id	sid	tid	token	lemma	pos
ejpam-6377	1	1	european	european	PROPN
ejpam-6377	1	2	journal	journal	PROPN
ejpam-6377	1	3	of	of	ADP
ejpam-6377	1	4	pure	pure	ADJ
ejpam-6377	1	5	and	and	CCONJ
ejpam-6377	1	6	applied	applied	ADJ
ejpam-6377	1	7	mathematics	mathematic	NOUN
ejpam-6377	1	8	2025	2025	NUM
ejpam-6377	1	9	,	,	PUNCT
ejpam-6377	1	10	vol	vol	NOUN
ejpam-6377	1	11	.	.	PROPN
ejpam-6377	1	12	18	18	NUM
ejpam-6377	1	13	,	,	PUNCT
ejpam-6377	1	14	issue	issue	NOUN
ejpam-6377	1	15	3	3	NUM
ejpam-6377	1	16	,	,	PUNCT
ejpam-6377	1	17	article	article	NOUN
ejpam-6377	1	18	number	number	NOUN
ejpam-6377	1	19	6377	6377	NUM
ejpam-6377	1	20	issn	issn	VERB
ejpam-6377	1	21	1307	1307	NUM
ejpam-6377	1	22	-	-	SYM
ejpam-6377	1	23	5543	5543	NUM
ejpam-6377	1	24	–	–	PUNCT
ejpam-6377	1	25	ejpam.com	ejpam.com	X
ejpam-6377	1	26	published	publish	VERB
ejpam-6377	1	27	by	by	ADP
ejpam-6377	1	28	new	new	PROPN
ejpam-6377	1	29	york	york	PROPN
ejpam-6377	1	30	business	business	PROPN
ejpam-6377	1	31	global	global	PROPN
ejpam-6377	1	32	an	an	DET
ejpam-6377	1	33	enhanced	enhanced	ADJ
ejpam-6377	1	34	conjugate	conjugate	ADJ
ejpam-6377	1	35	gradient	gradient	NOUN
ejpam-6377	1	36	method	method	NOUN
ejpam-6377	1	37	for	for	ADP
ejpam-6377	1	38	nonlinear	nonlinear	ADJ
ejpam-6377	1	39	minimization	minimization	NOUN
ejpam-6377	1	40	problems	problem	NOUN
ejpam-6377	1	41	ahmed	ahmed	PROPN
ejpam-6377	1	42	anwer	anwer	PROPN
ejpam-6377	1	43	mustafa1,∗	mustafa1,∗	PROPN
ejpam-6377	1	44	,	,	PUNCT
ejpam-6377	1	45	hussein	hussein	PROPN
ejpam-6377	1	46	ageel	ageel	PROPN
ejpam-6377	1	47	khatab2	khatab2	NOUN
ejpam-6377	1	48	1	1	NUM
ejpam-6377	1	49	department	department	NOUN
ejpam-6377	1	50	of	of	ADP
ejpam-6377	1	51	mathematics	mathematic	NOUN
ejpam-6377	1	52	,	,	PUNCT
ejpam-6377	1	53	college	college	NOUN
ejpam-6377	1	54	of	of	ADP
ejpam-6377	1	55	education	education	NOUN
ejpam-6377	1	56	,	,	PUNCT
ejpam-6377	1	57	university	university	NOUN
ejpam-6377	1	58	of	of	ADP
ejpam-6377	1	59	zakho	zakho	PROPN
ejpam-6377	1	60	,	,	PUNCT
ejpam-6377	1	61	kurdistan	kurdistan	ADJ
ejpam-6377	1	62	region	region	NOUN
ejpam-6377	1	63	,	,	PUNCT
ejpam-6377	1	64	iraq	iraq	PROPN
ejpam-6377	1	65	2	2	NUM
ejpam-6377	1	66	department	department	NOUN
ejpam-6377	1	67	of	of	ADP
ejpam-6377	1	68	mathematics	mathematic	NOUN
ejpam-6377	1	69	,	,	PUNCT
ejpam-6377	1	70	college	college	NOUN
ejpam-6377	1	71	of	of	ADP
ejpam-6377	1	72	science	science	NOUN
ejpam-6377	1	73	,	,	PUNCT
ejpam-6377	1	74	university	university	NOUN
ejpam-6377	1	75	of	of	ADP
ejpam-6377	1	76	zakho	zakho	PROPN
ejpam-6377	1	77	,	,	PUNCT
ejpam-6377	1	78	kurdistan	kurdistan	ADJ
ejpam-6377	1	79	region	region	NOUN
ejpam-6377	1	80	,	,	PUNCT
ejpam-6377	1	81	iraq	iraq	PROPN
ejpam-6377	1	82	abstract	abstract	NOUN
ejpam-6377	1	83	.	.	PUNCT
ejpam-6377	2	1	because	because	SCONJ
ejpam-6377	2	2	of	of	ADP
ejpam-6377	2	3	their	their	PRON
ejpam-6377	2	4	computing	computing	NOUN
ejpam-6377	2	5	efficiency	efficiency	NOUN
ejpam-6377	2	6	and	and	CCONJ
ejpam-6377	2	7	minimal	minimal	ADJ
ejpam-6377	2	8	memory	memory	NOUN
ejpam-6377	2	9	requirements	requirement	NOUN
ejpam-6377	2	10	,	,	PUNCT
ejpam-6377	2	11	conjugate	conjugate	ADJ
ejpam-6377	2	12	gradient	gradient	NOUN
ejpam-6377	2	13	techniques	technique	NOUN
ejpam-6377	2	14	are	be	AUX
ejpam-6377	2	15	a	a	DET
ejpam-6377	2	16	fundamental	fundamental	ADJ
ejpam-6377	2	17	family	family	NOUN
ejpam-6377	2	18	of	of	ADP
ejpam-6377	2	19	algorithms	algorithm	NOUN
ejpam-6377	2	20	for	for	ADP
ejpam-6377	2	21	handling	handle	VERB
ejpam-6377	2	22	large	large	ADJ
ejpam-6377	2	23	-	-	PUNCT
ejpam-6377	2	24	scale	scale	NOUN
ejpam-6377	2	25	unconstrained	unconstrained	ADJ
ejpam-6377	2	26	nonlinear	nonlinear	ADJ
ejpam-6377	2	27	optimization	optimization	NOUN
ejpam-6377	2	28	problems	problem	NOUN
ejpam-6377	2	29	.	.	PUNCT
ejpam-6377	3	1	a	a	DET
ejpam-6377	3	2	new	new	ADJ
ejpam-6377	3	3	version	version	NOUN
ejpam-6377	3	4	of	of	ADP
ejpam-6377	3	5	the	the	DET
ejpam-6377	3	6	hestenes	hestene	NOUN
ejpam-6377	3	7	-	-	PUNCT
ejpam-6377	3	8	stiefel	stiefel	NOUN
ejpam-6377	3	9	(	(	PUNCT
ejpam-6377	3	10	hs	hs	NOUN
ejpam-6377	3	11	)	)	PUNCT
ejpam-6377	3	12	technique	technique	NOUN
ejpam-6377	3	13	is	be	AUX
ejpam-6377	3	14	presented	present	VERB
ejpam-6377	3	15	in	in	ADP
ejpam-6377	3	16	this	this	DET
ejpam-6377	3	17	study	study	NOUN
ejpam-6377	3	18	with	with	ADP
ejpam-6377	3	19	the	the	DET
ejpam-6377	3	20	goal	goal	NOUN
ejpam-6377	3	21	of	of	ADP
ejpam-6377	3	22	improving	improve	VERB
ejpam-6377	3	23	convergence	convergence	NOUN
ejpam-6377	3	24	properties	property	NOUN
ejpam-6377	3	25	without	without	ADP
ejpam-6377	3	26	compromising	compromise	VERB
ejpam-6377	3	27	ease	ease	NOUN
ejpam-6377	3	28	of	of	ADP
ejpam-6377	3	29	use	use	NOUN
ejpam-6377	3	30	.	.	PUNCT
ejpam-6377	4	1	we	we	PRON
ejpam-6377	4	2	rigorously	rigorously	ADV
ejpam-6377	4	3	prove	prove	VERB
ejpam-6377	4	4	the	the	DET
ejpam-6377	4	5	global	global	ADJ
ejpam-6377	4	6	convergence	convergence	NOUN
ejpam-6377	4	7	qualities	quality	NOUN
ejpam-6377	4	8	of	of	ADP
ejpam-6377	4	9	the	the	DET
ejpam-6377	4	10	proposed	propose	VERB
ejpam-6377	4	11	approach	approach	NOUN
ejpam-6377	4	12	under	under	ADP
ejpam-6377	4	13	standard	standard	ADJ
ejpam-6377	4	14	assumptions	assumption	NOUN
ejpam-6377	4	15	and	and	CCONJ
ejpam-6377	4	16	show	show	VERB
ejpam-6377	4	17	that	that	SCONJ
ejpam-6377	4	18	it	it	PRON
ejpam-6377	4	19	meets	meet	VERB
ejpam-6377	4	20	the	the	DET
ejpam-6377	4	21	conjugacy	conjugacy	ADJ
ejpam-6377	4	22	,	,	PUNCT
ejpam-6377	4	23	descent	descent	NOUN
ejpam-6377	4	24	,	,	PUNCT
ejpam-6377	4	25	and	and	CCONJ
ejpam-6377	4	26	adequate	adequate	ADJ
ejpam-6377	4	27	descent	descent	NOUN
ejpam-6377	4	28	constraints	constraint	NOUN
ejpam-6377	4	29	.	.	PUNCT
ejpam-6377	5	1	numerous	numerous	ADJ
ejpam-6377	5	2	numerical	numerical	ADJ
ejpam-6377	5	3	tests	test	NOUN
ejpam-6377	5	4	,	,	PUNCT
ejpam-6377	5	5	covering	cover	VERB
ejpam-6377	5	6	a	a	DET
ejpam-6377	5	7	wide	wide	ADJ
ejpam-6377	5	8	range	range	NOUN
ejpam-6377	5	9	of	of	ADP
ejpam-6377	5	10	benchmark	benchmark	NOUN
ejpam-6377	5	11	issues	issue	NOUN
ejpam-6377	5	12	,	,	PUNCT
ejpam-6377	5	13	show	show	VERB
ejpam-6377	5	14	that	that	SCONJ
ejpam-6377	5	15	the	the	DET
ejpam-6377	5	16	suggested	suggest	VERB
ejpam-6377	5	17	strategy	strategy	NOUN
ejpam-6377	5	18	routinely	routinely	ADV
ejpam-6377	5	19	performs	perform	VERB
ejpam-6377	5	20	better	well	ADJ
ejpam-6377	5	21	than	than	ADP
ejpam-6377	5	22	the	the	DET
ejpam-6377	5	23	traditional	traditional	ADJ
ejpam-6377	5	24	hs	hs	NOUN
ejpam-6377	5	25	approach	approach	NOUN
ejpam-6377	5	26	in	in	ADP
ejpam-6377	5	27	terms	term	NOUN
ejpam-6377	5	28	of	of	ADP
ejpam-6377	5	29	function	function	NOUN
ejpam-6377	5	30	evaluations	evaluation	NOUN
ejpam-6377	5	31	and	and	CCONJ
ejpam-6377	5	32	iteration	iteration	NOUN
ejpam-6377	5	33	count	count	NOUN
ejpam-6377	5	34	.	.	PUNCT
ejpam-6377	6	1	2020	2020	NUM
ejpam-6377	6	2	mathematics	mathematic	NOUN
ejpam-6377	6	3	subject	subject	NOUN
ejpam-6377	6	4	classifications	classification	NOUN
ejpam-6377	6	5	:	:	PUNCT
ejpam-6377	6	6	65k05	65k05	NUM
ejpam-6377	6	7	,	,	PUNCT
ejpam-6377	6	8	46n10	46n10	NUM
ejpam-6377	6	9	,	,	PUNCT
ejpam-6377	6	10	90c26	90c26	NUM
ejpam-6377	6	11	,	,	PUNCT
ejpam-6377	6	12	90c30	90c30	NUM
ejpam-6377	6	13	key	key	ADJ
ejpam-6377	6	14	words	word	NOUN
ejpam-6377	6	15	and	and	CCONJ
ejpam-6377	6	16	phrases	phrase	NOUN
ejpam-6377	6	17	:	:	PUNCT
ejpam-6377	6	18	nonlinear	nonlinear	ADJ
ejpam-6377	6	19	optimization	optimization	NOUN
ejpam-6377	6	20	,	,	PUNCT
ejpam-6377	6	21	unconstrained	unconstrained	ADJ
ejpam-6377	6	22	optimization	optimization	NOUN
ejpam-6377	6	23	,	,	PUNCT
ejpam-6377	6	24	conjugate	conjugate	ADJ
ejpam-6377	6	25	gradient	gradient	NOUN
ejpam-6377	6	26	method	method	NOUN
ejpam-6377	6	27	,	,	PUNCT
ejpam-6377	6	28	descent	descent	NOUN
ejpam-6377	6	29	condition	condition	NOUN
ejpam-6377	6	30	,	,	PUNCT
ejpam-6377	6	31	global	global	ADJ
ejpam-6377	6	32	convergence	convergence	NOUN
ejpam-6377	6	33	1	1	NUM
ejpam-6377	6	34	.	.	PUNCT
ejpam-6377	6	35	introduction	introduction	NOUN
ejpam-6377	6	36	with	with	ADP
ejpam-6377	6	37	applications	application	NOUN
ejpam-6377	6	38	in	in	ADP
ejpam-6377	6	39	scientific	scientific	ADJ
ejpam-6377	6	40	computing	computing	NOUN
ejpam-6377	6	41	,	,	PUNCT
ejpam-6377	6	42	machine	machine	NOUN
ejpam-6377	6	43	learning	learning	NOUN
ejpam-6377	6	44	,	,	PUNCT
ejpam-6377	6	45	and	and	CCONJ
ejpam-6377	6	46	engineering	engineering	NOUN
ejpam-6377	6	47	design	design	NOUN
ejpam-6377	6	48	,	,	PUNCT
ejpam-6377	6	49	nonlinear	nonlinear	ADJ
ejpam-6377	6	50	unconstrained	unconstrained	ADJ
ejpam-6377	6	51	optimization	optimization	NOUN
ejpam-6377	6	52	remains	remain	VERB
ejpam-6377	6	53	a	a	DET
ejpam-6377	6	54	fundamental	fundamental	ADJ
ejpam-6377	6	55	topic	topic	NOUN
ejpam-6377	6	56	of	of	ADP
ejpam-6377	6	57	study	study	NOUN
ejpam-6377	6	58	in	in	ADP
ejpam-6377	6	59	numerical	numerical	ADJ
ejpam-6377	6	60	optimization	optimization	NOUN
ejpam-6377	6	61	[	[	X
ejpam-6377	6	62	1	1	NUM
ejpam-6377	6	63	]	]	PUNCT
ejpam-6377	6	64	.	.	PUNCT
ejpam-6377	7	1	iterative	iterative	NOUN
ejpam-6377	7	2	techniques	technique	NOUN
ejpam-6377	7	3	like	like	ADP
ejpam-6377	7	4	conjugate	conjugate	ADJ
ejpam-6377	7	5	gradient	gradient	NOUN
ejpam-6377	7	6	(	(	PUNCT
ejpam-6377	7	7	cg	cg	NOUN
ejpam-6377	7	8	)	)	PUNCT
ejpam-6377	7	9	algorithms	algorithm	NOUN
ejpam-6377	7	10	work	work	VERB
ejpam-6377	7	11	well	well	ADV
ejpam-6377	7	12	because	because	SCONJ
ejpam-6377	7	13	they	they	PRON
ejpam-6377	7	14	can	can	AUX
ejpam-6377	7	15	strike	strike	VERB
ejpam-6377	7	16	a	a	DET
ejpam-6377	7	17	compromise	compromise	NOUN
ejpam-6377	7	18	between	between	ADP
ejpam-6377	7	19	computing	compute	VERB
ejpam-6377	7	20	economy	economy	NOUN
ejpam-6377	7	21	and	and	CCONJ
ejpam-6377	7	22	convergence	convergence	NOUN
ejpam-6377	7	23	guarantees	guarantee	NOUN
ejpam-6377	7	24	.	.	PUNCT
ejpam-6377	8	1	numerous	numerous	ADJ
ejpam-6377	8	2	alterations	alteration	NOUN
ejpam-6377	8	3	to	to	ADP
ejpam-6377	8	4	traditional	traditional	ADJ
ejpam-6377	8	5	cg	cg	NOUN
ejpam-6377	8	6	techniques	technique	NOUN
ejpam-6377	8	7	have	have	AUX
ejpam-6377	8	8	been	be	AUX
ejpam-6377	8	9	put	put	VERB
ejpam-6377	8	10	forth	forth	ADP
ejpam-6377	8	11	recently	recently	ADV
ejpam-6377	8	12	in	in	ADP
ejpam-6377	8	13	an	an	DET
ejpam-6377	8	14	effort	effort	NOUN
ejpam-6377	8	15	to	to	PART
ejpam-6377	8	16	boost	boost	VERB
ejpam-6377	8	17	efficiency	efficiency	NOUN
ejpam-6377	8	18	and	and	CCONJ
ejpam-6377	8	19	guarantee	guarantee	VERB
ejpam-6377	8	20	convergence	convergence	NOUN
ejpam-6377	8	21	under	under	ADP
ejpam-6377	8	22	lax	lax	ADJ
ejpam-6377	8	23	circumstances	circumstance	NOUN
ejpam-6377	8	24	[	[	X
ejpam-6377	8	25	2	2	NUM
ejpam-6377	8	26	,	,	PUNCT
ejpam-6377	8	27	3	3	NUM
ejpam-6377	8	28	]	]	PUNCT
ejpam-6377	8	29	.	.	PUNCT
ejpam-6377	9	1	notably	notably	ADV
ejpam-6377	9	2	,	,	PUNCT
ejpam-6377	9	3	three	three	NUM
ejpam-6377	9	4	-	-	PUNCT
ejpam-6377	9	5	term	term	NOUN
ejpam-6377	9	6	formulations	formulation	NOUN
ejpam-6377	9	7	have	have	AUX
ejpam-6377	9	8	demonstrated	demonstrate	VERB
ejpam-6377	9	9	potential	potential	NOUN
ejpam-6377	9	10	for	for	ADP
ejpam-6377	9	11	reducing	reduce	VERB
ejpam-6377	9	12	storage	storage	NOUN
ejpam-6377	9	13	needs	need	NOUN
ejpam-6377	9	14	and	and	CCONJ
ejpam-6377	9	15	speeding	speed	VERB
ejpam-6377	9	16	up	up	ADP
ejpam-6377	9	17	convergence	convergence	NOUN
ejpam-6377	9	18	[	[	X
ejpam-6377	9	19	4	4	NUM
ejpam-6377	9	20	]	]	PUNCT
ejpam-6377	9	21	.	.	PUNCT
ejpam-6377	10	1	global	global	ADJ
ejpam-6377	10	2	convergence	convergence	NOUN
ejpam-6377	10	3	of	of	ADP
ejpam-6377	10	4	these	these	DET
ejpam-6377	10	5	cg	cg	NOUN
