	nondifferentiable	ADJ
ejpam-819	346	5	continuous	continuous	ADJ
ejpam-819	346	6	programming	programming	NOUN
ejpam-819	346	7	problems	problem	NOUN
ejpam-819	346	8	.	.	PUNCT
ejpam-819	347	1	j.	j.	PROPN
ejpam-819	347	2	math	math	PROPN
ejpam-819	347	3	.	.	PUNCT
ejpam-819	348	1	anal	anal	PROPN
ejpam-819	348	2	.	.	PUNCT
ejpam-819	348	3	appl	appl	PROPN
ejpam-819	348	4	.	.	PROPN
ejpam-819	348	5	,	,	PUNCT
ejpam-819	348	6	107:122–131	107:122–131	NUM
ejpam-819	348	7	,	,	PUNCT
ejpam-819	348	8	1985	1985	NUM
ejpam-819	348	9	.	.	PUNCT
ejpam-819	349	1	[	[	X
ejpam-819	349	2	3	3	X
ejpam-819	349	3	]	]	PUNCT
ejpam-819	349	4	x.	x.	PROPN
ejpam-819	349	5	chen	chen	PROPN
ejpam-819	349	6	.	.	PUNCT
ejpam-819	350	1	second	second	ADJ
ejpam-819	350	2	order	order	NOUN
ejpam-819	350	3	duality	duality	NOUN
ejpam-819	350	4	for	for	ADP
ejpam-819	350	5	the	the	DET
ejpam-819	350	6	variational	variational	ADJ
ejpam-819	350	7	problems	problem	NOUN
ejpam-819	350	8	.	.	PUNCT
ejpam-819	351	1	j.	j.	PROPN
ejpam-819	351	2	math	math	PROPN
ejpam-819	351	3	.	.	PUNCT
ejpam-819	352	1	anal	anal	PROPN
ejpam-819	352	2	.	.	PUNCT
ejpam-819	353	1	appl	appl	PROPN
ejpam-819	353	2	.	.	PROPN
ejpam-819	353	3	,	,	PUNCT
ejpam-819	353	4	286:261–270	286:261–270	NUM
ejpam-819	353	5	,	,	PUNCT
ejpam-819	353	6	2003	2003	NUM
ejpam-819	353	7	.	.	PUNCT
ejpam-819	354	1	[	[	X
ejpam-819	354	2	4	4	NUM
ejpam-819	354	3	]	]	PUNCT
ejpam-819	354	4	i.	i.	PROPN
ejpam-819	354	5	husain	husain	PROPN
ejpam-819	354	6	,	,	PUNCT
ejpam-819	354	7	a.	a.	PROPN
ejpam-819	354	8	ahmed	ahmed	PROPN
ejpam-819	354	9	,	,	PUNCT
ejpam-819	354	10	and	and	CCONJ
ejpam-819	354	11	m.	m.	NOUN
ejpam-819	354	12	masoodi	masoodi	PROPN
ejpam-819	354	13	.	.	PUNCT
ejpam-819	355	1	second	second	ADJ
ejpam-819	355	2	order	order	NOUN
ejpam-819	355	3	duality	duality	NOUN
ejpam-819	355	4	for	for	ADP
ejpam-819	355	5	variational	variational	ADJ
ejpam-819	355	6	problems	problem	NOUN
ejpam-819	355	7	.	.	PUNCT
ejpam-819	356	1	european	european	ADJ
ejpam-819	356	2	journal	journal	PROPN
ejpam-819	356	3	of	of	ADP
ejpam-819	356	4	pure	pure	ADJ
ejpam-819	356	5	and	and	CCONJ
ejpam-819	356	6	applied	applied	ADJ
ejpam-819	356	7	mathematics	mathematic	NOUN
ejpam-819	356	8	,	,	PUNCT
ejpam-819	356	9	2(2):278	2(2):278	NUM
ejpam-819	356	10	–	–	PUNCT
ejpam-819	356	11	295	295	NUM
ejpam-819	356	12	,	,	PUNCT
ejpam-819	356	13	2009	2009	NUM
ejpam-819	356	14	.	.	PUNCT
ejpam-819	357	1	references	reference	NOUN
ejpam-819	357	2	400	400	NUM
ejpam-819	357	3	[	[	X
ejpam-819	357	4	5	5	NUM
ejpam-819	357	5	]	]	X
ejpam-819	357	6	o.l	o.l	PROPN