ejpam-6377	10	6	variations	variation	NOUN
ejpam-6377	10	7	has	have	AUX
ejpam-6377	10	8	been	be	AUX
ejpam-6377	10	9	made	make	VERB
ejpam-6377	10	10	easier	easy	ADJ
ejpam-6377	10	11	by	by	ADP
ejpam-6377	10	12	improvements	improvement	NOUN
ejpam-6377	10	13	in	in	ADP
ejpam-6377	10	14	the	the	DET
ejpam-6377	10	15	line	line	NOUN
ejpam-6377	10	16	search	search	NOUN
ejpam-6377	10	17	algorithms	algorithm	NOUN
ejpam-6377	10	18	,	,	PUNCT
ejpam-6377	10	19	especially	especially	ADV
ejpam-6377	10	20	those	those	PRON
ejpam-6377	10	21	that	that	PRON
ejpam-6377	10	22	meet	meet	VERB
ejpam-6377	10	23	the	the	DET
ejpam-6377	10	24	strong	strong	ADJ
ejpam-6377	10	25	wolfe	wolfe	PROPN
ejpam-6377	10	26	criteria	criteria	PROPN
ejpam-6377	10	27	[	[	X
ejpam-6377	10	28	5	5	NUM
ejpam-6377	10	29	]	]	PUNCT
ejpam-6377	10	30	.	.	PUNCT
ejpam-6377	11	1	spectral	spectral	ADJ
ejpam-6377	11	2	∗corresponding	∗corresponde	VERB
ejpam-6377	11	3	author	author	NOUN
ejpam-6377	11	4	.	.	PUNCT
ejpam-6377	12	1	doi	doi	NOUN
ejpam-6377	12	2	:	:	PUNCT
ejpam-6377	12	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6377	https://doi.org/10.29020/nybg.ejpam.v18i3.6377	NOUN
ejpam-6377	12	4	email	email	NOUN
ejpam-6377	12	5	addresses	address	NOUN
ejpam-6377	12	6	:	:	PUNCT
ejpam-6377	12	7	ahmed.mustafa@uoz.edu.krd	ahmed.mustafa@uoz.edu.krd	NOUN
ejpam-6377	12	8	(	(	PUNCT
ejpam-6377	12	9	a.	a.	PROPN
ejpam-6377	12	10	a.	a.	PROPN
ejpam-6377	12	11	mustafa	mustafa	PROPN
ejpam-6377	12	12	)	)	PUNCT
ejpam-6377	12	13	,	,	PUNCT
ejpam-6377	12	14	hussein.khatab@uoz.edu.krd	hussein.khatab@uoz.edu.krd	PROPN
ejpam-6377	12	15	(	(	PUNCT
ejpam-6377	12	16	h.	h.	PROPN
ejpam-6377	12	17	a.	a.	PROPN
ejpam-6377	12	18	khatab	khatab	PROPN
ejpam-6377	12	19	)	)	PUNCT
ejpam-6377	12	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6377	13	1	1	1	NUM
ejpam-6377	13	2	copyright	copyright	NOUN
ejpam-6377	13	3	:	:	PUNCT
ejpam-6377	13	4	©	©	PROPN
ejpam-6377	13	5	2025	2025	NUM
ejpam-6377	13	6	the	the	DET
ejpam-6377	13	7	author(s	author(s	NOUN
ejpam-6377	13	8	)	)	PUNCT
ejpam-6377	13	9	.	.	PUNCT
ejpam-6377	14	1	(	(	PUNCT
ejpam-6377	14	2	cc	cc	NOUN
ejpam-6377	14	3	by	by	ADP
ejpam-6377	14	4	-	-	PUNCT
ejpam-6377	14	5	nc	nc	PROPN
ejpam-6377	14	6	4.0	4.0	NUM
ejpam-6377	14	7	)	)	PUNCT
ejpam-6377	14	8	a.	a.	NOUN
ejpam-6377	14	9	a.	a.	PROPN
ejpam-6377	14	10	mustafa	mustafa	PROPN
ejpam-6377	14	11	,	,	PUNCT
ejpam-6377	14	12	h.	h.	PROPN
ejpam-6377	14	13	a.	a.	PROPN
ejpam-6377	14	14	khatab	khatab	PROPN
ejpam-6377	14	15	/	/	SYM
ejpam-6377	14	16	eur	eur	PROPN
ejpam-6377	14	17	.	.	PUNCT
ejpam-6377	15	1	j.	j.	PROPN
ejpam-6377	15	2	pure	pure	PROPN
ejpam-6377	15	3	appl	appl	PROPN
ejpam-6377	15	4	.	.	PROPN
ejpam-6377	15	5	math	math	PROPN
ejpam-6377	15	6	,	,	PUNCT
ejpam-6377	15	7	18	18	NUM
ejpam-6377	15	8	(	(	PUNCT
ejpam-6377	15	9	3	3	NUM
ejpam-6377	15	10	)	)	PUNCT
ejpam-6377	15	11	(	(	PUNCT
ejpam-6377	15	12	2025	2025	NUM
ejpam-6377	15	13	)	)	PUNCT
ejpam-6377	15	14	,	,	PUNCT
ejpam-6377	15	15	6377	6377	NUM
ejpam-6377	15	16	2	2	NUM
ejpam-6377	15	17	of	of	ADP
ejpam-6377	15	18	12	12	NUM
ejpam-6377	15	19	conjugate	conjugate	ADJ
ejpam-6377	15	20	gradient	gradient	NOUN
ejpam-6377	15	21	techniques	technique	NOUN
ejpam-6377	15	22	,	,	PUNCT
ejpam-6377	15	23	which	which	PRON
ejpam-6377	15	24	dynamically	dynamically	ADV
ejpam-6377	15	25	integrate	integrate	VERB
ejpam-6377	15	26	curvature	curvature	NOUN
ejpam-6377	15	27	information	information	NOUN
ejpam-6377	15	28	into	into	ADP
ejpam-6377	15	29	parameter	parameter	NOUN
ejpam-6377	15	30	updates	update	NOUN
ejpam-6377	15	31	,	,	PUNCT
ejpam-6377	15	32	have	have	AUX
ejpam-6377	15	33	also	also	ADV
ejpam-6377	15	34	received	receive	VERB
ejpam-6377	15	35	fresh	fresh	ADJ
ejpam-6377	15	36	attention	attention	NOUN
ejpam-6377	15	37	[	[	X
ejpam-6377	15	38	6	6	NUM
ejpam-6377	15	39	,	,	PUNCT
ejpam-6377	15	40	7	7	NUM
ejpam-6377	15	41	]	]	PUNCT
ejpam-6377	15	42	.	.	PUNCT
ejpam-6377	16	1	large	large	ADJ
ejpam-6377	16	2	-	-	PUNCT
ejpam-6377	16	3	scale	scale	NOUN
ejpam-6377	16	4	optimization	optimization	NOUN
ejpam-6377	16	5	situations	situation	NOUN
ejpam-6377	16	6	,	,	PUNCT
ejpam-6377	16	7	such	such	ADJ
ejpam-6377	16	8	as	as	ADP
ejpam-6377	16	9	deep	deep	ADJ
ejpam-6377	16	10	learning	learning	NOUN
ejpam-6377	16	11	training	training	NOUN
ejpam-6377	16	12	procedures	procedure	NOUN
ejpam-6377	16	13	and	and	CCONJ
ejpam-6377	16	14	sparse	sparse	ADJ
ejpam-6377	16	15	regression	regression	NOUN
ejpam-6377	16	16	,	,	PUNCT
ejpam-6377	16	17	have	have	AUX
ejpam-6377	16	18	benefited	benefit	VERB
ejpam-6377	16	19	from	from	ADP
ejpam-6377	16	20	such	such	ADJ
ejpam-6377	16	21	advancements	advancement	NOUN
ejpam-6377	16	22	[	[	X
ejpam-6377	16	23	8	8	NUM
ejpam-6377	16	24	]	]	PUNCT
ejpam-6377	16	25	.	.	PUNCT
ejpam-6377	17	1	furthermore	furthermore	ADV
ejpam-6377	17	2	,	,	PUNCT
ejpam-6377	17	3	by	by	ADP
ejpam-6377	17	4	carefully	carefully	ADV
ejpam-6377	17	5	examining	examine	VERB
ejpam-6377	17	6	the	the	DET
ejpam-6377	17	7	adequate	adequate	ADJ
ejpam-6377	17	8	descent	descent	NOUN
ejpam-6377	17	9	and	and	CCONJ
ejpam-6377	17	10	conjugacy	conjugacy	ADJ
ejpam-6377	17	11	aspects	aspect	NOUN
ejpam-6377	17	12	of	of	ADP
ejpam-6377	17	13	cg	cg	NOUN
ejpam-6377	17	14	approaches	approach	NOUN
ejpam-6377	17	15	,	,	PUNCT
ejpam-6377	17	16	current	current	ADJ
ejpam-6377	17	17	research	research	NOUN
ejpam-6377	17	18	has	have	AUX
ejpam-6377	17	19	shown	show	VERB
ejpam-6377	17	20	their	their	PRON
ejpam-6377	17	21	theoretical	theoretical	ADJ
ejpam-6377	17	22	soundness	soundness	NOUN
ejpam-6377	17	23	[	[	X
ejpam-6377	17	24	9	9	NUM
ejpam-6377	17	25	,	,	PUNCT
ejpam-6377	17	26	10	10	NUM
ejpam-6377	17	27	]	]	PUNCT
ejpam-6377	17	28	.	.	PUNCT
ejpam-6377	18	1	these	these	DET
ejpam-6377	18	2	advancements	advancement	NOUN
ejpam-6377	18	3	highlight	highlight	VERB
ejpam-6377	18	4	the	the	DET
ejpam-6377	18	5	necessity	necessity	NOUN
ejpam-6377	18	6	of	of	ADP
ejpam-6377	18	7	more	more	ADJ
ejpam-6377	18	8	research	research	NOUN
ejpam-6377	18	9	into	into	ADP
ejpam-6377	18	10	hybrid	hybrid	NOUN
ejpam-6377	18	11	or	or	CCONJ
ejpam-6377	18	12	parameter	parameter	NOUN
ejpam-6377	18	13	-	-	PUNCT
ejpam-6377	18	14	adaptive	adaptive	ADJ
ejpam-6377	18	15	cg	cg	NOUN
ejpam-6377	18	16	techniques	technique	NOUN
ejpam-6377	18	17	that	that	PRON
ejpam-6377	18	18	maintain	maintain	VERB
ejpam-6377	18	19	desired	desire	VERB
ejpam-6377	18	20	convergence	convergence	NOUN
ejpam-6377	18	21	behavior	behavior	NOUN
ejpam-6377	18	22	in	in	ADP
ejpam-6377	18	23	a	a	DET
ejpam-6377	18	24	variety	variety	NOUN
ejpam-6377	18	25	of	of	ADP
ejpam-6377	18	26	issue	issue	NOUN
ejpam-6377	18	27	scenarios	scenario	NOUN
ejpam-6377	18	28	.	.	PUNCT
ejpam-6377	19	1	this	this	DET
ejpam-6377	19	2	paper	paper	NOUN
ejpam-6377	19	3	contributes	contribute	VERB
ejpam-6377	19	4	to	to	ADP
ejpam-6377	19	5	this	this	DET
ejpam-6377	19	6	ongoing	ongoing	ADJ
ejpam-6377	19	7	research	research	NOUN
ejpam-6377	19	8	by	by	ADP
ejpam-6377	19	9	introducing	introduce	VERB
ejpam-6377	19	10	a	a	DET
ejpam-6377	19	11	modified	modified	ADJ
ejpam-6377	19	12	cg	cg	NOUN
ejpam-6377	19	13	method	method	NOUN
ejpam-6377	19	14	with	with	ADP
ejpam-6377	19	15	demonstrable	demonstrable	ADJ
ejpam-6377	19	16	performance	performance	NOUN
ejpam-6377	19	17	gains	gain	NOUN
ejpam-6377	19	18	on	on	ADP
ejpam-6377	19	19	classical	classical	ADJ
ejpam-6377	19	20	benchmark	benchmark	NOUN
ejpam-6377	19	21	problems	problem	NOUN
ejpam-6377	19	22	.	.	PUNCT
ejpam-6377	20	1	consider	consider	VERB
ejpam-6377	20	2	the	the	DET
ejpam-6377	20	3	unconstrained	unconstrained	ADJ
ejpam-6377	20	4	optimization	optimization	NOUN
ejpam-6377	20	5	problem	problem	NOUN
ejpam-6377	20	6	:	:	PUNCT
ejpam-6377	20	7	min	min	PROPN
ejpam-6377	20	8	f(x	f(x	PROPN
ejpam-6377	20	9	)	)	PUNCT
ejpam-6377	20	10	,	,	PUNCT
ejpam-6377	20	11	x	x	PUNCT
ejpam-6377	20	12	∈	∈	PROPN
ejpam-6377	20	13	rn	rn	PROPN
ejpam-6377	20	14	(	(	PUNCT
ejpam-6377	20	15	1.1	1.1	NUM
ejpam-6377	20	16	)	)	PUNCT
ejpam-6377	20	17	where	where	SCONJ
ejpam-6377	20	18	f	f	X
ejpam-6377	20	19	:	:	PUNCT
ejpam-6377	20	20	rn	rn	PROPN
ejpam-6377	20	21	→	→	SYM
ejpam-6377	20	22	r	r	NOUN
ejpam-6377	20	23	is	be	AUX
ejpam-6377	20	24	a	a	DET
ejpam-6377	20	25	real	real	ADV
ejpam-6377	20	26	-	-	PUNCT
ejpam-6377	20	27	valued	value	VERB
ejpam-6377	20	28	,	,	PUNCT
ejpam-6377	20	29	continuously	continuously	ADV
ejpam-6377	20	30	differentiable	differentiable	ADJ
ejpam-6377	20	31	function	function	NOUN
ejpam-6377	20	32	.	.	PUNCT
ejpam-6377	21	1	a	a	DET
ejpam-6377	21	2	nonlinear	nonlinear	ADJ
ejpam-6377	21	3	conjugate	conjugate	ADJ
ejpam-6377	21	4	gradient	gradient	NOUN
ejpam-6377	21	5	method	method	NOUN
ejpam-6377	21	6	generates	generate	VERB
ejpam-6377	21	7	a	a	DET
ejpam-6377	21	8	sequence	sequence	NOUN
ejpam-6377	21	9	{	{	PUNCT
ejpam-6377	21	10	xk	xk	NOUN
ejpam-6377	21	11	}	}	PUNCT
ejpam-6377	21	12	,	,	PUNCT
ejpam-6377	21	13	k	k	X
ejpam-6377	21	14	≥	≥	PROPN
ejpam-6377	21	15	0	0	NUM
ejpam-6377	21	16	,	,	PUNCT
ejpam-6377	21	17	starting	start	VERB
ejpam-6377	21	18	from	from	ADP
ejpam-6377	21	19	an	an	DET
ejpam-6377	21	20	initial	initial	ADJ
ejpam-6377	21	21	guess	guess	NOUN
ejpam-6377	21	22	x0	x0	PROPN
ejpam-6377	21	23	∈	∈	PROPN
ejpam-6377	21	24	rn	rn	PROPN
ejpam-6377	21	25	,	,	PUNCT
ejpam-6377	21	26	using	use	VERB
ejpam-6377	21	27	the	the	DET
ejpam-6377	21	28	recurrence	recurrence	NOUN
ejpam-6377	21	29	xk+1	xk+1	PUNCT
ejpam-6377	22	1	=	=	SYM
ejpam-6377	22	2	xk	xk	PROPN
ejpam-6377	23	1	+	+	NUM
ejpam-6377	23	2	αkdk	αkdk	NOUN
ejpam-6377	23	3	(	(	PUNCT
ejpam-6377	23	4	1.2	1.2	NUM
ejpam-6377	23	5	)	)	PUNCT
ejpam-6377	23	6	where	where	SCONJ
ejpam-6377	23	7	vk	vk	ADV
ejpam-6377	23	8	=	=	SYM
ejpam-6377	23	9	xk+1	xk+1	PROPN
ejpam-6377	23	10	−	−	PROPN
ejpam-6377	24	1	xk	xk	PROPN
ejpam-6377	24	2	,	,	PUNCT
ejpam-6377	24	3	αk	αk	PRON
ejpam-6377	24	4	is	be	AUX
ejpam-6377	24	5	positive	positive	ADJ
ejpam-6377	24	6	step	step	NOUN
ejpam-6377	24	7	size	size	NOUN
ejpam-6377	24	8	and	and	CCONJ
ejpam-6377	24	9	is	be	AUX
ejpam-6377	24	10	obtained	obtain	VERB
ejpam-6377	24	11	by	by	ADP
ejpam-6377	24	12	some	some	DET
ejpam-6377	24	13	line	line	NOUN
ejpam-6377	24	14	searches	search	NOUN
ejpam-6377	24	15	,	,	PUNCT
ejpam-6377	24	16	and	and	CCONJ
ejpam-6377	24	17	dk	dk	PROPN
ejpam-6377	24	18	is	be	AUX
ejpam-6377	24	19	a	a	DET
ejpam-6377	24	20	search	search	NOUN
ejpam-6377	24	21	direction	direction	NOUN
ejpam-6377	24	22	.	.	PUNCT
ejpam-6377	25	1	the	the	DET
ejpam-6377	25	2	conjugate	conjugate	ADJ
ejpam-6377	25	3	gradient	gradient	NOUN
ejpam-6377	25	4	method	method	NOUN
ejpam-6377	25	5	’s	’s	PART
ejpam-6377	25	6	simplicity	simplicity	NOUN
ejpam-6377	25	7	and	and	CCONJ
ejpam-6377	25	8	extremely	extremely	ADV
ejpam-6377	25	9	low	low	ADJ
ejpam-6377	25	10	memory	memory	NOUN
ejpam-6377	25	11	requirements	requirement	NOUN
ejpam-6377	25	12	make	make	VERB
ejpam-6377	25	13	it	it	PRON
ejpam-6377	25	14	a	a	DET
ejpam-6377	25	15	potent	potent	ADJ
ejpam-6377	25	16	line	line	NOUN
ejpam-6377	25	17	search	search	NOUN
ejpam-6377	25	18	technique	technique	NOUN
ejpam-6377	25	19	for	for	ADP
ejpam-6377	25	20	resolving	resolve	VERB
ejpam-6377	25	21	large	large	ADJ
ejpam-6377	25	22	-	-	PUNCT
ejpam-6377	25	23	scale	scale	NOUN
ejpam-6377	25	24	optimization	optimization	NOUN
ejpam-6377	25	25	problems	problem	NOUN
ejpam-6377	25	26	.	.	PUNCT
ejpam-6377	26	1	the	the	DET
ejpam-6377	26	2	search	search	NOUN
ejpam-6377	26	3	direction	direction	NOUN
ejpam-6377	26	4	dk	dk	PROPN
ejpam-6377	26	5	of	of	ADP
ejpam-6377	26	6	the	the	DET
ejpam-6377	26	7	conjugate	conjugate	ADJ
ejpam-6377	26	8	gradient	gradient	NOUN
ejpam-6377	26	9	methods	method	NOUN
ejpam-6377	26	10	is	be	AUX
ejpam-6377	26	11	given	give	VERB
ejpam-6377	26	12	by	by	ADP
ejpam-6377	26	13	:	:	PUNCT
ejpam-6377	26	14	dk+1	dk+1	X
ejpam-6377	26	15	=	=	SYM
ejpam-6377	26	16	−gk+1	−gk+1	PROPN
ejpam-6377	26	17	+	+	CCONJ
ejpam-6377	26	18	βkdk	βkdk	NOUN
ejpam-6377	26	19	,	,	PUNCT
ejpam-6377	26	20	k	k	PROPN
ejpam-6377	26	21	≥	≥	PROPN
ejpam-6377	26	22	0	0	NUM
ejpam-6377	26	23	,	,	PUNCT
ejpam-6377	26	24	d0	d0	NOUN
ejpam-6377	26	25	=	=	SYM
ejpam-6377	26	26	−g0	−g0	PROPN
ejpam-6377	26	27	(	(	PUNCT
ejpam-6377	26	28	1.3	1.3	NUM
ejpam-6377	26	29	)	)	PUNCT
ejpam-6377	26	30	where	where	SCONJ
ejpam-6377	26	31	gk+1	gk+1	NOUN
ejpam-6377	26	32	=	=	SYM
ejpam-6377	26	33	∇f(xk+1	∇f(xk+1	ADP
ejpam-6377	26	34	)	)	PUNCT
ejpam-6377	26	35	and	and	CCONJ
ejpam-6377	26	36	βk	βk	NOUN
ejpam-6377	26	37	is	be	AUX
ejpam-6377	26	38	a	a	DET
ejpam-6377	26	39	scalar	scalar	NOUN
ejpam-6377	26	40	.	.	PUNCT
ejpam-6377	27	1	many	many	ADJ
ejpam-6377	27	2	formulas	formula	NOUN
ejpam-6377	27	3	for	for	ADP
ejpam-6377	27	4	βk	βk	NOUN
ejpam-6377	27	5	are	be	AUX
ejpam-6377	27	6	suggested	suggest	VERB
ejpam-6377	27	7	,	,	PUNCT
ejpam-6377	27	8	like	like	ADP
ejpam-6377	27	9	fletcher	fletcher	PROPN
ejpam-6377	27	10	-	-	PUNCT
ejpam-6377	27	11	reeves	reeves	PROPN
ejpam-6377	27	12	(	(	PUNCT
ejpam-6377	27	13	fr	fr	PROPN
ejpam-6377	27	14	)	)	PUNCT
ejpam-6377	28	1	[	[	X
ejpam-6377	28	2	11	11	NUM
ejpam-6377	28	3	]	]	PUNCT
ejpam-6377	28	4	,	,	PUNCT
ejpam-6377	28	5	dai	dai	PROPN
ejpam-6377	28	6	and	and	CCONJ
ejpam-6377	28	7	yuan	yuan	PROPN
ejpam-6377	28	8	(	(	PUNCT
ejpam-6377	28	9	dy	dy	X
ejpam-6377	28	10	)	)	PUNCT
ejpam-6377	29	1	[	[	X
ejpam-6377	29	2	12	12	NUM
ejpam-6377	29	3	]	]	PUNCT
ejpam-6377	29	4	,	,	PUNCT
ejpam-6377	29	5	hestenes	hestenes	PROPN
ejpam-6377	29	6	-	-	PUNCT
ejpam-6377	29	7	stiefel	stiefel	NOUN
ejpam-6377	29	8	(	(	PUNCT
ejpam-6377	29	9	hs	hs	X
ejpam-6377	29	10	)	)	PUNCT
ejpam-6377	30	1	[	[	X
ejpam-6377	30	2	13	13	NUM
ejpam-6377	30	3	]	]	PUNCT
ejpam-6377	30	4	,	,	PUNCT
ejpam-6377	30	5	polakribiere	polakribiere	NOUN
ejpam-6377	30	6	-	-	PUNCT
ejpam-6377	30	7	polyak	polyak	NOUN
ejpam-6377	30	8	(	(	PUNCT
ejpam-6377	30	9	prp	prp	PROPN
ejpam-6377	30	10	)	)	PUNCT
ejpam-6377	31	1	[	[	X
ejpam-6377	31	2	14	14	NUM
ejpam-6377	31	3	]	]	PUNCT
ejpam-6377	31	4	,	,	PUNCT
ejpam-6377	31	5	conjugate	conjugate	ADJ
ejpam-6377	31	6	descent	descent	NOUN
ejpam-6377	31	7	(	(	PUNCT
ejpam-6377	31	8	cd	cd	PROPN
ejpam-6377	31	9	)	)	PUNCT
ejpam-6377	32	1	[	[	X
ejpam-6377	32	2	15	15	NUM
ejpam-6377	32	3	]	]	PUNCT
ejpam-6377	32	4	,	,	PUNCT
ejpam-6377	32	5	and	and	CCONJ
ejpam-6377	32	6	liu	liu	PROPN
ejpam-6377	32	7	-	-	PUNCT
ejpam-6377	32	8	storey	storey	NOUN
ejpam-6377	32	9	(	(	PUNCT
ejpam-6377	32	10	ls	ls	PROPN
ejpam-6377	32	11	)	)	PUNCT
ejpam-6377	32	12	method	method	NOUN
ejpam-6377	32	13	[	[	X
ejpam-6377	32	14	16	16	NUM
ejpam-6377	32	15	]	]	PUNCT
ejpam-6377	32	16	,	,	PUNCT
ejpam-6377	32	17	these	these	DET
ejpam-6377	32	18	formulas	formula	NOUN
ejpam-6377	32	19	are	be	AUX
ejpam-6377	32	20	as	as	SCONJ
ejpam-6377	32	21	follows	follow	VERB
ejpam-6377	32	22	:	:	PUNCT
ejpam-6377	32	23	βfr	βfr	PROPN
ejpam-6377	32	24	k	k	X
ejpam-6377	33	1	=	=	PUNCT
ejpam-6377	33	2	∥gk+1∥2	∥gk+1∥2	PROPN
ejpam-6377	33	3	∥gk∥2	∥gk∥2	PROPN
ejpam-6377	34	1	(	(	PUNCT
ejpam-6377	34	2	1.4	1.4	NUM
ejpam-6377	34	3	)	)	PUNCT
ejpam-6377	34	4	βdy	βdy	NOUN
ejpam-6377	35	1	k	k	PROPN
ejpam-6377	35	2	=	=	PUNCT
ejpam-6377	35	3	∥gk+1∥2	∥gk+1∥2	PROPN
ejpam-6377	35	4	dtk	dtk	PROPN
ejpam-6377	35	5	(	(	PUNCT
ejpam-6377	35	6	gk+1	gk+1	NOUN
ejpam-6377	35	7	−	−	PROPN
ejpam-6377	35	8	gk	gk	PROPN
ejpam-6377	35	9	)	)	PUNCT
ejpam-6377	35	10	(	(	PUNCT
ejpam-6377	35	11	1.5	1.5	NUM
ejpam-6377	35	12	)	)	PUNCT
ejpam-6377	35	13	βhs	βhs	NOUN
ejpam-6377	35	14	k	k	PROPN
ejpam-6377	36	1	=	=	PUNCT
ejpam-6377	36	2	gtk+1(gk+1	gtk+1(gk+1	PROPN
ejpam-6377	36	3	−	−	PROPN
ejpam-6377	36	4	gk	gk	PROPN
ejpam-6377	36	5	)	)	PUNCT
ejpam-6377	36	6	dtk	dtk	PROPN
ejpam-6377	36	7	(	(	PUNCT
ejpam-6377	36	8	gk+1	gk+1	NOUN
ejpam-6377	36	9	−	−	PROPN
ejpam-6377	36	10	gk	gk	PROPN
ejpam-6377	36	11	)	)	PUNCT
ejpam-6377	36	12	(	(	PUNCT
ejpam-6377	36	13	1.6	1.6	NUM
ejpam-6377	36	14	)	)	PUNCT
ejpam-6377	36	15	βprp	βprp	NOUN
ejpam-6377	37	1	k	k	NOUN
ejpam-6377	37	2	=	=	PUNCT
ejpam-6377	37	3	gtk+1(gk+1	gtk+1(gk+1	PROPN
ejpam-6377	37	4	−	−	PROPN
ejpam-6377	37	5	gk	gk	PROPN
ejpam-6377	37	6	)	)	PUNCT
ejpam-6377	37	7	∥gk∥2	∥gk∥2	PROPN
ejpam-6377	38	1	(	(	PUNCT
ejpam-6377	38	2	1.7	1.7	NUM
ejpam-6377	38	3	)	)	PUNCT
ejpam-6377	38	4	βcd	βcd	VERB
ejpam-6377	38	5	k	k	NOUN
ejpam-6377	39	1	=	=	PRON
ejpam-6377	39	2	∥gk+1∥2	∥gk+1∥2	X
ejpam-6377	39	3	−dtk	−dtk	ADV
ejpam-6377	39	4	gk	gk	PROPN
ejpam-6377	39	5	(	(	PUNCT
ejpam-6377	39	6	1.8	1.8	NUM
ejpam-6377	39	7	)	)	PUNCT
ejpam-6377	39	8	a.	a.	NOUN
ejpam-6377	39	9	a.	a.	PROPN
ejpam-6377	39	10	mustafa	mustafa	PROPN
ejpam-6377	39	11	,	,	PUNCT
ejpam-6377	39	12	h.	h.	PROPN
ejpam-6377	39	13	a.	a.	PROPN
ejpam-6377	39	14	khatab	khatab	PROPN
ejpam-6377	39	15	/	/	SYM
ejpam-6377	39	16	eur	eur	PROPN
ejpam-6377	39	17	.	.	PUNCT
ejpam-6377	40	1	j.	j.	PROPN
ejpam-6377	40	2	pure	pure	PROPN
ejpam-6377	40	3	appl	appl	PROPN
ejpam-6377	40	4	.	.	PROPN
ejpam-6377	40	5	math	math	PROPN
ejpam-6377	40	6	,	,	PUNCT
ejpam-6377	40	7	18	18	NUM
ejpam-6377	40	8	(	(	PUNCT
ejpam-6377	40	9	3	3	NUM
ejpam-6377	40	10	)	)	PUNCT
ejpam-6377	40	11	(	(	PUNCT
ejpam-6377	40	12	2025	2025	NUM
ejpam-6377	40	13	)	)	PUNCT
ejpam-6377	40	14	,	,	PUNCT
ejpam-6377	40	15	6377	6377	NUM
ejpam-6377	40	16	3	3	NUM
ejpam-6377	40	17	of	of	ADP
ejpam-6377	40	18	12	12	NUM
ejpam-6377	40	19	βls	βls	NOUN
ejpam-6377	40	20	k	k	NOUN
ejpam-6377	41	1	=	=	PUNCT
ejpam-6377	41	2	gtk+1(gk+1	gtk+1(gk+1	PROPN
ejpam-6377	41	3	−	−	PROPN
ejpam-6377	41	4	gk	gk	PROPN
ejpam-6377	41	5	)	)	PUNCT
ejpam-6377	41	6	−dtk	−dtk	ADV
ejpam-6377	41	7	gk	gk	PROPN
ejpam-6377	41	8	(	(	PUNCT
ejpam-6377	41	9	1.9	1.9	NUM
ejpam-6377	41	10	)	)	PUNCT
ejpam-6377	41	11	where	where	SCONJ
ejpam-6377	41	12	yk	yk	NOUN
ejpam-6377	41	13	=	=	PROPN
ejpam-6377	41	14	gk+1	gk+1	PROPN
ejpam-6377	41	15	−	−	PROPN
ejpam-6377	41	16	gk	gk	PROPN
ejpam-6377	41	17	,	,	PUNCT
ejpam-6377	41	18	and	and	CCONJ
ejpam-6377	41	19	the	the	DET
ejpam-6377	41	20	symbol	symbol	NOUN
ejpam-6377	41	21	∥	∥	X
ejpam-6377	41	22	·	·	PUNCT
ejpam-6377	41	23	∥	∥	PUNCT
ejpam-6377	41	24	denotes	denote	VERB
ejpam-6377	41	25	the	the	DET
ejpam-6377	41	26	euclidean	euclidean	ADJ
ejpam-6377	41	27	norm	norm	NOUN
ejpam-6377	41	28	of	of	ADP
ejpam-6377	41	29	vectors	vector	NOUN
ejpam-6377	41	30	.	.	PUNCT
ejpam-6377	42	1	also	also	ADV
ejpam-6377	42	2	,	,	PUNCT
ejpam-6377	42	3	many	many	ADJ
ejpam-6377	42	4	parameters	parameter	NOUN
ejpam-6377	42	5	are	be	AUX
ejpam-6377	42	6	proposed	propose	VERB
ejpam-6377	42	7	:	:	PUNCT
ejpam-6377	42	8	hussein	hussein	PROPN
ejpam-6377	42	9	ageel	ageel	PROPN
ejpam-6377	42	10	khatab	khatab	PROPN
ejpam-6377	42	11	and	and	CCONJ
ejpam-6377	42	12	salah	salah	PROPN
ejpam-6377	42	13	gazi	gazi	PROPN
ejpam-6377	42	14	shareef	shareef	PROPN
ejpam-6377	42	15	suggested	suggest	VERB
ejpam-6377	42	16	a	a	DET
ejpam-6377	42	17	new	new	ADJ
ejpam-6377	42	18	conjugate	conjugate	ADJ
ejpam-6377	42	19	gradient	gradient	NOUN
ejpam-6377	42	20	method	method	NOUN
ejpam-6377	42	21	for	for	ADP
ejpam-6377	42	22	solving	solve	VERB
ejpam-6377	42	23	nonlinear	nonlinear	ADJ
ejpam-6377	42	24	unconstrained	unconstrained	ADJ
ejpam-6377	42	25	optimization	optimization	NOUN
ejpam-6377	42	26	problems	problem	NOUN
ejpam-6377	42	27	by	by	ADP
ejpam-6377	42	28	using	use	VERB
ejpam-6377	42	29	three	three	NUM
ejpam-6377	42	30	terms	term	NOUN
ejpam-6377	42	31	conjugate	conjugate	VERB
ejpam-6377	42	32	gradient	gradient	ADJ
ejpam-6377	42	33	method	method	NOUN
ejpam-6377	42	34	[	[	X
ejpam-6377	42	35	4	4	NUM
ejpam-6377	42	36	]	]	PUNCT
ejpam-6377	42	37	.	.	PUNCT
ejpam-6377	43	1	ahmed	ahmed	PROPN
ejpam-6377	43	2	anwer	anwer	PROPN
ejpam-6377	43	3	mustafa	mustafa	PROPN
ejpam-6377	43	4	[	[	X
ejpam-6377	43	5	6	6	NUM
ejpam-6377	43	6	]	]	PUNCT
ejpam-6377	43	7	proposed	propose	VERB
ejpam-6377	43	8	a	a	DET
ejpam-6377	43	9	novel	novel	ADJ
ejpam-6377	43	10	algorithm	algorithm	NOUN
ejpam-6377	43	11	to	to	PART
ejpam-6377	43	12	perform	perform	VERB
ejpam-6377	43	13	spectral	spectral	ADJ
ejpam-6377	43	14	conjugate	conjugate	ADJ
ejpam-6377	43	15	gradient	gradient	ADJ
ejpam-6377	43	16	descent	descent	NOUN
ejpam-6377	43	17	for	for	ADP
ejpam-6377	43	18	an	an	DET
ejpam-6377	43	19	unconstrained	unconstrained	ADJ
ejpam-6377	43	20	,	,	PUNCT
ejpam-6377	43	21	nonlinear	nonlinear	ADJ
ejpam-6377	43	22	optimization	optimization	NOUN
ejpam-6377	43	23	problem	problem	NOUN
ejpam-6377	43	24	.	.	PUNCT
ejpam-6377	44	1	the	the	DET
ejpam-6377	44	2	same	same	ADJ
ejpam-6377	44	3	researcher	researcher	NOUN
ejpam-6377	44	4	suggested	suggest	VERB
ejpam-6377	44	5	another	another	DET
ejpam-6377	44	6	algorithm	algorithm	NOUN
ejpam-6377	44	7	,	,	PUNCT
ejpam-6377	44	8	see	see	VERB
ejpam-6377	44	9	[	[	X
ejpam-6377	44	10	7	7	NUM
ejpam-6377	44	11	]	]	PUNCT
ejpam-6377	44	12	.	.	PUNCT
ejpam-6377	45	1	the	the	DET
ejpam-6377	45	2	properties	property	NOUN
ejpam-6377	45	3	of	of	ADP
ejpam-6377	45	4	conjugate	conjugate	ADJ
ejpam-6377	45	5	gradient	gradient	NOUN
ejpam-6377	45	6	methods	method	NOUN
ejpam-6377	45	7	have	have	AUX
ejpam-6377	45	8	been	be	AUX
ejpam-6377	45	9	explored	explore	VERB
ejpam-6377	45	10	greatly	greatly	ADV
ejpam-6377	45	11	through	through	ADP
ejpam-6377	45	12	their	their	PRON
ejpam-6377	45	13	global	global	ADJ
ejpam-6377	45	14	convergence	convergence	NOUN
ejpam-6377	45	15	properties	property	NOUN
ejpam-6377	45	16	.	.	PUNCT
ejpam-6377	46	1	global	global	ADJ
ejpam-6377	46	2	convergence	convergence	NOUN
ejpam-6377	46	3	results	result	VERB
ejpam-6377	46	4	for	for	ADP
ejpam-6377	46	5	the	the	DET
ejpam-6377	46	6	fr	fr	ADJ
ejpam-6377	46	7	method	method	NOUN
ejpam-6377	46	8	without	without	ADP
ejpam-6377	46	9	regular	regular	ADJ
ejpam-6377	46	10	restarts	restart	NOUN
ejpam-6377	46	11	and	and	CCONJ
ejpam-6377	46	12	in	in	ADP
ejpam-6377	46	13	exact	exact	ADJ
ejpam-6377	46	14	line	line	NOUN
ejpam-6377	46	15	search	search	NOUN
ejpam-6377	46	16	have	have	AUX
ejpam-6377	46	17	been	be	AUX
ejpam-6377	46	18	obtained	obtain	VERB
ejpam-6377	46	19	by	by	ADP
ejpam-6377	46	20	zoutendijk	zoutendijk	X
ejpam-6377	46	21	[	[	X
ejpam-6377	46	22	17	17	NUM
ejpam-6377	46	23	]	]	PUNCT
ejpam-6377	46	24	,	,	PUNCT
ejpam-6377	46	25	and	and	CCONJ
ejpam-6377	46	26	by	by	ADP
ejpam-6377	46	27	al	al	PROPN
ejpam-6377	46	28	-	-	PUNCT
ejpam-6377	46	29	baali	baali	PROPN
ejpam-6377	46	30	[	[	X
ejpam-6377	46	31	18	18	NUM
ejpam-6377	46	32	]	]	PUNCT
ejpam-6377	46	33	in	in	ADP
ejpam-6377	46	34	connection	connection	NOUN
ejpam-6377	46	35	with	with	ADP
ejpam-6377	46	36	inexact	inexact	ADJ
ejpam-6377	46	37	line	line	NOUN
ejpam-6377	46	38	searches	search	NOUN
ejpam-6377	46	39	.	.	PUNCT
ejpam-6377	47	1	dai	dai	PROPN
ejpam-6377	47	2	and	and	CCONJ
ejpam-6377	47	3	yuan	yuan	PROPN
ejpam-6377	48	1	[	[	X
ejpam-6377	48	2	12	12	NUM
ejpam-6377	48	3	]	]	PUNCT
ejpam-6377	48	4	shown	show	VERB
ejpam-6377	48	5	that	that	SCONJ
ejpam-6377	48	6	the	the	DET
ejpam-6377	48	7	dy	dy	NOUN
ejpam-6377	48	8	method	method	NOUN
ejpam-6377	48	9	is	be	AUX
ejpam-6377	48	10	descent	descent	NOUN
ejpam-6377	48	11	and	and	CCONJ
ejpam-6377	48	12	globally	globally	ADV
ejpam-6377	48	13	convergent	convergent	ADJ
ejpam-6377	48	14	if	if	SCONJ
ejpam-6377	48	15	the	the	DET
ejpam-6377	48	16	wolfe	wolfe	PROPN
ejpam-6377	48	17	line	line	NOUN
ejpam-6377	48	18	search	search	NOUN
ejpam-6377	48	19	f(xk	f(xk	PROPN
ejpam-6377	48	20	+	+	CCONJ
ejpam-6377	48	21	αkdk)−	αkdk)−	NUM
ejpam-6377	48	22	f(xk	f(xk	NOUN
ejpam-6377	48	23	)	)	PUNCT
ejpam-6377	48	24	≤	≤	NOUN
ejpam-6377	49	1	c1αkg	c1αkg	PROPN
ejpam-6377	49	2	t	t	PROPN
ejpam-6377	49	3	k	k	PROPN
ejpam-6377	49	4	dk	dk	PROPN