ejpam-819	357	7	.	.	PROPN
ejpam-819	357	8	mangasarian	mangasarian	PROPN
ejpam-819	357	9	.	.	PUNCT
ejpam-819	358	1	second	second	ADJ
ejpam-819	358	2	and	and	CCONJ
ejpam-819	358	3	higher	high	ADJ
ejpam-819	358	4	order	order	NOUN
ejpam-819	358	5	duality	duality	NOUN
ejpam-819	358	6	in	in	ADP
ejpam-819	358	7	non	non	ADJ
ejpam-819	358	8	linear	linear	PROPN
ejpam-819	358	9	programming	programming	NOUN
ejpam-819	358	10	.	.	PUNCT
ejpam-819	359	1	j.	j.	PROPN
ejpam-819	359	2	math	math	PROPN
ejpam-819	359	3	.	.	PUNCT
ejpam-819	360	1	anal	anal	PROPN
ejpam-819	360	2	.	.	PUNCT
ejpam-819	361	1	appl	appl	PROPN
ejpam-819	361	2	.	.	PROPN
ejpam-819	361	3	,	,	PUNCT
ejpam-819	362	1	51:605–620	51:605–620	PROPN
ejpam-819	362	2	,	,	PUNCT
ejpam-819	362	3	1979	1979	NUM
ejpam-819	362	4	.	.	PUNCT
ejpam-819	363	1	[	[	X
ejpam-819	363	2	6	6	NUM
ejpam-819	363	3	]	]	PUNCT
ejpam-819	363	4	b.	b.	PROPN
ejpam-819	363	5	mond	mond	PROPN
ejpam-819	363	6	.	.	PUNCT
ejpam-819	364	1	second	second	ADJ
ejpam-819	364	2	order	order	NOUN
ejpam-819	364	3	duality	duality	NOUN
ejpam-819	364	4	in	in	ADP
ejpam-819	364	5	non	non	ADJ
ejpam-819	364	6	-	-	ADJ
ejpam-819	364	7	linear	linear	ADJ
ejpam-819	364	8	programming	programming	NOUN
ejpam-819	364	9	.	.	PUNCT
ejpam-819	365	1	opsearch	opsearch	PROPN
ejpam-819	365	2	,	,	PUNCT
ejpam-819	365	3	11:90–99	11:90–99	NUM
ejpam-819	365	4	,	,	PUNCT
ejpam-819	365	5	1974	1974	NUM
ejpam-819	365	6	.	.	PUNCT
ejpam-819	366	1	[	[	X
ejpam-819	366	2	7	7	X
ejpam-819	366	3	]	]	X
ejpam-819	366	4	b.	b.	PROPN
ejpam-819	366	5	mond	mond	PROPN
ejpam-819	366	6	and	and	CCONJ
ejpam-819	366	7	m.a	m.a	PROPN
ejpam-819	366	8	.	.	PROPN
ejpam-819	366	9	hanson	hanson	PROPN
ejpam-819	366	10	.	.	PUNCT
ejpam-819	367	1	duality	duality	NOUN
ejpam-819	367	2	for	for	ADP
ejpam-819	367	3	variational	variational	ADJ
ejpam-819	367	4	problems	problem	NOUN
ejpam-819	367	5	.	.	PUNCT
ejpam-819	368	1	j.	j.	PROPN
ejpam-819	368	2	math	math	PROPN
ejpam-819	368	3	.	.	PUNCT
ejpam-819	369	1	anal	anal	PROPN
ejpam-819	369	2	.	.	PUNCT
ejpam-819	370	1	appl	appl	PROPN
ejpam-819	370	2	.	.	PROPN
ejpam-819	370	3	,	,	PUNCT
ejpam-819	370	4	18:355–364	18:355–364	NUM
ejpam-819	370	5	,	,	PUNCT
ejpam-819	370	6	1965	1965	NUM
ejpam-819	370	7	.	.	PUNCT
ejpam-819	371	1	[	[	X
ejpam-819	371	2	8	8	NUM
ejpam-819	371	3	]	]	X
ejpam-819	371	4	b.	b.	PROPN
ejpam-819	371	5	mond	mond	PROPN
ejpam-819	371	6	and	and	CCONJ
ejpam-819	371	7	i.	i.	PROPN
ejpam-819	371	8	husain	husain	PROPN
ejpam-819	371	9	.	.	PUNCT
ejpam-819	372	1	sufficient	sufficient	ADJ