ejpam-6377	49	5	,	,	PUNCT
ejpam-6377	49	6	gtk+1dk	gtk+1dk	PROPN
ejpam-6377	49	7	≥	≥	PROPN
ejpam-6377	49	8	c2	c2	PROPN
ejpam-6377	49	9	g	g	PROPN
ejpam-6377	49	10	t	t	PROPN
ejpam-6377	49	11	k	k	PROPN
ejpam-6377	49	12	dk	dk	PROPN
ejpam-6377	49	13	is	be	AUX
ejpam-6377	49	14	used	use	VERB
ejpam-6377	49	15	.	.	PUNCT
ejpam-6377	50	1	the	the	DET
ejpam-6377	50	2	structure	structure	NOUN
ejpam-6377	50	3	of	of	ADP
ejpam-6377	50	4	this	this	DET
ejpam-6377	50	5	paper	paper	NOUN
ejpam-6377	50	6	is	be	AUX
ejpam-6377	50	7	as	as	SCONJ
ejpam-6377	50	8	follows	follow	VERB
ejpam-6377	50	9	:	:	PUNCT
ejpam-6377	50	10	in	in	ADP
ejpam-6377	50	11	section	section	NOUN
ejpam-6377	50	12	2	2	NUM
ejpam-6377	50	13	,	,	PUNCT
ejpam-6377	50	14	a	a	DET
ejpam-6377	50	15	new	new	ADJ
ejpam-6377	50	16	conjugate	conjugate	ADJ
ejpam-6377	50	17	gradient	gradient	NOUN
ejpam-6377	50	18	method	method	NOUN
ejpam-6377	50	19	will	will	AUX
ejpam-6377	50	20	be	be	AUX
ejpam-6377	50	21	proposed	propose	VERB
ejpam-6377	50	22	.	.	PUNCT
ejpam-6377	51	1	its	its	PRON
ejpam-6377	51	2	conjugacy	conjugacy	ADJ
ejpam-6377	51	3	condition	condition	NOUN
ejpam-6377	51	4	,	,	PUNCT
ejpam-6377	51	5	descent	descent	NOUN
ejpam-6377	51	6	condition	condition	NOUN
ejpam-6377	51	7	,	,	PUNCT
ejpam-6377	51	8	and	and	CCONJ
ejpam-6377	51	9	sufficient	sufficient	ADJ
ejpam-6377	51	10	descent	descent	NOUN
ejpam-6377	51	11	condition	condition	NOUN
ejpam-6377	51	12	will	will	AUX
ejpam-6377	51	13	be	be	AUX
ejpam-6377	51	14	proved	prove	VERB
ejpam-6377	51	15	in	in	ADP
ejpam-6377	51	16	section	section	NOUN
ejpam-6377	51	17	3	3	NUM
ejpam-6377	51	18	.	.	PUNCT
ejpam-6377	52	1	in	in	ADP
ejpam-6377	52	2	section	section	NOUN
ejpam-6377	52	3	4	4	NUM
ejpam-6377	52	4	,	,	PUNCT
ejpam-6377	52	5	its	its	PRON
ejpam-6377	52	6	global	global	ADJ
ejpam-6377	52	7	convergence	convergence	NOUN
ejpam-6377	52	8	will	will	AUX
ejpam-6377	52	9	be	be	AUX
ejpam-6377	52	10	examined	examine	VERB
ejpam-6377	52	11	.	.	PUNCT
ejpam-6377	53	1	some	some	DET
ejpam-6377	53	2	numerical	numerical	ADJ
ejpam-6377	53	3	experiments	experiment	NOUN
ejpam-6377	53	4	about	about	ADP
ejpam-6377	53	5	this	this	DET
ejpam-6377	53	6	new	new	ADJ
ejpam-6377	53	7	conjugate	conjugate	ADJ
ejpam-6377	53	8	gradient	gradient	NOUN
ejpam-6377	53	9	method	method	NOUN
ejpam-6377	53	10	will	will	AUX
ejpam-6377	53	11	be	be	AUX
ejpam-6377	53	12	presented	present	VERB
ejpam-6377	53	13	in	in	ADP
ejpam-6377	53	14	section	section	NOUN
ejpam-6377	53	15	5	5	NUM
ejpam-6377	53	16	,	,	PUNCT
ejpam-6377	53	17	and	and	CCONJ
ejpam-6377	53	18	the	the	DET
ejpam-6377	53	19	conclusion	conclusion	NOUN
ejpam-6377	53	20	will	will	AUX
ejpam-6377	53	21	be	be	AUX
ejpam-6377	53	22	provided	provide	VERB
ejpam-6377	53	23	in	in	ADP
ejpam-6377	53	24	section	section	NOUN
ejpam-6377	53	25	6	6	NUM
ejpam-6377	53	26	.	.	NOUN
ejpam-6377	54	1	2	2	NUM
ejpam-6377	54	2	.	.	X
ejpam-6377	54	3	new	new	ADJ
ejpam-6377	54	4	conjugate	conjugate	ADJ
ejpam-6377	54	5	gradient	gradient	NOUN
ejpam-6377	54	6	method	method	NOUN
ejpam-6377	54	7	and	and	CCONJ
ejpam-6377	54	8	its	its	PRON
ejpam-6377	54	9	algorithm	algorithm	NOUN
ejpam-6377	54	10	in	in	ADP
ejpam-6377	54	11	this	this	DET
ejpam-6377	54	12	section	section	NOUN
ejpam-6377	54	13	,	,	PUNCT
ejpam-6377	54	14	we	we	PRON
ejpam-6377	54	15	develop	develop	VERB
ejpam-6377	54	16	a	a	DET
ejpam-6377	54	17	modified	modify	VERB
ejpam-6377	54	18	nonlinear	nonlinear	NOUN
ejpam-6377	54	19	hs	hs	PROPN
ejpam-6377	54	20	method	method	NOUN
ejpam-6377	54	21	for	for	ADP
ejpam-6377	54	22	solving	solve	VERB
ejpam-6377	54	23	nonlinear	nonlinear	ADJ
ejpam-6377	54	24	unconstrained	unconstrained	ADJ
ejpam-6377	54	25	optimization	optimization	NOUN
ejpam-6377	54	26	problems	problem	NOUN
ejpam-6377	54	27	.	.	PUNCT
ejpam-6377	55	1	to	to	PART
ejpam-6377	55	2	obtain	obtain	VERB
ejpam-6377	55	3	the	the	DET
ejpam-6377	55	4	generated	generate	VERB
ejpam-6377	55	5	sufficient	sufficient	ADJ
ejpam-6377	55	6	descent	descent	NOUN
ejpam-6377	55	7	direction	direction	NOUN
ejpam-6377	55	8	,	,	PUNCT
ejpam-6377	55	9	hager	hager	NOUN
ejpam-6377	55	10	and	and	CCONJ
ejpam-6377	55	11	zhang	zhang	PROPN
ejpam-6377	56	1	[	[	X
ejpam-6377	56	2	19	19	NUM
ejpam-6377	56	3	]	]	PUNCT
ejpam-6377	56	4	showed	show	VERB
ejpam-6377	56	5	a	a	DET
ejpam-6377	56	6	new	new	ADJ
ejpam-6377	56	7	conjugate	conjugate	ADJ
ejpam-6377	56	8	gradient	gradient	NOUN
ejpam-6377	56	9	method	method	NOUN
ejpam-6377	56	10	(	(	PUNCT
ejpam-6377	56	11	cg	cg	NOUN
ejpam-6377	56	12	-	-	PUNCT
ejpam-6377	56	13	c	c	NOUN
ejpam-6377	56	14	)	)	PUNCT
ejpam-6377	56	15	obtained	obtain	VERB
ejpam-6377	56	16	by	by	ADP
ejpam-6377	56	17	modifying	modify	VERB
ejpam-6377	56	18	the	the	DET
ejpam-6377	56	19	hs	hs	PROPN
ejpam-6377	56	20	method	method	NOUN
ejpam-6377	56	21	,	,	PUNCT
ejpam-6377	56	22	which	which	PRON
ejpam-6377	56	23	generates	generate	VERB
ejpam-6377	56	24	sufficient	sufficient	ADJ
ejpam-6377	56	25	descent	descent	NOUN
ejpam-6377	56	26	directions	direction	NOUN
ejpam-6377	56	27	at	at	ADP
ejpam-6377	56	28	each	each	DET
ejpam-6377	56	29	step	step	NOUN
ejpam-6377	56	30	,	,	PUNCT
ejpam-6377	56	31	without	without	ADP
ejpam-6377	56	32	relying	rely	VERB
ejpam-6377	56	33	on	on	ADP
ejpam-6377	56	34	any	any	DET
ejpam-6377	56	35	line	line	NOUN
ejpam-6377	56	36	search	search	NOUN
ejpam-6377	56	37	.	.	PUNCT
ejpam-6377	57	1	the	the	DET
ejpam-6377	57	2	scalar	scalar	NOUN
ejpam-6377	57	3	βk	βk	NOUN
ejpam-6377	57	4	in	in	ADP
ejpam-6377	57	5	cg	cg	NOUN
ejpam-6377	57	6	-	-	PUNCT
ejpam-6377	57	7	c	c	NOUN
ejpam-6377	57	8	method	method	NOUN
ejpam-6377	57	9	is	be	AUX
ejpam-6377	57	10	determined	determine	VERB
ejpam-6377	57	11	by	by	ADP
ejpam-6377	57	12	βnhs	βnhs	NOUN
ejpam-6377	57	13	k	k	PROPN
ejpam-6377	57	14	=	=	SYM
ejpam-6377	57	15	max	max	PROPN
ejpam-6377	57	16	{	{	PUNCT
ejpam-6377	57	17	βn	βn	PROPN
ejpam-6377	57	18	k	k	PROPN
ejpam-6377	57	19	,	,	PUNCT
ejpam-6377	57	20	µk	µk	INTJ
ejpam-6377	57	21	}	}	PUNCT
ejpam-6377	57	22	(	(	PUNCT
ejpam-6377	57	23	2.1	2.1	NUM
ejpam-6377	57	24	)	)	PUNCT
ejpam-6377	57	25	where	where	SCONJ
ejpam-6377	57	26	βn	βn	NOUN
ejpam-6377	57	27	k	k	PROPN
ejpam-6377	57	28	=	=	PUNCT
ejpam-6377	57	29	gtk+1yk	gtk+1yk	PROPN
ejpam-6377	57	30	dtk	dtk	PROPN
ejpam-6377	57	31	yk	yk	PROPN
ejpam-6377	57	32	−	−	PROPN
ejpam-6377	57	33	2∥yk∥2gtk+1dk	2∥yk∥2gtk+1dk	PROPN
ejpam-6377	57	34	(	(	PUNCT
ejpam-6377	57	35	dtk	dtk	PROPN
ejpam-6377	57	36	yk	yk	PROPN
ejpam-6377	57	37	)	)	PUNCT
ejpam-6377	57	38	2	2	NUM
ejpam-6377	57	39	,	,	PUNCT
ejpam-6377	57	40	µk	µk	NOUN
ejpam-6377	57	41	=	=	SYM
ejpam-6377	57	42	1	1	NUM
ejpam-6377	57	43	∥dk∥min{∥gk∥	∥dk∥min{∥gk∥	PROPN
ejpam-6377	57	44	,	,	PUNCT
ejpam-6377	57	45	µ	µ	NOUN
ejpam-6377	57	46	}	}	PUNCT
ejpam-6377	57	47	,	,	PUNCT
ejpam-6377	57	48	and	and	CCONJ
ejpam-6377	57	49	µ	µ	X
ejpam-6377	57	50	>	>	X
ejpam-6377	57	51	0	0	NUM
ejpam-6377	57	52	is	be	AUX
ejpam-6377	57	53	a	a	DET
ejpam-6377	57	54	constant	constant	ADJ
ejpam-6377	57	55	.	.	PUNCT
ejpam-6377	58	1	with	with	ADP
ejpam-6377	58	2	the	the	DET
ejpam-6377	58	3	weak	weak	ADJ
ejpam-6377	58	4	wolfe	wolfe	PROPN
ejpam-6377	58	5	-	-	PUNCT
ejpam-6377	58	6	powell	powell	PROPN
ejpam-6377	58	7	line	line	NOUN
ejpam-6377	58	8	search	search	NOUN
ejpam-6377	58	9	,	,	PUNCT
ejpam-6377	58	10	hager	hager	NOUN
ejpam-6377	58	11	and	and	CCONJ
ejpam-6377	58	12	zhang	zhang	PROPN
ejpam-6377	59	1	[	[	X
ejpam-6377	59	2	19	19	NUM
ejpam-6377	59	3	]	]	PUNCT
ejpam-6377	59	4	established	establish	VERB
ejpam-6377	59	5	a	a	DET
ejpam-6377	59	6	global	global	ADJ
ejpam-6377	59	7	convergence	convergence	NOUN
ejpam-6377	59	8	result	result	NOUN
ejpam-6377	59	9	for	for	ADP
ejpam-6377	59	10	(	(	PUNCT
ejpam-6377	59	11	2.1	2.1	NUM
ejpam-6377	59	12	)	)	PUNCT
ejpam-6377	59	13	when	when	SCONJ
ejpam-6377	59	14	the	the	DET
ejpam-6377	59	15	objective	objective	ADJ
ejpam-6377	59	16	function	function	NOUN
ejpam-6377	59	17	f(x	f(x	PROPN
ejpam-6377	59	18	)	)	PUNCT
ejpam-6377	59	19	is	be	AUX
ejpam-6377	59	20	a	a	DET
ejpam-6377	59	21	general	general	ADJ
ejpam-6377	59	22	nonlinear	nonlinear	ADJ
ejpam-6377	59	23	function	function	NOUN
ejpam-6377	59	24	.	.	PUNCT
ejpam-6377	60	1	a.	a.	NOUN
ejpam-6377	60	2	a.	a.	PROPN
ejpam-6377	60	3	mustafa	mustafa	PROPN
ejpam-6377	60	4	,	,	PUNCT
ejpam-6377	60	5	h.	h.	PROPN
ejpam-6377	60	6	a.	a.	PROPN
ejpam-6377	60	7	khatab	khatab	PROPN
ejpam-6377	60	8	/	/	SYM
ejpam-6377	60	9	eur	eur	PROPN
ejpam-6377	60	10	.	.	PUNCT
ejpam-6377	61	1	j.	j.	PROPN
ejpam-6377	61	2	pure	pure	PROPN
ejpam-6377	61	3	appl	appl	PROPN
ejpam-6377	61	4	.	.	PROPN
ejpam-6377	61	5	math	math	PROPN
ejpam-6377	61	6	,	,	PUNCT
ejpam-6377	61	7	18	18	NUM
ejpam-6377	61	8	(	(	PUNCT
ejpam-6377	61	9	3	3	NUM
ejpam-6377	61	10	)	)	PUNCT
ejpam-6377	61	11	(	(	PUNCT
ejpam-6377	61	12	2025	2025	NUM
ejpam-6377	61	13	)	)	PUNCT
ejpam-6377	61	14	,	,	PUNCT
ejpam-6377	61	15	6377	6377	NUM
ejpam-6377	61	16	4	4	NUM
ejpam-6377	61	17	of	of	ADP
ejpam-6377	61	18	12	12	NUM
ejpam-6377	61	19	also	also	ADV
ejpam-6377	61	20	,	,	PUNCT
ejpam-6377	61	21	hussein	hussein	PROPN
ejpam-6377	61	22	ageel	ageel	PROPN
ejpam-6377	61	23	khatab	khatab	PROPN
ejpam-6377	61	24	and	and	CCONJ
ejpam-6377	61	25	salah	salah	PROPN
ejpam-6377	61	26	gazi	gazi	PROPN
ejpam-6377	61	27	shareef	shareef	PROPN
ejpam-6377	62	1	[	[	X
ejpam-6377	62	2	20	20	NUM
ejpam-6377	62	3	]	]	PUNCT
ejpam-6377	62	4	suggested	suggest	VERB
ejpam-6377	62	5	the	the	DET
ejpam-6377	62	6	following	follow	VERB
ejpam-6377	62	7	conjugate	conjugate	ADJ
ejpam-6377	62	8	gradient	gradient	NOUN
ejpam-6377	62	9	method	method	NOUN
ejpam-6377	63	1	βnew	βnew	ADJ
ejpam-6377	63	2	k	k	PROPN
ejpam-6377	64	1	=	=	PROPN
ejpam-6377	64	2	gtk+1yk	gtk+1yk	PROPN
ejpam-6377	64	3	dtk	dtk	PROPN
ejpam-6377	64	4	yk	yk	PROPN
ejpam-6377	64	5	−	−	PROPN
ejpam-6377	64	6	gtk+1vk	gtk+1vk	PROPN
ejpam-6377	64	7	dtk	dtk	PROPN
ejpam-6377	64	8	yk	yk	PROPN
ejpam-6377	64	9	−	−	PROPN
ejpam-6377	64	10	µ	µ	PROPN
ejpam-6377	64	11	gtk+1dk	gtk+1dk	PROPN
ejpam-6377	64	12	dtk	dtk	PROPN
ejpam-6377	64	13	yk	yk	PROPN
ejpam-6377	64	14	∥gk∥2	∥gk∥2	PROPN
ejpam-6377	64	15	gtk	gtk	PROPN
ejpam-6377	64	16	yk	yk	PROPN
ejpam-6377	64	17	(	(	PUNCT
ejpam-6377	64	18	2.2	2.2	NUM
ejpam-6377	64	19	)	)	PUNCT
ejpam-6377	64	20	where	where	SCONJ
ejpam-6377	64	21	µ	µ	X
ejpam-6377	64	22	∈	∈	X
ejpam-6377	64	23	(	(	PUNCT
ejpam-6377	64	24	0	0	NUM
ejpam-6377	64	25	,	,	PUNCT
ejpam-6377	64	26	1	1	NUM
ejpam-6377	64	27	)	)	PUNCT
ejpam-6377	64	28	.	.	PUNCT
ejpam-6377	65	1	we	we	PRON
ejpam-6377	65	2	suggest	suggest	VERB
ejpam-6377	65	3	a	a	DET
ejpam-6377	65	4	new	new	ADJ
ejpam-6377	65	5	parameter	parameter	NOUN
ejpam-6377	65	6	as	as	SCONJ
ejpam-6377	65	7	follows	follow	VERB
ejpam-6377	65	8	:	:	PUNCT
ejpam-6377	66	1	βnew	βnew	PROPN
ejpam-6377	66	2	k	k	PROPN
ejpam-6377	67	1	=	=	PUNCT
ejpam-6377	68	1	gtk+1yk	gtk+1yk	PROPN
ejpam-6377	68	2	dtk	dtk	PROPN
ejpam-6377	68	3	yk	yk	PROPN
ejpam-6377	68	4	−	−	PROPN
ejpam-6377	68	5	µ	µ	X
ejpam-6377	68	6	∥gk+1∥2∥vk∥2∥xk+1∥	∥gk+1∥2∥vk∥2∥xk+1∥	PROPN
ejpam-6377	68	7	(	(	PUNCT
ejpam-6377	68	8	dtk	dtk	PROPN
ejpam-6377	68	9	yk	yk	PROPN
ejpam-6377	68	10	)	)	PUNCT
ejpam-6377	68	11	2	2	NUM
ejpam-6377	68	12	gtk+1dk	gtk+1dk	PROPN
ejpam-6377	68	13	(	(	PUNCT
ejpam-6377	68	14	2.3	2.3	NUM
ejpam-6377	68	15	)	)	PUNCT
ejpam-6377	68	16	where	where	SCONJ
ejpam-6377	68	17	µ	µ	X
ejpam-6377	68	18	>	>	X
ejpam-6377	68	19	0	0	X
ejpam-6377	68	20	.	.	PUNCT
ejpam-6377	69	1	algorithm	algorithm	NOUN
ejpam-6377	69	2	of	of	ADP
ejpam-6377	69	3	the	the	DET
ejpam-6377	69	4	new	new	ADJ
ejpam-6377	69	5	conjugate	conjugate	ADJ
ejpam-6377	69	6	gradient	gradient	NOUN
ejpam-6377	69	7	method	method	NOUN
ejpam-6377	69	8	(	(	PUNCT
ejpam-6377	69	9	βnew	βnew	ADJ
ejpam-6377	69	10	k	k	NOUN
ejpam-6377	69	11	)	)	PUNCT
ejpam-6377	69	12	step	step	NOUN
ejpam-6377	69	13	1	1	NUM
ejpam-6377	69	14	:	:	PUNCT
ejpam-6377	69	15	select	select	VERB
ejpam-6377	69	16	x0	x0	PROPN
ejpam-6377	69	17	and	and	CCONJ
ejpam-6377	69	18	ε	ε	PROPN
ejpam-6377	69	19	=	=	SYM
ejpam-6377	69	20	10−5	10−5	NUM
ejpam-6377	69	21	.	.	PUNCT
ejpam-6377	70	1	step	step	NOUN
ejpam-6377	70	2	2	2	NUM
ejpam-6377	70	3	:	:	PUNCT
ejpam-6377	70	4	set	set	VERB
ejpam-6377	70	5	d0	d0	NOUN
ejpam-6377	70	6	=	=	SYM
ejpam-6377	70	7	−g0	−g0	PROPN
ejpam-6377	70	8	,	,	PUNCT
ejpam-6377	70	9	gk	gk	PROPN
ejpam-6377	70	10	=	=	SYM
ejpam-6377	70	11	∇f(xk	∇f(xk	NOUN
ejpam-6377	70	12	)	)	PUNCT
ejpam-6377	70	13	,	,	PUNCT
ejpam-6377	70	14	set	set	VERB
ejpam-6377	70	15	k	k	PROPN
ejpam-6377	71	1	=	=	PUNCT
ejpam-6377	72	1	0	0	X
ejpam-6377	72	2	.	.	PUNCT
ejpam-6377	73	1	step	step	NOUN
ejpam-6377	73	2	3	3	NUM
ejpam-6377	73	3	:	:	PUNCT
ejpam-6377	73	4	compute	compute	VERB
ejpam-6377	73	5	the	the	DET
ejpam-6377	73	6	step	step	NOUN
ejpam-6377	73	7	length	length	NOUN
ejpam-6377	74	1	αk	αk	INTJ
ejpam-6377	74	2	>	>	X
ejpam-6377	74	3	0	0	PUNCT
ejpam-6377	75	1	satisfying	satisfy	VERB
ejpam-6377	75	2	the	the	DET
ejpam-6377	75	3	wolfe	wolfe	PROPN
ejpam-6377	75	4	line	line	NOUN
ejpam-6377	75	5	search	search	NOUN
ejpam-6377	75	6	conditions	condition	NOUN
ejpam-6377	75	7	f(xk	f(xk	PROPN
ejpam-6377	75	8	+	+	CCONJ
ejpam-6377	75	9	αkdk)−	αkdk)−	NUM
ejpam-6377	75	10	f(xk	f(xk	NOUN
ejpam-6377	75	11	)	)	PUNCT
ejpam-6377	75	12	≤	≤	NOUN
ejpam-6377	75	13	c1αkg	c1αkg	PROPN
ejpam-6377	75	14	t	t	PROPN
ejpam-6377	75	15	k	k	PROPN
ejpam-6377	75	16	dk	dk	PROPN
ejpam-6377	75	17	,	,	PUNCT
ejpam-6377	75	18	|gtk+1dk|	|gtk+1dk|	ADV
ejpam-6377	75	19	≤	≤	NOUN
ejpam-6377	75	20	c2|gtk	c2|gtk	PUNCT
ejpam-6377	75	21	dk|	dk|	NOUN
ejpam-6377	75	22	,	,	PUNCT
ejpam-6377	75	23	where	where	SCONJ
ejpam-6377	75	24	0	0	X
ejpam-6377	75	25	<	<	X
ejpam-6377	75	26	c1	c1	PROPN
ejpam-6377	75	27	<	<	X
ejpam-6377	75	28	c2	c2	PROPN
ejpam-6377	75	29	<	<	X
ejpam-6377	75	30	1	1	X
ejpam-6377	75	31	.	.	PUNCT
ejpam-6377	75	32	step	step	NOUN
ejpam-6377	75	33	4	4	NUM
ejpam-6377	75	34	:	:	PUNCT
ejpam-6377	75	35	compute	compute	NOUN
ejpam-6377	75	36	xk+1	xk+1	NOUN
ejpam-6377	75	37	=	=	SYM
ejpam-6377	75	38	xk	xk	PROPN
ejpam-6377	76	1	+	+	CCONJ
ejpam-6377	76	2	αkdk	αkdk	NOUN
ejpam-6377	76	3	,	,	PUNCT
ejpam-6377	76	4	gk+1	gk+1	NOUN
ejpam-6377	76	5	=	=	SYM
ejpam-6377	77	1	∇f(xk+1	∇f(xk+1	PROPN
ejpam-6377	77	2	)	)	PUNCT
ejpam-6377	77	3	,	,	PUNCT
ejpam-6377	77	4	if	if	SCONJ
ejpam-6377	77	5	∥gk+1∥	∥gk+1∥	NUM
ejpam-6377	77	6	≤	≤	NUM
ejpam-6377	77	7	ε	ε	PROPN
ejpam-6377	77	8	,	,	PUNCT
ejpam-6377	77	9	then	then	ADV
ejpam-6377	77	10	stop	stop	VERB
ejpam-6377	77	11	.	.	PUNCT
ejpam-6377	78	1	step	step	NOUN
ejpam-6377	78	2	5	5	NUM
ejpam-6377	78	3	:	:	PUNCT
ejpam-6377	78	4	compute	compute	VERB
ejpam-6377	78	5	βnew	βnew	PROPN
ejpam-6377	78	6	k	k	PROPN
ejpam-6377	78	7	by	by	ADP
ejpam-6377	78	8	equation	equation	NOUN
ejpam-6377	78	9	(	(	PUNCT
ejpam-6377	78	10	2.3	2.3	NUM
ejpam-6377	78	11	)	)	PUNCT
ejpam-6377	78	12	.	.	PUNCT
ejpam-6377	79	1	step	step	NOUN
ejpam-6377	79	2	6	6	NUM
ejpam-6377	79	3	:	:	PUNCT
ejpam-6377	79	4	compute	compute	NOUN
ejpam-6377	79	5	dk+1	dk+1	NOUN
ejpam-6377	79	6	=	=	SYM
ejpam-6377	79	7	−gk+1	−gk+1	PROPN
ejpam-6377	79	8	+	+	CCONJ
ejpam-6377	79	9	βnew	βnew	ADJ
ejpam-6377	79	10	k	k	PROPN
ejpam-6377	79	11	dk	dk	PROPN
ejpam-6377	79	12	.	.	PROPN
ejpam-6377	79	13	step	step	NOUN
ejpam-6377	79	14	7	7	NUM
ejpam-6377	79	15	:	:	PUNCT
ejpam-6377	79	16	if	if	SCONJ
ejpam-6377	79	17	|gtk+1gk|	|gtk+1gk|	ADV
ejpam-6377	79	18	>	>	X
ejpam-6377	79	19	0.2∥gk+1∥2	0.2∥gk+1∥2	NOUN
ejpam-6377	79	20	,	,	PUNCT
ejpam-6377	79	21	then	then	ADV
ejpam-6377	79	22	go	go	VERB
ejpam-6377	79	23	to	to	PART
ejpam-6377	79	24	step	step	VERB
ejpam-6377	79	25	2	2	NUM
ejpam-6377	79	26	.	.	PUNCT
ejpam-6377	80	1	otherwise	otherwise	ADV
ejpam-6377	80	2	,	,	PUNCT
ejpam-6377	80	3	k	k	PROPN
ejpam-6377	80	4	=	=	PUNCT
ejpam-6377	80	5	k	k	PROPN
ejpam-6377	81	1	+	+	PROPN
ejpam-6377	81	2	1	1	NUM
ejpam-6377	81	3	,	,	PUNCT
ejpam-6377	81	4	and	and	CCONJ
ejpam-6377	81	5	go	go	VERB
ejpam-6377	81	6	to	to	PART
ejpam-6377	81	7	step	step	VERB
ejpam-6377	81	8	3	3	NUM
ejpam-6377	81	9	.	.	PUNCT
ejpam-6377	81	10	a.	a.	PROPN
ejpam-6377	81	11	a.	a.	PROPN
ejpam-6377	81	12	mustafa	mustafa	PROPN
ejpam-6377	81	13	,	,	PUNCT
ejpam-6377	81	14	h.	h.	PROPN
ejpam-6377	81	15	a.	a.	PROPN
ejpam-6377	81	16	khatab	khatab	PROPN
ejpam-6377	81	17	/	/	SYM
ejpam-6377	81	18	eur	eur	PROPN
ejpam-6377	81	19	.	.	PUNCT
ejpam-6377	82	1	j.	j.	PROPN
ejpam-6377	82	2	pure	pure	PROPN
ejpam-6377	82	3	appl	appl	PROPN
ejpam-6377	82	4	.	.	PROPN
ejpam-6377	82	5	math	math	PROPN
ejpam-6377	82	6	,	,	PUNCT
ejpam-6377	82	7	18	18	NUM
ejpam-6377	82	8	(	(	PUNCT
ejpam-6377	82	9	3	3	NUM
ejpam-6377	82	10	)	)	PUNCT
ejpam-6377	82	11	(	(	PUNCT
ejpam-6377	82	12	2025	2025	NUM
ejpam-6377	82	13	)	)	PUNCT
ejpam-6377	82	14	,	,	PUNCT
ejpam-6377	82	15	6377	6377	NUM
ejpam-6377	82	16	5	5	NUM
ejpam-6377	82	17	of	of	ADP
ejpam-6377	82	18	12	12	NUM
ejpam-6377	82	19	3	3	NUM
ejpam-6377	82	20	.	.	PUNCT
ejpam-6377	83	1	conjugacy	conjugacy	ADJ
ejpam-6377	83	2	condition	condition	NOUN
ejpam-6377	83	3	,	,	PUNCT
ejpam-6377	83	4	descent	descent	NOUN
ejpam-6377	83	5	condition	condition	NOUN
ejpam-6377	83	6	,	,	PUNCT
ejpam-6377	83	7	and	and	CCONJ
ejpam-6377	83	8	sufficient	sufficient	ADJ
ejpam-6377	83	9	condition	condition	NOUN
ejpam-6377	83	10	in	in	ADP
ejpam-6377	83	11	this	this	DET
ejpam-6377	83	12	section	section	NOUN
ejpam-6377	83	13	,	,	PUNCT
ejpam-6377	83	14	we	we	PRON
ejpam-6377	83	15	will	will	AUX
ejpam-6377	83	16	prove	prove	VERB
ejpam-6377	83	17	the	the	DET
ejpam-6377	83	18	conjugacy	conjugacy	ADJ
ejpam-6377	83	19	condition	condition	NOUN
ejpam-6377	83	20	,	,	PUNCT
ejpam-6377	83	21	descent	descent	NOUN
ejpam-6377	83	22	condition	condition	NOUN
ejpam-6377	83	23	,	,	PUNCT
ejpam-6377	83	24	and	and	CCONJ
ejpam-6377	83	25	sufficient	sufficient	ADJ
ejpam-6377	83	26	of	of	ADP
ejpam-6377	83	27	the	the	DET
ejpam-6377	83	28	new	new	ADJ
ejpam-6377	83	29	method	method	NOUN
ejpam-6377	83	30	.	.	PUNCT
ejpam-6377	84	1	theorem	theorem	NOUN
ejpam-6377	84	2	1	1	NUM
ejpam-6377	84	3	:	:	PUNCT
ejpam-6377	84	4	assume	assume	VERB
ejpam-6377	84	5	that	that	SCONJ
ejpam-6377	84	6	the	the	DET
ejpam-6377	84	7	sequence	sequence	NOUN
ejpam-6377	84	8	{	{	PUNCT
ejpam-6377	84	9	xk	xk	ADJ
ejpam-6377	84	10	}	}	PUNCT
ejpam-6377	84	11	is	be	AUX
ejpam-6377	84	12	generated	generate	VERB
ejpam-6377	84	13	by	by	ADP
ejpam-6377	84	14	(	(	PUNCT
ejpam-6377	84	15	1.2	1.2	NUM
ejpam-6377	84	16	)	)	PUNCT
ejpam-6377	84	17	,	,	PUNCT
ejpam-6377	84	18	then	then	ADV
ejpam-6377	84	19	the	the	DET
ejpam-6377	84	20	new	new	ADJ
ejpam-6377	84	21	method	method	NOUN
ejpam-6377	84	22	(	(	PUNCT
ejpam-6377	84	23	2.3	2.3	NUM
ejpam-6377	84	24	)	)	PUNCT
ejpam-6377	84	25	satisfies	satisfy	VERB
ejpam-6377	84	26	the	the	DET
ejpam-6377	84	27	conjugacy	conjugacy	PROPN
ejpam-6377	84	28	condition	condition	NOUN
ejpam-6377	84	29	,	,	PUNCT
ejpam-6377	84	30	i.e.	i.e.	X
ejpam-6377	84	31	dtk+1yk	dtk+1yk	PROPN
ejpam-6377	84	32	=	=	SYM
ejpam-6377	84	33	t	t	PROPN
ejpam-6377	84	34	gtk+1vk	gtk+1vk	PROPN
ejpam-6377	84	35	,	,	PUNCT
ejpam-6377	84	36	where	where	SCONJ
ejpam-6377	84	37	t	t	PROPN
ejpam-6377	84	38	>	>	X
ejpam-6377	84	39	0	0	X
ejpam-6377	84	40	.	.	PUNCT
ejpam-6377	85	1	proof	proof	NOUN
ejpam-6377	85	2	:	:	PUNCT
ejpam-6377	85	3	by	by	ADP
ejpam-6377	85	4	putting	put	VERB
ejpam-6377	85	5	(	(	PUNCT
ejpam-6377	85	6	2.3	2.3	NUM
ejpam-6377	85	7	)	)	PUNCT
ejpam-6377	85	8	in	in	ADP
ejpam-6377	85	9	equation	equation	NOUN
ejpam-6377	85	10	(	(	PUNCT
ejpam-6377	85	11	1.3	1.3	NUM
ejpam-6377	85	12	)	)	PUNCT
ejpam-6377	85	13	to	to	PART
ejpam-6377	85	14	get	get	VERB
ejpam-6377	85	15	dk+1	dk+1	NOUN
ejpam-6377	85	16	=	=	SYM
ejpam-6377	85	17	−gk+1	−gk+1	PROPN
ejpam-6377	85	18	+	+	CCONJ
ejpam-6377	85	19	βnew	βnew	ADJ
ejpam-6377	85	20	k	k	PROPN
ejpam-6377	85	21	dk	dk	PROPN
ejpam-6377	85	22	or	or	CCONJ
ejpam-6377	85	23	,	,	PUNCT
ejpam-6377	85	24	dk+1	dk+1	X
ejpam-6377	85	25	=	=	SYM
ejpam-6377	85	26	−gk+1	−gk+1	PROPN
ejpam-6377	85	27	+	+	CCONJ
ejpam-6377	85	28	(	(	PUNCT
ejpam-6377	85	29	gtk+1yk	gtk+1yk	PROPN
ejpam-6377	85	30	dtk	dtk	PROPN
ejpam-6377	85	31	yk	yk	PROPN
ejpam-6377	85	32	−	−	PROPN
ejpam-6377	85	33	µ	µ	X
ejpam-6377	85	34	∥gk+1∥2∥vk∥2∥xk+1∥	∥gk+1∥2∥vk∥2∥xk+1∥	PROPN
ejpam-6377	85	35	(	(	PUNCT
ejpam-6377	85	36	dtk	dtk	PROPN
ejpam-6377	85	37	yk	yk	PROPN
ejpam-6377	85	38	)	)	PUNCT
ejpam-6377	85	39	2	2	NUM
ejpam-6377	85	40	gtk+1dk	gtk+1dk	PROPN
ejpam-6377	85	41	)	)	PUNCT
ejpam-6377	86	1	dk	dk	PROPN
ejpam-6377	86	2	(	(	PUNCT
ejpam-6377	86	3	2.4	2.4	NUM
ejpam-6377	86	4	)	)	PUNCT
ejpam-6377	86	5	multiply	multiply	ADP
ejpam-6377	86	6	both	both	DET
ejpam-6377	86	7	sides	side	NOUN
ejpam-6377	86	8	of	of	ADP
ejpam-6377	86	9	equation	equation	NOUN
ejpam-6377	86	10	(	(	PUNCT
ejpam-6377	86	11	2.4	2.4	NUM
ejpam-6377	86	12	)	)	PUNCT
ejpam-6377	86	13	by	by	ADP
ejpam-6377	86	14	yk	yk	PROPN
ejpam-6377	86	15	from	from	ADP
ejpam-6377	86	16	right	right	ADJ
ejpam-6377	86	17	-	-	PUNCT
ejpam-6377	86	18	hand	hand	NOUN
ejpam-6377	86	19	side	side	NOUN
ejpam-6377	86	20	,	,	PUNCT
ejpam-6377	86	21	we	we	PRON
ejpam-6377	86	22	get	get	VERB
ejpam-6377	86	23	dtk+1yk	dtk+1yk	ADJ
ejpam-6377	86	24	=	=	SYM
ejpam-6377	86	25	−gtk+1yk	−gtk+1yk	PROPN
ejpam-6377	86	26	+	+	CCONJ
ejpam-6377	87	1	gtk+1yk	gtk+1yk	PROPN
ejpam-6377	87	2	dtk	dtk	PROPN
ejpam-6377	87	3	yk	yk	PROPN
ejpam-6377	87	4	dtk	dtk	PROPN
ejpam-6377	87	5	yk	yk	PROPN
ejpam-6377	87	6	−	−	PROPN
ejpam-6377	87	7	µ	µ	X
ejpam-6377	87	8	∥gk+1∥2∥vk∥2∥xk+1∥	∥gk+1∥2∥vk∥2∥xk+1∥	PROPN
ejpam-6377	87	9	(	(	PUNCT
ejpam-6377	87	10	dtk	dtk	PROPN
ejpam-6377	87	11	yk	yk	PROPN
ejpam-6377	87	12	)	)	PUNCT
ejpam-6377	87	13	2	2	NUM
ejpam-6377	88	1	gtk+1dkd	gtk+1dkd	PROPN
ejpam-6377	88	2	t	t	PROPN
ejpam-6377	88	3	k	k	PROPN
ejpam-6377	88	4	yk	yk	PROPN
ejpam-6377	88	5	or	or	CCONJ
ejpam-6377	88	6	,	,	PUNCT
ejpam-6377	88	7	dtk+1yk	dtk+1yk	PROPN
ejpam-6377	88	8	=	=	SYM
ejpam-6377	88	9	−µ	−µ	NOUN
ejpam-6377	88	10	∥gk+1∥2∥vk∥2∥xk+1∥	∥gk+1∥2∥vk∥2∥xk+1∥	PROPN
ejpam-6377	88	11	dtk	dtk	PROPN
ejpam-6377	88	12	yk	yk	PROPN
ejpam-6377	88	13	gtk+1dk	gtk+1dk	PROPN
ejpam-6377	88	14	(	(	PUNCT
ejpam-6377	88	15	2.5	2.5	NUM
ejpam-6377	88	16	)	)	PUNCT
ejpam-6377	88	17	implies	imply	VERB
ejpam-6377	88	18	that	that	SCONJ
ejpam-6377	88	19	dtk+1yk	dtk+1yk	PROPN
ejpam-6377	88	20	=	=	PUNCT
ejpam-6377	88	21	−	−	PROPN
ejpam-6377	88	22	(	(	PUNCT
ejpam-6377	88	23	µ	µ	NOUN
ejpam-6377	88	24	1	1	NUM
ejpam-6377	88	25	αk	αk	ADP
ejpam-6377	88	26	∥gk+1∥2∥vk∥2∥xk+1∥	∥gk+1∥2∥vk∥2∥xk+1∥	PROPN
ejpam-6377	88	27	dtk	dtk	PROPN
ejpam-6377	88	28	yk	yk	PROPN
ejpam-6377	88	29	)	)	PUNCT
ejpam-6377	88	30	gtk+1vk	gtk+1vk	PROPN
ejpam-6377	88	31	(	(	PUNCT
ejpam-6377	88	32	2.6	2.6	NUM
ejpam-6377	88	33	)	)	PUNCT
ejpam-6377	88	34	suppose	suppose	VERB
ejpam-6377	88	35	that	that	SCONJ
ejpam-6377	88	36	t	t	NOUN
ejpam-6377	88	37	=	=	SYM
ejpam-6377	88	38	(	(	PUNCT
ejpam-6377	88	39	µ	µ	X
ejpam-6377	88	40	1	1	NUM
ejpam-6377	88	41	αk	αk	ADP
ejpam-6377	88	42	∥gk+1∥2∥vk∥2∥xk+1∥	∥gk+1∥2∥vk∥2∥xk+1∥	PROPN
ejpam-6377	88	43	dtk	dtk	PROPN
ejpam-6377	88	44	yk	yk	PROPN
ejpam-6377	88	45	)	)	PUNCT
ejpam-6377	88	46	then	then	ADV
ejpam-6377	88	47	,	,	PUNCT
ejpam-6377	88	48	dtk+1yk	dtk+1yk	PROPN
ejpam-6377	88	49	=	=	SYM
ejpam-6377	88	50	−t	−t	NOUN
ejpam-6377	88	51	gtk+1vk	gtk+1vk	NOUN
ejpam-6377	88	52	theorem	theorem	VERB
ejpam-6377	88	53	2	2	NUM
ejpam-6377	88	54	:	:	PUNCT
ejpam-6377	88	55	assume	assume	VERB
ejpam-6377	88	56	that	that	SCONJ
ejpam-6377	88	57	the	the	DET
ejpam-6377	88	58	sequence	sequence	NOUN
ejpam-6377	88	59	{	{	PUNCT
ejpam-6377	88	60	xk	xk	ADJ
ejpam-6377	88	61	}	}	PUNCT
ejpam-6377	88	62	is	be	AUX
ejpam-6377	88	63	generated	generate	VERB