ejpam-819	372	2	optimality	optimality	NOUN
ejpam-819	372	3	criteria	criterion	NOUN
ejpam-819	372	4	and	and	CCONJ
ejpam-819	372	5	duality	duality	NOUN
ejpam-819	372	6	for	for	ADP
ejpam-819	372	7	variational	variational	ADJ
ejpam-819	372	8	problem	problem	NOUN
ejpam-819	372	9	with	with	ADP
ejpam-819	372	10	generalized	generalized	ADJ
ejpam-819	372	11	invexity	invexity	NOUN
ejpam-819	372	12	.	.	PUNCT
ejpam-819	373	1	journal	journal	NOUN
ejpam-819	373	2	of	of	ADP
ejpam-819	373	3	the	the	DET
ejpam-819	373	4	australian	australian	ADJ
ejpam-819	373	5	mathematical	mathematical	ADJ
ejpam-819	373	6	society	society	NOUN
ejpam-819	373	7	(	(	PUNCT
ejpam-819	373	8	ser	ser	NOUN
ejpam-819	373	9	b	b	PROPN
ejpam-819	373	10	)	)	PUNCT
ejpam-819	373	11	,	,	PUNCT
ejpam-819	373	12	31:108–121	31:108–121	NUM
ejpam-819	373	13	,	,	PUNCT
ejpam-819	373	14	1989	1989	NUM
ejpam-819	373	15	.	.	PUNCT
ejpam-819	374	1	[	[	X
ejpam-819	374	2	9	9	NUM
ejpam-819	374	3	]	]	X
ejpam-819	374	4	b.	b.	PROPN
ejpam-819	374	5	mond	mond	PROPN
ejpam-819	374	6	and	and	CCONJ
ejpam-819	374	7	t.	t.	PROPN
ejpam-819	374	8	weir	weir	PROPN
ejpam-819	374	9	.	.	PUNCT
ejpam-819	375	1	generalized	generalize	VERB
ejpam-819	375	2	convexity	convexity	NOUN
ejpam-819	375	3	and	and	CCONJ
ejpam-819	375	4	higher	high	ADJ
ejpam-819	375	5	order	order	NOUN
ejpam-819	375	6	duality	duality	NOUN
ejpam-819	375	7	.	.	PUNCT
ejpam-819	376	1	j.	j.	PROPN
ejpam-819	376	2	math	math	PROPN
ejpam-819	376	3	.	.	PUNCT
ejpam-819	377	1	anal	anal	PROPN
ejpam-819	377	2	.	.	PUNCT
ejpam-819	378	1	app	app	PROPN
ejpam-819	378	2	.	.	PROPN
ejpam-819	378	3	,	,	PUNCT
ejpam-819	379	1	46:169–174	46:169–174	PROPN
ejpam-819	379	2	,	,	PUNCT
ejpam-819	379	3	1974	1974	NUM
ejpam-819	379	4	.	.	PUNCT
ejpam-819	380	1	[	[	X
ejpam-819	380	2	10	10	NUM
ejpam-819	380	3	]	]	PUNCT
ejpam-819	380	4	j.	j.	PROPN
ejpam-819	380	5	zhang	zhang	PROPN
ejpam-819	380	6	and	and	CCONJ
ejpam-819	380	7	b.	b.	PROPN
ejpam-819	380	8	mond	mond	PROPN
ejpam-819	380	9	.	.	PUNCT
ejpam-819	381	1	duality	duality	NOUN
ejpam-819	381	2	for	for	ADP
ejpam-819	381	3	a	a	DET
ejpam-819	381	4	nondifferentiable	nondifferentiable	ADJ
ejpam-819	381	5	programming	programming	NOUN
ejpam-819	381	6	problem	problem	NOUN
ejpam-819	381	7	.	.	PUNCT
ejpam-819	382	1	bulletin	bulletin	NOUN
ejpam-819	382	2	australian	australian	ADJ
ejpam-819	382	3	mathematical	mathematical	ADJ
ejpam-819	382	4	society	society	NOUN
ejpam-819	382	5	,	,	PUNCT
ejpam-819	382	6	55:20–44	55:20–44	NUM
ejpam-819	382	7	,	,	PUNCT
ejpam-819	382	8	1997	1997	NUM
ejpam-819	382	9	.	.	PUNCT