ejpam-6377	88	64	by	by	ADP
ejpam-6377	88	65	(	(	PUNCT
ejpam-6377	88	66	1.2	1.2	NUM
ejpam-6377	88	67	)	)	PUNCT
ejpam-6377	88	68	,	,	PUNCT
ejpam-6377	88	69	then	then	ADV
ejpam-6377	88	70	the	the	DET
ejpam-6377	88	71	search	search	NOUN
ejpam-6377	88	72	direction	direction	NOUN
ejpam-6377	88	73	(	(	PUNCT
ejpam-6377	88	74	1.3	1.3	NUM
ejpam-6377	88	75	)	)	PUNCT
ejpam-6377	88	76	of	of	ADP
ejpam-6377	88	77	the	the	DET
ejpam-6377	88	78	new	new	ADJ
ejpam-6377	88	79	method	method	NOUN
ejpam-6377	88	80	(	(	PUNCT
ejpam-6377	88	81	2.3	2.3	NUM
ejpam-6377	88	82	)	)	PUNCT
ejpam-6377	88	83	satisfies	satisfy	VERB
ejpam-6377	88	84	the	the	DET
ejpam-6377	88	85	descent	descent	NOUN
ejpam-6377	88	86	condition	condition	NOUN
ejpam-6377	88	87	,	,	PUNCT
ejpam-6377	88	88	i.e.	i.e.	X
ejpam-6377	88	89	dtk+1gk+1	dtk+1gk+1	X
ejpam-6377	88	90	≤	≤	X
ejpam-6377	88	91	0	0	NUM
ejpam-6377	88	92	with	with	ADP
ejpam-6377	88	93	exact	exact	ADJ
ejpam-6377	88	94	and	and	CCONJ
ejpam-6377	88	95	inexact	inexact	ADJ
ejpam-6377	88	96	line	line	NOUN
ejpam-6377	88	97	search	search	NOUN
ejpam-6377	88	98	.	.	PUNCT
ejpam-6377	89	1	proof	proof	NOUN
ejpam-6377	89	2	:	:	PUNCT
ejpam-6377	89	3	we	we	PRON
ejpam-6377	89	4	will	will	AUX
ejpam-6377	89	5	prove	prove	VERB
ejpam-6377	89	6	by	by	ADP
ejpam-6377	89	7	mathematical	mathematical	ADJ
ejpam-6377	89	8	induction	induction	NOUN
ejpam-6377	89	9	.	.	PUNCT
ejpam-6377	90	1	if	if	SCONJ
ejpam-6377	90	2	k	k	PROPN
ejpam-6377	90	3	=	=	SYM
ejpam-6377	90	4	0	0	PROPN
ejpam-6377	90	5	,	,	PUNCT
ejpam-6377	90	6	then	then	ADV
ejpam-6377	90	7	,	,	PUNCT
ejpam-6377	90	8	d0	d0	PROPN
ejpam-6377	90	9	=	=	SYM
ejpam-6377	90	10	−g0	−g0	PROPN
ejpam-6377	90	11	,	,	PUNCT
ejpam-6377	90	12	dt0	dt0	NOUN
ejpam-6377	90	13	g0	g0	NOUN
ejpam-6377	90	14	=	=	SYM
ejpam-6377	90	15	−gt0	−gt0	NOUN
ejpam-6377	90	16	g0	g0	NOUN
ejpam-6377	90	17	=	=	PUNCT
ejpam-6377	90	18	−∥g0∥2	−∥g0∥2	PRON
ejpam-6377	90	19	≤	≤	NUM
ejpam-6377	90	20	0	0	NUM
ejpam-6377	90	21	,	,	PUNCT
ejpam-6377	90	22	we	we	PRON
ejpam-6377	90	23	suppose	suppose	VERB
ejpam-6377	90	24	that	that	SCONJ
ejpam-6377	90	25	dtk	dtk	PROPN
ejpam-6377	90	26	gk	gk	PROPN
ejpam-6377	90	27	≤	≤	PROPN
ejpam-6377	90	28	0	0	NUM
ejpam-6377	90	29	.	.	PUNCT
ejpam-6377	90	30	a.	a.	PROPN
ejpam-6377	90	31	a.	a.	PROPN
ejpam-6377	90	32	mustafa	mustafa	PROPN
ejpam-6377	90	33	,	,	PUNCT
ejpam-6377	90	34	h.	h.	PROPN
ejpam-6377	90	35	a.	a.	PROPN
ejpam-6377	90	36	khatab	khatab	PROPN
ejpam-6377	90	37	/	/	SYM
ejpam-6377	90	38	eur	eur	PROPN
ejpam-6377	90	39	.	.	PUNCT
ejpam-6377	91	1	j.	j.	PROPN
ejpam-6377	91	2	pure	pure	PROPN
ejpam-6377	91	3	appl	appl	PROPN
ejpam-6377	91	4	.	.	PROPN
ejpam-6377	91	5	math	math	PROPN
ejpam-6377	91	6	,	,	PUNCT
ejpam-6377	91	7	18	18	NUM
ejpam-6377	91	8	(	(	PUNCT
ejpam-6377	91	9	3	3	NUM
ejpam-6377	91	10	)	)	PUNCT
ejpam-6377	91	11	(	(	PUNCT
ejpam-6377	91	12	2025	2025	NUM
ejpam-6377	91	13	)	)	PUNCT
ejpam-6377	91	14	,	,	PUNCT
ejpam-6377	91	15	6377	6377	NUM
ejpam-6377	91	16	6	6	NUM
ejpam-6377	91	17	of	of	ADP
ejpam-6377	91	18	12	12	NUM
ejpam-6377	91	19	now	now	ADV
ejpam-6377	91	20	,	,	PUNCT
ejpam-6377	91	21	we	we	PRON
ejpam-6377	91	22	prove	prove	VERB
ejpam-6377	91	23	the	the	DET
ejpam-6377	91	24	case	case	NOUN
ejpam-6377	91	25	k+	k+	NOUN
ejpam-6377	91	26	1	1	X
ejpam-6377	91	27	.	.	X
ejpam-6377	91	28	from	from	ADP
ejpam-6377	91	29	(	(	PUNCT
ejpam-6377	91	30	1.3	1.3	NUM
ejpam-6377	91	31	)	)	PUNCT
ejpam-6377	91	32	and	and	CCONJ
ejpam-6377	91	33	(	(	PUNCT
ejpam-6377	91	34	2.3	2.3	NUM
ejpam-6377	91	35	)	)	PUNCT
ejpam-6377	91	36	,	,	PUNCT
ejpam-6377	91	37	we	we	PRON
ejpam-6377	91	38	have	have	VERB
ejpam-6377	91	39	(	(	PUNCT
ejpam-6377	91	40	2.4	2.4	NUM
ejpam-6377	91	41	)	)	PUNCT
ejpam-6377	91	42	,	,	PUNCT
ejpam-6377	91	43	multiply	multiply	VERB
ejpam-6377	91	44	both	both	DET
ejpam-6377	91	45	sides	side	NOUN
ejpam-6377	91	46	of	of	ADP
ejpam-6377	91	47	equation	equation	NOUN
ejpam-6377	91	48	(	(	PUNCT
ejpam-6377	91	49	2.4	2.4	NUM
ejpam-6377	91	50	)	)	PUNCT
ejpam-6377	91	51	by	by	ADP
ejpam-6377	91	52	gk+1	gk+1	NOUN
ejpam-6377	91	53	from	from	ADP
ejpam-6377	91	54	the	the	DET
ejpam-6377	91	55	right	right	ADJ
ejpam-6377	91	56	-	-	PUNCT
ejpam-6377	91	57	hand	hand	NOUN
ejpam-6377	91	58	side	side	NOUN
ejpam-6377	91	59	,	,	PUNCT
ejpam-6377	91	60	we	we	PRON
ejpam-6377	91	61	get	get	VERB
ejpam-6377	91	62	dtk+1gk+1	dtk+1gk+1	NOUN
ejpam-6377	92	1	=	=	PUNCT
ejpam-6377	92	2	−gtk+1gk+1	−gtk+1gk+1	PROPN
ejpam-6377	93	1	+	+	CCONJ
ejpam-6377	93	2	gtk+1yk	gtk+1yk	PROPN
ejpam-6377	93	3	dtk	dtk	PROPN
ejpam-6377	93	4	yk	yk	PROPN
ejpam-6377	93	5	dtk	dtk	PROPN
ejpam-6377	93	6	gk+1	gk+1	VERB
ejpam-6377	93	7	−	−	PROPN
ejpam-6377	93	8	µ	µ	X
ejpam-6377	93	9	∥gk+1∥2∥vk∥2∥xk+1∥	∥gk+1∥2∥vk∥2∥xk+1∥	X
ejpam-6377	93	10	(	(	PUNCT
ejpam-6377	93	11	dtk	dtk	PROPN
ejpam-6377	93	12	yk	yk	PROPN
ejpam-6377	93	13	)	)	PUNCT
ejpam-6377	93	14	2	2	NUM
ejpam-6377	93	15	gtk+1dkd	gtk+1dkd	PROPN
ejpam-6377	93	16	t	t	PROPN
ejpam-6377	93	17	k	k	PROPN
ejpam-6377	93	18	gk+1	gk+1	NOUN
ejpam-6377	93	19	(	(	PUNCT
ejpam-6377	93	20	2.7	2.7	NUM
ejpam-6377	93	21	)	)	PUNCT
ejpam-6377	93	22	if	if	SCONJ
ejpam-6377	93	23	the	the	DET
ejpam-6377	93	24	step	step	NOUN
ejpam-6377	93	25	length	length	NOUN
ejpam-6377	93	26	αk	αk	NOUN
ejpam-6377	93	27	is	be	AUX
ejpam-6377	93	28	chosen	choose	VERB
ejpam-6377	93	29	by	by	ADP
ejpam-6377	93	30	an	an	DET
ejpam-6377	93	31	exact	exact	ADJ
ejpam-6377	93	32	line	line	NOUN
ejpam-6377	93	33	search	search	NOUN
ejpam-6377	93	34	which	which	PRON
ejpam-6377	93	35	requires	require	VERB
ejpam-6377	93	36	dtk	dtk	PROPN
ejpam-6377	93	37	gk+1	gk+1	NOUN
ejpam-6377	93	38	=	=	SYM
ejpam-6377	93	39	0	0	NUM
ejpam-6377	93	40	,	,	PUNCT
ejpam-6377	93	41	then	then	ADV
ejpam-6377	93	42	the	the	DET
ejpam-6377	93	43	proof	proof	NOUN
ejpam-6377	93	44	is	be	AUX
ejpam-6377	93	45	complete	complete	ADJ
ejpam-6377	93	46	.	.	PUNCT
ejpam-6377	94	1	if	if	SCONJ
ejpam-6377	94	2	the	the	DET
ejpam-6377	94	3	step	step	NOUN
ejpam-6377	94	4	length	length	NOUN
ejpam-6377	94	5	αk	αk	NOUN
ejpam-6377	94	6	is	be	AUX
ejpam-6377	94	7	chosen	choose	VERB
ejpam-6377	94	8	by	by	ADP
ejpam-6377	94	9	inexact	inexact	ADJ
ejpam-6377	94	10	line	line	NOUN
ejpam-6377	94	11	search	search	NOUN
ejpam-6377	94	12	which	which	PRON
ejpam-6377	94	13	requires	require	VERB
ejpam-6377	94	14	dtk	dtk	PROPN
ejpam-6377	94	15	gk+1	gk+1	NOUN
ejpam-6377	94	16	̸=	̸=	PROPN
ejpam-6377	94	17	0	0	NUM
ejpam-6377	94	18	,	,	PUNCT
ejpam-6377	94	19	then	then	ADV
ejpam-6377	94	20	the	the	DET
ejpam-6377	94	21	first	first	ADJ
ejpam-6377	94	22	two	two	NUM
ejpam-6377	94	23	terms	term	NOUN
ejpam-6377	94	24	on	on	ADP
ejpam-6377	94	25	the	the	DET
ejpam-6377	94	26	right	right	ADJ
ejpam-6377	94	27	-	-	PUNCT
ejpam-6377	94	28	hand	hand	NOUN
ejpam-6377	94	29	side	side	NOUN
ejpam-6377	94	30	of	of	ADP
ejpam-6377	94	31	equation	equation	NOUN
ejpam-6377	94	32	(	(	PUNCT
ejpam-6377	94	33	2.7	2.7	NUM
ejpam-6377	94	34	)	)	PUNCT
ejpam-6377	94	35	are	be	AUX
ejpam-6377	94	36	less	less	ADJ
ejpam-6377	94	37	than	than	ADP
ejpam-6377	94	38	or	or	CCONJ
ejpam-6377	94	39	equal	equal	ADJ
ejpam-6377	94	40	to	to	ADP
ejpam-6377	94	41	zero	zero	NUM
ejpam-6377	94	42	since	since	SCONJ
ejpam-6377	94	43	hs	hs	PROPN
ejpam-6377	94	44	satisfies	satisfy	VERB
ejpam-6377	94	45	the	the	DET
ejpam-6377	94	46	descent	descent	NOUN
ejpam-6377	94	47	condition	condition	NOUN
ejpam-6377	94	48	.	.	PUNCT
ejpam-6377	95	1	the	the	DET
ejpam-6377	95	2	third	third	ADJ
ejpam-6377	95	3	term	term	NOUN
ejpam-6377	95	4	is	be	AUX
ejpam-6377	95	5	less	less	ADJ
ejpam-6377	95	6	than	than	ADP
ejpam-6377	95	7	or	or	CCONJ
ejpam-6377	95	8	equal	equal	ADJ
ejpam-6377	95	9	to	to	ADP
ejpam-6377	95	10	zero	zero	NUM
ejpam-6377	95	11	,	,	PUNCT
ejpam-6377	95	12	so	so	SCONJ
ejpam-6377	95	13	we	we	PRON
ejpam-6377	95	14	get	get	VERB
ejpam-6377	95	15	dtk+1gk+1	dtk+1gk+1	PUNCT
ejpam-6377	95	16	≤	≤	NUM
ejpam-6377	95	17	−µ	−µ	ADP
ejpam-6377	95	18	∥gk+1∥2∥vk∥2∥xk+1∥	∥gk+1∥2∥vk∥2∥xk+1∥	PROPN
ejpam-6377	95	19	(	(	PUNCT
ejpam-6377	95	20	dtk	dtk	PROPN
ejpam-6377	95	21	yk	yk	PROPN
ejpam-6377	95	22	)	)	PUNCT
ejpam-6377	95	23	2	2	NUM
ejpam-6377	95	24	(	(	PUNCT
ejpam-6377	95	25	gtk+1dk	gtk+1dk	PROPN
ejpam-6377	95	26	)	)	PUNCT
ejpam-6377	95	27	2	2	NUM
ejpam-6377	95	28	(	(	PUNCT
ejpam-6377	95	29	2.8	2.8	NUM
ejpam-6377	95	30	)	)	PUNCT
ejpam-6377	95	31	then	then	ADV
ejpam-6377	95	32	,	,	PUNCT
ejpam-6377	95	33	dtk+1gk+1	dtk+1gk+1	VERB
ejpam-6377	95	34	≤	≤	ADV
ejpam-6377	95	35	0	0	NUM
ejpam-6377	95	36	.	.	PUNCT
ejpam-6377	96	1	theorem	theorem	NOUN
ejpam-6377	96	2	3	3	NUM
ejpam-6377	96	3	:	:	PUNCT
ejpam-6377	96	4	assume	assume	VERB
ejpam-6377	96	5	that	that	SCONJ
ejpam-6377	96	6	the	the	DET
ejpam-6377	96	7	sequence	sequence	NOUN
ejpam-6377	96	8	{	{	PUNCT
ejpam-6377	96	9	xk	xk	ADJ
ejpam-6377	96	10	}	}	PUNCT
ejpam-6377	96	11	is	be	AUX
ejpam-6377	96	12	generated	generate	VERB
ejpam-6377	96	13	by	by	ADP
ejpam-6377	96	14	(	(	PUNCT
ejpam-6377	96	15	1.2	1.2	NUM
ejpam-6377	96	16	)	)	PUNCT
ejpam-6377	96	17	,	,	PUNCT
ejpam-6377	96	18	then	then	ADV
ejpam-6377	96	19	the	the	DET
ejpam-6377	96	20	search	search	NOUN
ejpam-6377	96	21	direction	direction	NOUN
ejpam-6377	96	22	(	(	PUNCT
ejpam-6377	96	23	1.3	1.3	NUM
ejpam-6377	96	24	)	)	PUNCT
ejpam-6377	96	25	with	with	ADP
ejpam-6377	96	26	the	the	DET
ejpam-6377	96	27	new	new	ADJ
ejpam-6377	96	28	method	method	NOUN
ejpam-6377	96	29	(	(	PUNCT
ejpam-6377	96	30	2.3	2.3	NUM
ejpam-6377	96	31	)	)	PUNCT
ejpam-6377	96	32	satisfies	satisfy	VERB
ejpam-6377	96	33	the	the	DET
ejpam-6377	96	34	sufficient	sufficient	ADJ
ejpam-6377	96	35	descent	descent	NOUN
ejpam-6377	96	36	condition	condition	NOUN
ejpam-6377	96	37	,	,	PUNCT
ejpam-6377	96	38	i.e.	i.e.	X
ejpam-6377	96	39	dtk+1gk+1	dtk+1gk+1	X
ejpam-6377	96	40	≤	≤	PROPN
ejpam-6377	96	41	−c∥gk+1∥2	−c∥gk+1∥2	NOUN
ejpam-6377	96	42	.	.	PUNCT
ejpam-6377	97	1	proof	proof	NOUN
ejpam-6377	97	2	:	:	PUNCT
ejpam-6377	97	3	we	we	PRON
ejpam-6377	97	4	multiply	multiply	VERB
ejpam-6377	97	5	the	the	DET
ejpam-6377	97	6	right	right	ADJ
ejpam-6377	97	7	-	-	PUNCT
ejpam-6377	97	8	hand	hand	NOUN
ejpam-6377	97	9	side	side	NOUN
ejpam-6377	97	10	of	of	ADP
ejpam-6377	97	11	inequality	inequality	NOUN
ejpam-6377	97	12	(	(	PUNCT
ejpam-6377	97	13	2.8	2.8	NUM
ejpam-6377	97	14	)	)	PUNCT
ejpam-6377	97	15	by	by	ADP
ejpam-6377	97	16	∥gk+1∥2	∥gk+1∥2	PROPN
ejpam-6377	97	17	∥gk+1∥2	∥gk+1∥2	NOUN
ejpam-6377	97	18	,	,	PUNCT
ejpam-6377	97	19	we	we	PRON
ejpam-6377	97	20	get	get	VERB
ejpam-6377	97	21	dtk+1gk+1	dtk+1gk+1	PUNCT
ejpam-6377	97	22	≤	≤	NUM
ejpam-6377	97	23	−µ	−µ	ADP
ejpam-6377	97	24	∥gk+1∥2∥vk∥2∥xk+1∥	∥gk+1∥2∥vk∥2∥xk+1∥	PROPN
ejpam-6377	97	25	(	(	PUNCT
ejpam-6377	97	26	dtk	dtk	PROPN
ejpam-6377	97	27	yk	yk	PROPN
ejpam-6377	97	28	)	)	PUNCT
ejpam-6377	97	29	2	2	NUM
ejpam-6377	97	30	(	(	PUNCT
ejpam-6377	97	31	gtk+1dk	gtk+1dk	PROPN
ejpam-6377	97	32	)	)	PUNCT
ejpam-6377	97	33	2	2	NUM
ejpam-6377	97	34	(	(	PUNCT
ejpam-6377	97	35	∥gk+1∥2	∥gk+1∥2	NOUN
ejpam-6377	97	36	∥gk+1∥2	∥gk+1∥2	X
ejpam-6377	97	37	)	)	PUNCT
ejpam-6377	97	38	(	(	PUNCT
ejpam-6377	97	39	2.9	2.9	NUM
ejpam-6377	97	40	)	)	PUNCT
ejpam-6377	97	41	suppose	suppose	VERB
ejpam-6377	97	42	that	that	SCONJ
ejpam-6377	97	43	c	c	PROPN
ejpam-6377	97	44	=	=	SYM
ejpam-6377	97	45	µ	µ	X
ejpam-6377	97	46	∥gk+1∥2∥vk∥2∥xk+1∥	∥gk+1∥2∥vk∥2∥xk+1∥	PROPN
ejpam-6377	97	47	∥gk+1∥2(dtk	∥gk+1∥2(dtk	NOUN
ejpam-6377	97	48	yk)2	yk)2	PROPN
ejpam-6377	97	49	(	(	PUNCT
ejpam-6377	97	50	gtk+1dk	gtk+1dk	PROPN
ejpam-6377	97	51	)	)	PUNCT
ejpam-6377	97	52	2	2	NUM
ejpam-6377	97	53	then	then	ADV
ejpam-6377	97	54	,	,	PUNCT
ejpam-6377	97	55	dtk+1gk+1	dtk+1gk+1	X
ejpam-6377	97	56	≤	≤	X
ejpam-6377	97	57	−c∥gk+1∥2	−c∥gk+1∥2	NOUN
ejpam-6377	97	58	4	4	NUM
ejpam-6377	97	59	.	.	PUNCT
ejpam-6377	97	60	convergence	convergence	NOUN
ejpam-6377	97	61	analysis	analysis	NOUN
ejpam-6377	97	62	assume	assume	VERB
ejpam-6377	97	63	that	that	SCONJ
ejpam-6377	97	64	:	:	PUNCT
ejpam-6377	97	65	•	•	ADP
ejpam-6377	97	66	the	the	DET
ejpam-6377	97	67	level	level	NOUN
ejpam-6377	97	68	set	set	NOUN
ejpam-6377	97	69	s	s	PART
ejpam-6377	97	70	=	=	PUNCT
ejpam-6377	97	71	{	{	PUNCT
ejpam-6377	97	72	x	x	PROPN
ejpam-6377	97	73	∈	∈	PROPN
ejpam-6377	97	74	rn	rn	PROPN
ejpam-6377	97	75	:	:	PUNCT
ejpam-6377	97	76	f(x	f(x	PROPN
ejpam-6377	97	77	)	)	PUNCT
ejpam-6377	97	78	≤	≤	NUM
ejpam-6377	97	79	f(x0	f(x0	NOUN
ejpam-6377	97	80	)	)	PUNCT
ejpam-6377	97	81	}	}	PUNCT
ejpam-6377	97	82	is	be	AUX
ejpam-6377	97	83	bounded	bound	VERB
ejpam-6377	97	84	.	.	PUNCT
ejpam-6377	98	1	•	•	NUM
ejpam-6377	98	2	in	in	ADP
ejpam-6377	98	3	a	a	DET
ejpam-6377	98	4	neighborhood	neighborhood	NOUN
ejpam-6377	98	5	n	n	NOUN
ejpam-6377	98	6	of	of	ADP
ejpam-6377	98	7	s	s	PROPN
ejpam-6377	98	8	,	,	PUNCT
ejpam-6377	98	9	the	the	DET
ejpam-6377	98	10	function	function	NOUN
ejpam-6377	98	11	f	f	PROPN
ejpam-6377	98	12	is	be	AUX
ejpam-6377	98	13	continuously	continuously	ADV
ejpam-6377	98	14	differentiable	differentiable	ADJ
ejpam-6377	98	15	and	and	CCONJ
ejpam-6377	98	16	its	its	PRON
ejpam-6377	98	17	gradient	gradient	NOUN
ejpam-6377	98	18	is	be	AUX
ejpam-6377	98	19	lipschitz	lipschitz	NOUN
ejpam-6377	98	20	continuous	continuous	ADJ
ejpam-6377	98	21	,	,	PUNCT
ejpam-6377	98	22	i.e.	i.e.	X
ejpam-6377	98	23	,	,	PUNCT
ejpam-6377	98	24	there	there	PRON
ejpam-6377	98	25	exists	exist	VERB
ejpam-6377	98	26	a	a	DET
ejpam-6377	98	27	constant	constant	ADJ
ejpam-6377	98	28	l	l	NOUN
ejpam-6377	98	29	>	>	X
ejpam-6377	98	30	0	0	NUM
ejpam-6377	98	31	such	such	ADJ
ejpam-6377	98	32	that	that	SCONJ
ejpam-6377	98	33	∥g(x)−	∥g(x)−	PROPN
ejpam-6377	98	34	g(y)∥	g(y)∥	VERB
ejpam-6377	98	35	≤	≤	PUNCT
ejpam-6377	98	36	l∥x−	l∥x−	ADV
ejpam-6377	98	37	y∥	y∥	VERB
ejpam-6377	98	38	for	for	ADP
ejpam-6377	98	39	all	all	DET
ejpam-6377	98	40	x	x	NOUN
ejpam-6377	98	41	,	,	PUNCT
ejpam-6377	98	42	y	y	PROPN
ejpam-6377	98	43	∈	∈	PROPN
ejpam-6377	98	44	n.	n.	PROPN
ejpam-6377	98	45	a.	a.	PROPN
ejpam-6377	98	46	a.	a.	PROPN
ejpam-6377	98	47	mustafa	mustafa	PROPN
ejpam-6377	98	48	,	,	PUNCT
ejpam-6377	98	49	h.	h.	PROPN
ejpam-6377	98	50	a.	a.	PROPN
ejpam-6377	98	51	khatab	khatab	PROPN
ejpam-6377	98	52	/	/	SYM
ejpam-6377	98	53	eur	eur	PROPN
ejpam-6377	98	54	.	.	PUNCT
ejpam-6377	99	1	j.	j.	PROPN
ejpam-6377	99	2	pure	pure	PROPN
ejpam-6377	99	3	appl	appl	PROPN
ejpam-6377	99	4	.	.	PROPN
ejpam-6377	99	5	math	math	PROPN
ejpam-6377	99	6	,	,	PUNCT
ejpam-6377	99	7	18	18	NUM
ejpam-6377	99	8	(	(	PUNCT
ejpam-6377	99	9	3	3	NUM
ejpam-6377	99	10	)	)	PUNCT
ejpam-6377	99	11	(	(	PUNCT
ejpam-6377	99	12	2025	2025	NUM
ejpam-6377	99	13	)	)	PUNCT
ejpam-6377	99	14	,	,	PUNCT
ejpam-6377	99	15	6377	6377	NUM
ejpam-6377	99	16	7	7	NUM
ejpam-6377	99	17	of	of	ADP
ejpam-6377	99	18	12	12	NUM
ejpam-6377	99	19	under	under	ADP
ejpam-6377	99	20	these	these	DET
ejpam-6377	99	21	assumptions	assumption	NOUN
ejpam-6377	99	22	on	on	ADP
ejpam-6377	99	23	f	f	PROPN
ejpam-6377	100	1	,	,	PUNCT
ejpam-6377	100	2	there	there	PRON
ejpam-6377	100	3	exists	exist	VERB
ejpam-6377	100	4	a	a	DET
ejpam-6377	100	5	constant	constant	ADJ
ejpam-6377	100	6	ρ	ρ	PROPN
ejpam-6377	100	7	≥	≥	NOUN
ejpam-6377	100	8	0	0	NUM
ejpam-6377	100	9	such	such	ADJ
ejpam-6377	100	10	that	that	DET
ejpam-6377	100	11	∥g(x)∥	∥g(x)∥	PROPN
ejpam-6377	100	12	≤	≤	PROPN
ejpam-6377	100	13	ρ	ρ	PROPN
ejpam-6377	100	14	,	,	PUNCT
ejpam-6377	100	15	for	for	ADP
ejpam-6377	100	16	all	all	DET
ejpam-6377	100	17	x	x	SYM
ejpam-6377	100	18	∈	∈	PROPN
ejpam-6377	100	19	s.	s.	PROPN
ejpam-6377	100	20	in	in	ADP
ejpam-6377	100	21	[	[	X
ejpam-6377	100	22	5	5	NUM
ejpam-6377	100	23	]	]	PUNCT
ejpam-6377	100	24	,	,	PUNCT
ejpam-6377	100	25	it	it	PRON
ejpam-6377	100	26	is	be	AUX
ejpam-6377	100	27	proved	prove	VERB
ejpam-6377	100	28	that	that	SCONJ
ejpam-6377	100	29	for	for	ADP
ejpam-6377	100	30	any	any	DET
ejpam-6377	100	31	conjugate	conjugate	ADJ
ejpam-6377	100	32	gradient	gradient	NOUN
ejpam-6377	100	33	method	method	NOUN
ejpam-6377	100	34	with	with	ADP
ejpam-6377	100	35	a	a	DET
ejpam-6377	100	36	strong	strong	ADJ
ejpam-6377	100	37	wolfe	wolfe	NOUN
ejpam-6377	100	38	line	line	NOUN
ejpam-6377	100	39	search	search	VERB
ejpam-6377	100	40	the	the	DET
ejpam-6377	100	41	following	follow	VERB
ejpam-6377	100	42	general	general	ADJ
ejpam-6377	100	43	result	result	NOUN
ejpam-6377	100	44	holds	hold	VERB
ejpam-6377	100	45	:	:	PUNCT
ejpam-6377	100	46	lemma	lemma	PROPN
ejpam-6377	100	47	1	1	NUM
ejpam-6377	100	48	:	:	PUNCT
ejpam-6377	100	49	let	let	VERB
ejpam-6377	100	50	assumption	assumption	NOUN
ejpam-6377	100	51	(	(	PUNCT
ejpam-6377	100	52	i	i	NOUN
ejpam-6377	100	53	)	)	PUNCT
ejpam-6377	100	54	and	and	CCONJ
ejpam-6377	100	55	(	(	PUNCT
ejpam-6377	100	56	ii	ii	NOUN
ejpam-6377	100	57	)	)	PUNCT
ejpam-6377	100	58	hold	hold	VERB
ejpam-6377	100	59	and	and	CCONJ
ejpam-6377	100	60	consider	consider	VERB
ejpam-6377	100	61	any	any	DET
ejpam-6377	100	62	conjugate	conjugate	ADJ
ejpam-6377	100	63	gradient	gradient	NOUN
ejpam-6377	100	64	method	method	NOUN
ejpam-6377	100	65	(	(	PUNCT
ejpam-6377	100	66	1.3	1.3	NUM
ejpam-6377	100	67	)	)	PUNCT
ejpam-6377	100	68	and	and	CCONJ
ejpam-6377	100	69	(	(	PUNCT
ejpam-6377	100	70	2.3	2.3	NUM
ejpam-6377	100	71	)	)	PUNCT
ejpam-6377	100	72	,	,	PUNCT
ejpam-6377	100	73	where	where	SCONJ
ejpam-6377	100	74	dk	dk	PROPN
ejpam-6377	100	75	is	be	AUX
ejpam-6377	100	76	a	a	DET
ejpam-6377	100	77	descent	descent	NOUN
ejpam-6377	100	78	direction	direction	NOUN
ejpam-6377	100	79	and	and	CCONJ
ejpam-6377	100	80	αk	αk	NOUN
ejpam-6377	100	81	is	be	AUX
ejpam-6377	100	82	obtained	obtain	VERB
ejpam-6377	100	83	by	by	ADP
ejpam-6377	100	84	the	the	DET
ejpam-6377	100	85	strong	strong	ADJ
ejpam-6377	100	86	wolfe	wolfe	PROPN
ejpam-6377	100	87	line	line	NOUN
ejpam-6377	100	88	search	search	NOUN
ejpam-6377	100	89	.	.	PUNCT
ejpam-6377	101	1	if	if	SCONJ
ejpam-6377	101	2	∑	∑	PUNCT
ejpam-6377	101	3	k≥1	k≥1	PROPN
ejpam-6377	101	4	1	1	NUM
ejpam-6377	101	5	∥dk+1∥2	∥dk+1∥2	NOUN
ejpam-6377	101	6	=	=	SYM
ejpam-6377	101	7	∞	∞	PROPN
ejpam-6377	101	8	(	(	PUNCT
ejpam-6377	101	9	4.1	4.1	NUM
ejpam-6377	101	10	)	)	PUNCT
ejpam-6377	101	11	then	then	ADV
ejpam-6377	101	12	,	,	PUNCT
ejpam-6377	101	13	lim	lim	PROPN
ejpam-6377	101	14	k→∞	k→∞	NOUN
ejpam-6377	101	15	∥gk+1∥	∥gk+1∥	NUM
ejpam-6377	101	16	=	=	NOUN
ejpam-6377	101	17	0	0	NUM
ejpam-6377	101	18	.	.	PUNCT
ejpam-6377	102	1	(	(	PUNCT
ejpam-6377	102	2	4.2	4.2	NUM
ejpam-6377	102	3	)	)	PUNCT
ejpam-6377	102	4	for	for	ADP
ejpam-6377	102	5	a	a	DET
ejpam-6377	102	6	uniformly	uniformly	ADJ
ejpam-6377	102	7	convex	convex	NOUN
ejpam-6377	102	8	function	function	NOUN
ejpam-6377	102	9	which	which	PRON
ejpam-6377	102	10	satisfies	satisfy	VERB
ejpam-6377	102	11	the	the	DET
ejpam-6377	102	12	above	above	ADJ
ejpam-6377	102	13	assumptions	assumption	NOUN
ejpam-6377	102	14	,	,	PUNCT
ejpam-6377	102	15	we	we	PRON
ejpam-6377	102	16	can	can	AUX
ejpam-6377	102	17	prove	prove	VERB
ejpam-6377	102	18	that	that	SCONJ
ejpam-6377	102	19	the	the	DET
ejpam-6377	102	20	norm	norm	NOUN
ejpam-6377	102	21	of	of	ADP
ejpam-6377	102	22	dk+1	dk+1	NOUN
ejpam-6377	102	23	given	give	VERB
ejpam-6377	102	24	by	by	ADP
ejpam-6377	102	25	(	(	PUNCT
ejpam-6377	102	26	1.3	1.3	NUM
ejpam-6377	102	27	)	)	PUNCT
ejpam-6377	102	28	and	and	CCONJ
ejpam-6377	102	29	(	(	PUNCT
ejpam-6377	102	30	2.3	2.3	NUM
ejpam-6377	102	31	)	)	PUNCT
ejpam-6377	102	32	is	be	AUX
ejpam-6377	102	33	bounded	bound	VERB
ejpam-6377	102	34	above	above	ADV
ejpam-6377	102	35	.	.	PUNCT
ejpam-6377	103	1	assume	assume	VERB
ejpam-6377	103	2	that	that	SCONJ
ejpam-6377	103	3	the	the	DET
ejpam-6377	103	4	function	function	NOUN
ejpam-6377	103	5	f	f	PROPN
ejpam-6377	103	6	is	be	AUX
ejpam-6377	103	7	uniformly	uniformly	ADV
ejpam-6377	103	8	convex	convex	NOUN
ejpam-6377	103	9	,	,	PUNCT
ejpam-6377	103	10	i.e.	i.e.	X
ejpam-6377	103	11	,	,	PUNCT
ejpam-6377	103	12	there	there	PRON
ejpam-6377	103	13	exists	exist	VERB
ejpam-6377	103	14	a	a	DET
ejpam-6377	103	15	constant	constant	ADJ
ejpam-6377	103	16	δ	δ	PROPN
ejpam-6377	103	17	≥	≥	NUM
ejpam-6377	103	18	0	0	NUM
ejpam-6377	103	19	,	,	PUNCT
ejpam-6377	103	20	such	such	ADJ
ejpam-6377	103	21	that	that	PRON
ejpam-6377	103	22	for	for	ADP
ejpam-6377	103	23	all	all	DET
ejpam-6377	103	24	x	x	NOUN
ejpam-6377	103	25	,	,	PUNCT
ejpam-6377	103	26	xk	xk	PROPN
ejpam-6377	103	27	∈	∈	PROPN
ejpam-6377	103	28	s	s	PART
ejpam-6377	103	29	(	(	PUNCT
ejpam-6377	103	30	g(x)−	g(x)−	PROPN
ejpam-6377	103	31	g(xk	g(xk	PROPN
ejpam-6377	103	32	)	)	PUNCT
ejpam-6377	103	33	)	)	PUNCT
ejpam-6377	103	34	t	t	PROPN
ejpam-6377	103	35	(	(	PUNCT
ejpam-6377	103	36	x−	x−	PROPN
ejpam-6377	103	37	xk	xk	PROPN
ejpam-6377	103	38	)	)	PUNCT
ejpam-6377	103	39	≥	≥	PROPN
ejpam-6377	103	40	δ∥x−	δ∥x−	PROPN
ejpam-6377	103	41	xk∥2	xk∥2	PROPN
ejpam-6377	103	42	.	.	PUNCT
ejpam-6377	104	1	(	(	PUNCT
ejpam-6377	104	2	4.3	4.3	NUM
ejpam-6377	104	3	)	)	PUNCT
ejpam-6377	104	4	and	and	CCONJ
ejpam-6377	104	5	the	the	DET
ejpam-6377	104	6	step	step	NOUN
ejpam-6377	104	7	length	length	NOUN
ejpam-6377	104	8	αk	αk	NOUN
ejpam-6377	104	9	is	be	AUX
ejpam-6377	104	10	given	give	VERB
ejpam-6377	104	11	by	by	ADP
ejpam-6377	104	12	a	a	DET
ejpam-6377	104	13	strong	strong	ADJ
ejpam-6377	104	14	wolfe	wolfe	PROPN
ejpam-6377	104	15	line	line	NOUN
ejpam-6377	104	16	search	search	NOUN
ejpam-6377	104	17	:	:	PUNCT
ejpam-6377	104	18	f(xk	f(xk	PROPN
ejpam-6377	104	19	+	+	NUM
ejpam-6377	104	20	αkdk	αkdk	NOUN
ejpam-6377	104	21	)	)	PUNCT
ejpam-6377	104	22	≤	≤	NUM
ejpam-6377	104	23	f(xk	f(xk	PROPN
ejpam-6377	104	24	)	)	PUNCT
ejpam-6377	104	25	+	+	CCONJ
ejpam-6377	105	1	c1αkg	c1αkg	NOUN
ejpam-6377	105	2	t	t	NOUN
ejpam-6377	105	3	k	k	PROPN
ejpam-6377	105	4	dk	dk	PROPN
ejpam-6377	105	5	(	(	PUNCT
ejpam-6377	105	6	4.4)∣∣∇f(xk	4.4)∣∣∇f(xk	NUM
ejpam-6377	105	7	+	+	NUM
ejpam-6377	105	8	αkdk	αkdk	NOUN
ejpam-6377	105	9	)	)	PUNCT
ejpam-6377	105	10	tdk	tdk	NOUN
ejpam-6377	105	11	∣∣	∣∣	X
ejpam-6377	105	12	≤	≤	X
ejpam-6377	105	13	c2|gtk	c2|gtk	PUNCT
ejpam-6377	105	14	dk|	dk|	X
ejpam-6377	105	15	(	(	PUNCT
ejpam-6377	105	16	4.5	4.5	NUM
ejpam-6377	105	17	)	)	PUNCT
ejpam-6377	105	18	using	use	VERB
ejpam-6377	105	19	lemma	lemma	PROPN
ejpam-6377	105	20	1	1	NUM
ejpam-6377	105	21	the	the	DET
ejpam-6377	105	22	following	following	ADJ
ejpam-6377	105	23	result	result	NOUN
ejpam-6377	105	24	can	can	AUX
ejpam-6377	105	25	be	be	AUX
ejpam-6377	105	26	proved	prove	VERB
ejpam-6377	105	27	.	.	PUNCT
ejpam-6377	106	1	theorem	theorem	ADJ
ejpam-6377	106	2	4	4	NUM
ejpam-6377	106	3	:	:	PUNCT
ejpam-6377	106	4	suppose	suppose	VERB
ejpam-6377	106	5	that	that	SCONJ
ejpam-6377	106	6	the	the	DET
ejpam-6377	106	7	assumptions	assumption	NOUN
ejpam-6377	106	8	(	(	PUNCT
ejpam-6377	106	9	i	i	NOUN
ejpam-6377	106	10	)	)	PUNCT
ejpam-6377	106	11	and	and	CCONJ
ejpam-6377	106	12	(	(	PUNCT
ejpam-6377	106	13	ii	ii	NOUN
ejpam-6377	106	14	)	)	PUNCT
ejpam-6377	106	15	hold	hold	VERB
ejpam-6377	106	16	.	.	PUNCT
ejpam-6377	107	1	consider	consider	VERB
ejpam-6377	107	2	the	the	DET
ejpam-6377	107	3	algorithm	algorithm	NOUN
ejpam-6377	107	4	(	(	PUNCT
ejpam-6377	107	5	2.3	2.3	NUM
ejpam-6377	107	6	)	)	PUNCT
ejpam-6377	107	7	and	and	CCONJ
ejpam-6377	107	8	where	where	SCONJ
ejpam-6377	107	9	µ	µ	X
ejpam-6377	107	10	>	>	X
ejpam-6377	107	11	0	0	PUNCT
ejpam-6377	108	1	and	and	CCONJ
ejpam-6377	108	2	αk	αk	NOUN
ejpam-6377	108	3	is	be	AUX
ejpam-6377	108	4	obtained	obtain	VERB
ejpam-6377	108	5	by	by	ADP
ejpam-6377	108	6	a	a	DET
ejpam-6377	108	7	strong	strong	ADJ
ejpam-6377	108	8	wolfe	wolfe	PROPN
ejpam-6377	108	9	line	line	NOUN
ejpam-6377	108	10	search	search	NOUN
ejpam-6377	108	11	.	.	PUNCT
ejpam-6377	109	1	if	if	SCONJ
ejpam-6377	109	2	dk	dk	PROPN
ejpam-6377	109	3	tends	tend	VERB
ejpam-6377	109	4	to	to	ADP
ejpam-6377	109	5	zero	zero	NUM
ejpam-6377	109	6	and	and	CCONJ
ejpam-6377	109	7	there	there	PRON
ejpam-6377	109	8	exist	exist	VERB
ejpam-6377	109	9	nonnegative	nonnegative	ADJ
ejpam-6377	109	10	constants	constant	NOUN
ejpam-6377	109	11	η1	η1	NOUN
ejpam-6377	109	12	and	and	CCONJ
ejpam-6377	109	13	η2	η2	VERB
ejpam-6377	109	14	such	such	ADJ
ejpam-6377	109	15	that	that	SCONJ
ejpam-6377	109	16	∥gk∥2	∥gk∥2	PROPN
ejpam-6377	109	17	≥	≥	PROPN
ejpam-6377	109	18	η1∥vk∥2	η1∥vk∥2	PROPN
ejpam-6377	109	19	and	and	CCONJ
ejpam-6377	109	20	∥gk+1∥2	∥gk+1∥2	ADJ
ejpam-6377	109	21	≤	≤	ADJ
ejpam-6377	109	22	η2∥vk∥	η2∥vk∥	PROPN
ejpam-6377	109	23	(	(	PUNCT
ejpam-6377	109	24	4.6	4.6	NUM
ejpam-6377	109	25	)	)	PUNCT
ejpam-6377	109	26	and	and	CCONJ
ejpam-6377	109	27	f	f	PROPN
ejpam-6377	109	28	is	be	AUX
ejpam-6377	109	29	a	a	DET
ejpam-6377	109	30	uniformly	uniformly	ADV
ejpam-6377	109	31	convex	convex	NOUN
ejpam-6377	109	32	function	function	NOUN
ejpam-6377	109	33	,	,	PUNCT
ejpam-6377	109	34	then	then	ADV
ejpam-6377	109	35	lim	lim	PROPN
ejpam-6377	109	36	k→∞	k→∞	NOUN
ejpam-6377	109	37	gk+1	gk+1	AUX
ejpam-6377	110	1	=	=	SYM
ejpam-6377	110	2	0	0	PUNCT
ejpam-6377	110	3	(	(	PUNCT
ejpam-6377	110	4	4.7	4.7	NUM
ejpam-6377	110	5	)	)	PUNCT
ejpam-6377	110	6	proof	proof	NOUN
ejpam-6377	110	7	:	:	PUNCT
ejpam-6377	110	8	consider	consider	VERB
ejpam-6377	110	9	the	the	DET
ejpam-6377	110	10	new	new	ADJ
ejpam-6377	110	11	method	method	NOUN
ejpam-6377	110	12	βnew	βnew	ADJ
ejpam-6377	110	13	k	k	PROPN
ejpam-6377	110	14	=	=	PROPN
ejpam-6377	110	15	gtk+1yk	gtk+1yk	PROPN
ejpam-6377	110	16	dtk	dtk	PROPN
ejpam-6377	110	17	yk	yk	PROPN
ejpam-6377	110	18	−	−	PROPN
ejpam-6377	110	19	µ	µ	X
ejpam-6377	110	20	∥gk+1∥2∥vk∥2∥xk+1∥	∥gk+1∥2∥vk∥2∥xk+1∥	PROPN
ejpam-6377	110	21	(	(	PUNCT
ejpam-6377	110	22	dtk	dtk	PROPN
ejpam-6377	110	23	yk	yk	PROPN
ejpam-6377	110	24	)	)	PUNCT
ejpam-6377	110	25	2	2	NUM
ejpam-6377	110	26	gtk+1dk	gtk+1dk	NOUN
ejpam-6377	110	27	or	or	CCONJ
ejpam-6377	110	28	,	,	PUNCT
ejpam-6377	110	29	|βnew	|βnew	VERB
ejpam-6377	110	30	k	k	PROPN
ejpam-6377	111	1	|	|	ADV
ejpam-6377	111	2	=	=	SYM
ejpam-6377	112	1	|	|	ADV
ejpam-6377	112	2	gtk+1yk	gtk+1yk	PROPN
ejpam-6377	112	3	dtk	dtk	PROPN
ejpam-6377	112	4	yk	yk	PROPN
ejpam-6377	112	5	−	−	PROPN
ejpam-6377	112	6	µ	µ	X
ejpam-6377	112	7	∥gk+1∥2∥vk∥2∥xk+1∥	∥gk+1∥2∥vk∥2∥xk+1∥	PROPN
ejpam-6377	112	8	(	(	PUNCT
ejpam-6377	112	9	dtk	dtk	PROPN
ejpam-6377	112	10	yk	yk	PROPN
ejpam-6377	112	11	)	)	PUNCT
ejpam-6377	112	12	2	2	NUM
ejpam-6377	112	13	gtk+1dk|	gtk+1dk|	PROPN
ejpam-6377	112	14	a.	a.	NOUN
ejpam-6377	112	15	a.	a.	PROPN
ejpam-6377	112	16	mustafa	mustafa	PROPN
ejpam-6377	112	17	,	,	PUNCT
ejpam-6377	112	18	h.	h.	PROPN
ejpam-6377	112	19	a.	a.	PROPN
ejpam-6377	112	20	khatab	khatab	PROPN
ejpam-6377	112	21	/	/	SYM
ejpam-6377	112	22	eur	eur	PROPN
ejpam-6377	112	23	.	.	PUNCT
ejpam-6377	113	1	j.	j.	PROPN
ejpam-6377	113	2	pure	pure	PROPN
ejpam-6377	113	3	appl	appl	PROPN
ejpam-6377	113	4	.	.	PROPN
ejpam-6377	113	5	math	math	PROPN
ejpam-6377	113	6	,	,	PUNCT
ejpam-6377	113	7	18	18	NUM
ejpam-6377	113	8	(	(	PUNCT
ejpam-6377	113	9	3	3	NUM
ejpam-6377	113	10	)	)	PUNCT
ejpam-6377	113	11	(	(	PUNCT
ejpam-6377	113	12	2025	2025	NUM
ejpam-6377	113	13	)	)	PUNCT
ejpam-6377	113	14	,	,	PUNCT
ejpam-6377	113	15	6377	6377	NUM
ejpam-6377	113	16	8	8	NUM
ejpam-6377	113	17	of	of	ADP
ejpam-6377	113	18	12	12	NUM
ejpam-6377	113	19	this	this	PRON
ejpam-6377	113	20	implies	imply	VERB
ejpam-6377	113	21	that	that	PRON
ejpam-6377	113	22	|βnew	|βnew	VERB
ejpam-6377	114	1	k	k	PROPN
ejpam-6377	115	1	|	|	ADV
ejpam-6377	115	2	≤	≤	PROPN
ejpam-6377	115	3	∥gk+1∥∥yk∥	∥gk+1∥∥yk∥	VERB
ejpam-6377	115	4	dtk	dtk	PROPN
ejpam-6377	115	5	yk	yk	PROPN
ejpam-6377	115	6	+	+	PROPN
ejpam-6377	115	7	µ	µ	X
ejpam-6377	115	8	∥gk+1∥2∥vk∥2∥xk+1∥	∥gk+1∥2∥vk∥2∥xk+1∥	PROPN
ejpam-6377	115	9	αk(d	αk(d	PROPN
ejpam-6377	115	10	t	t	PROPN
ejpam-6377	115	11	k	k	PROPN
ejpam-6377	115	12	yk	yk	PROPN
ejpam-6377	115	13	)	)	PUNCT
ejpam-6377	115	14	2	2	NUM
ejpam-6377	115	15	∥gk+1∥∥vk∥	∥gk+1∥∥vk∥	NOUN
ejpam-6377	115	16	here	here	ADV
ejpam-6377	115	17	,	,	PUNCT
ejpam-6377	115	18	|βnew	|βnew	VERB
ejpam-6377	115	19	k	k	PROPN
ejpam-6377	116	1	|	|	ADV
ejpam-6377	116	2	≤	≤	NUM
ejpam-6377	116	3	ρl∥vk∥∥vk∥	ρl∥vk∥∥vk∥	NOUN
ejpam-6377	116	4	δ∥vk∥2	δ∥vk∥2	NOUN
ejpam-6377	116	5	+	+	CCONJ
ejpam-6377	116	6	µ	µ	X
ejpam-6377	116	7	η2∥vk∥∥vk∥2∥xk+1∥	η2∥vk∥∥vk∥2∥xk+1∥	NOUN
ejpam-6377	116	8	αk(δ∥vk∥2)2	αk(δ∥vk∥2)2	PROPN
ejpam-6377	116	9	ρ∥vk∥	ρ∥vk∥	PROPN
ejpam-6377	116	10	or	or	CCONJ
ejpam-6377	116	11	,	,	PUNCT
ejpam-6377	116	12	|βnew	|βnew	VERB
ejpam-6377	116	13	k	k	PROPN
ejpam-6377	117	1	|	|	ADV
ejpam-6377	117	2	≤	≤	NUM
ejpam-6377	117	3	ρl	ρl	ADP
ejpam-6377	117	4	δ	δ	PROPN
ejpam-6377	117	5	+	+	NOUN
ejpam-6377	117	6	µη2	µη2	PROPN
ejpam-6377	117	7	ρ∥xk+1∥	ρ∥xk+1∥	PROPN
ejpam-6377	117	8	αkδ	αkδ	NOUN
ejpam-6377	117	9	now	now	ADV
ejpam-6377	117	10	,	,	PUNCT
ejpam-6377	117	11	∥dk+1∥	∥dk+1∥	NUM
ejpam-6377	117	12	≤	≤	NUM
ejpam-6377	117	13	∥gk+1∥+	∥gk+1∥+	NOUN
ejpam-6377	117	14	1	1	NUM
ejpam-6377	117	15	αk	αk	NOUN
ejpam-6377	117	16	(	(	PUNCT
ejpam-6377	117	17	ρl	ρl	ADP
ejpam-6377	117	18	δ	δ	PROPN
ejpam-6377	117	19	+	+	NOUN
ejpam-6377	117	20	µη2	µη2	PROPN
ejpam-6377	117	21	ρ∥xk+1∥	ρ∥xk+1∥	PROPN
ejpam-6377	117	22	αkδ	αkδ	NOUN
ejpam-6377	117	23	)	)	PUNCT
ejpam-6377	117	24	∥vk∥	∥vk∥	NOUN
ejpam-6377	117	25	implies	imply	VERB
ejpam-6377	117	26	that	that	SCONJ
ejpam-6377	117	27	∥dk+1∥	∥dk+1∥	NUM
ejpam-6377	117	28	≤	≤	NUM
ejpam-6377	117	29	ρ+	ρ+	NUM
ejpam-6377	117	30	1	1	NUM
ejpam-6377	117	31	αk	αk	NOUN
ejpam-6377	117	32	(	(	PUNCT
ejpam-6377	117	33	ρl	ρl	ADP
ejpam-6377	117	34	δ	δ	PROPN
ejpam-6377	117	35	+	+	NOUN
ejpam-6377	117	36	µη2	µη2	PROPN
ejpam-6377	117	37	ρ∥xk+1∥	ρ∥xk+1∥	PROPN
ejpam-6377	117	38	αkδ	αkδ	NOUN
ejpam-6377	117	39	)	)	PUNCT
ejpam-6377	117	40	d1	d1	PROPN
ejpam-6377	117	41	where	where	SCONJ
ejpam-6377	117	42	d1	d1	PROPN
ejpam-6377	117	43	=	=	SYM
ejpam-6377	117	44	{	{	PUNCT
ejpam-6377	117	45	y−z	y−z	PROPN
ejpam-6377	117	46	}	}	PUNCT
ejpam-6377	117	47	,	,	PUNCT
ejpam-6377	117	48	y	y	PROPN
ejpam-6377	117	49	,	,	PUNCT
ejpam-6377	117	50	z	z	PROPN
ejpam-6377	117	51	∈	∈	PROPN
ejpam-6377	117	52	s	s	VERB
ejpam-6377	117	53	is	be	AUX
ejpam-6377	117	54	the	the	DET
ejpam-6377	117	55	diameter	diameter	NOUN
ejpam-6377	117	56	of	of	ADP
ejpam-6377	117	57	the	the	DET
ejpam-6377	117	58	level	level	NOUN
ejpam-6377	117	59	set	set	VERB
ejpam-6377	117	60	s.	s.	PROPN
ejpam-6377	117	61	there	there	PRON
ejpam-6377	117	62	exists	exist	VERB
ejpam-6377	117	63	a	a	DET
ejpam-6377	117	64	constant	constant	ADJ
ejpam-6377	117	65	d2	d2	NOUN
ejpam-6377	117	66	such	such	ADJ
ejpam-6377	117	67	that	that	SCONJ
ejpam-6377	117	68	∥xk+1∥	∥xk+1∥	NUM
ejpam-6377	117	69	≤	≤	NUM
ejpam-6377	117	70	d2	d2	NOUN
ejpam-6377	117	71	,	,	PUNCT
ejpam-6377	117	72	then	then	ADV
ejpam-6377	117	73	∥dk+1∥	∥dk+1∥	NUM
ejpam-6377	117	74	≤	≤	X
ejpam-6377	117	75	ρ+	ρ+	NUM
ejpam-6377	117	76	1	1	NUM
ejpam-6377	117	77	αk	αk	NOUN
ejpam-6377	117	78	(	(	PUNCT
ejpam-6377	117	79	ρl	ρl	ADP
ejpam-6377	117	80	δ	δ	PROPN
ejpam-6377	117	81	+	+	NOUN
ejpam-6377	117	82	µη2	µη2	ADJ
ejpam-6377	117	83	ρd2	ρd2	NOUN
ejpam-6377	117	84	αkδ	αkδ	NOUN
ejpam-6377	117	85	)	)	PUNCT
ejpam-6377	117	86	d1	d1	PROPN
ejpam-6377	117	87	showing	show	VERB
ejpam-6377	117	88	that	that	SCONJ
ejpam-6377	117	89	(	(	PUNCT
ejpam-6377	117	90	4.1	4.1	NUM
ejpam-6377	117	91	)	)	PUNCT
ejpam-6377	117	92	is	be	AUX
ejpam-6377	117	93	true	true	ADJ
ejpam-6377	117	94	.	.	PUNCT
ejpam-6377	118	1	by	by	ADP
ejpam-6377	118	2	lemma	lemma	PROPN
ejpam-6377	118	3	1	1	NUM
ejpam-6377	118	4	,	,	PUNCT
ejpam-6377	118	5	it	it	PRON
ejpam-6377	118	6	follows	follow	VERB
ejpam-6377	118	7	that	that	SCONJ
ejpam-6377	118	8	(	(	PUNCT
ejpam-6377	118	9	4.2	4.2	NUM
ejpam-6377	118	10	)	)	PUNCT
ejpam-6377	118	11	is	be	AUX
ejpam-6377	118	12	true	true	ADJ
ejpam-6377	118	13	,	,	PUNCT
ejpam-6377	118	14	which	which	PRON
ejpam-6377	118	15	for	for	ADP
ejpam-6377	118	16	uniformly	uniformly	ADV
ejpam-6377	118	17	convex	convex	NOUN
ejpam-6377	118	18	functions	function	NOUN
ejpam-6377	118	19	is	be	AUX
ejpam-6377	118	20	equivalent	equivalent	ADJ
ejpam-6377	118	21	to	to	ADP
ejpam-6377	118	22	(	(	PUNCT
ejpam-6377	118	23	4.7	4.7	NUM
ejpam-6377	118	24	)	)	PUNCT
ejpam-6377	118	25	.	.	PUNCT
ejpam-6377	119	1	5	5	X
ejpam-6377	119	2	.	.	X
ejpam-6377	119	3	numerical	numerical	ADJ
ejpam-6377	119	4	results	result	NOUN
ejpam-6377	119	5	we	we	PRON
ejpam-6377	119	6	compared	compare	VERB
ejpam-6377	119	7	the	the	DET
ejpam-6377	119	8	new	new	ADJ
ejpam-6377	119	9	method	method	NOUN
ejpam-6377	119	10	with	with	ADP
ejpam-6377	119	11	the	the	DET
ejpam-6377	119	12	conjugate	conjugate	ADJ
ejpam-6377	119	13	gradient	gradient	NOUN
ejpam-6377	119	14	(	(	PUNCT
ejpam-6377	119	15	hs	hs	NOUN
ejpam-6377	119	16	)	)	PUNCT
ejpam-6377	119	17	method	method	NOUN
ejpam-6377	119	18	in	in	ADP
ejpam-6377	119	19	this	this	DET
ejpam-6377	119	20	section	section	NOUN
ejpam-6377	119	21	,	,	PUNCT
ejpam-6377	119	22	the	the	DET
ejpam-6377	119	23	comparative	comparative	ADJ
ejpam-6377	119	24	tests	test	NOUN
ejpam-6377	119	25	involve	involve	VERB
ejpam-6377	119	26	well	well	ADV
ejpam-6377	119	27	-	-	PUNCT
ejpam-6377	119	28	known	know	VERB
ejpam-6377	119	29	nonlinear	nonlinear	ADJ
ejpam-6377	119	30	problems	problem	NOUN
ejpam-6377	119	31	(	(	PUNCT
ejpam-6377	119	32	standard	standard	ADJ
ejpam-6377	119	33	test	test	NOUN
ejpam-6377	119	34	function	function	NOUN
ejpam-6377	119	35	)	)	PUNCT
ejpam-6377	119	36	with	with	ADP
ejpam-6377	119	37	different	different	ADJ
ejpam-6377	119	38	dimensions	dimension	NOUN
ejpam-6377	119	39	n	n	NOUN
ejpam-6377	119	40	=	=	SYM
ejpam-6377	119	41	10	10	NUM
ejpam-6377	119	42	,	,	PUNCT
ejpam-6377	119	43	300	300	NUM
ejpam-6377	119	44	,	,	PUNCT
ejpam-6377	119	45	1000	1000	NUM
ejpam-6377	119	46	,	,	PUNCT
ejpam-6377	119	47	and	and	CCONJ
ejpam-6377	119	48	4000	4000	NUM
ejpam-6377	119	49	,	,	PUNCT
ejpam-6377	119	50	all	all	DET
ejpam-6377	119	51	programs	program	NOUN
ejpam-6377	119	52	are	be	AUX
ejpam-6377	119	53	written	write	VERB
ejpam-6377	119	54	in	in	ADP
ejpam-6377	119	55	fortran90	fortran90	NOUN
ejpam-6377	119	56	language	language	NOUN
ejpam-6377	119	57	and	and	CCONJ
ejpam-6377	119	58	for	for	ADP
ejpam-6377	119	59	all	all	DET
ejpam-6377	119	60	cases	case	NOUN
ejpam-6377	119	61	the	the	DET
ejpam-6377	119	62	stopping	stopping	NOUN
ejpam-6377	119	63	condition	condition	NOUN
ejpam-6377	119	64	is	be	AUX
ejpam-6377	119	65	∥gk+1∥	∥gk+1∥	NUM
ejpam-6377	119	66	≤	≤	NUM
ejpam-6377	119	67	10−5	10−5	NUM
ejpam-6377	119	68	.	.	PUNCT
ejpam-6377	120	1	the	the	DET
ejpam-6377	120	2	results	result	NOUN
ejpam-6377	120	3	given	give	VERB
ejpam-6377	120	4	in	in	ADP
ejpam-6377	120	5	table	table	NOUN
ejpam-6377	120	6	1	1	NUM
ejpam-6377	120	7	specifically	specifically	ADV
ejpam-6377	120	8	quote	quote	VERB
ejpam-6377	120	9	the	the	DET
ejpam-6377	120	10	number	number	NOUN
ejpam-6377	120	11	of	of	ADP
ejpam-6377	120	12	function	function	NOUN
ejpam-6377	120	13	nof	nof	PROPN
ejpam-6377	120	14	and	and	CCONJ
ejpam-6377	120	15	the	the	DET
ejpam-6377	120	16	number	number	NOUN
ejpam-6377	120	17	of	of	ADP
ejpam-6377	120	18	iteration	iteration	PROPN
ejpam-6377	120	19	noi	noi	PROPN
ejpam-6377	120	20	.	.	PUNCT
ejpam-6377	121	1	more	more	ADJ
ejpam-6377	121	2	experimental	experimental	ADJ
ejpam-6377	121	3	results	result	NOUN
ejpam-6377	121	4	in	in	ADP
ejpam-6377	121	5	table	table	NOUN
ejpam-6377	121	6	1	1	NUM
ejpam-6377	121	7	and	and	CCONJ
ejpam-6377	121	8	the	the	DET
ejpam-6377	121	9	figures	figure	NOUN
ejpam-6377	121	10	confirm	confirm	VERB
ejpam-6377	121	11	that	that	SCONJ
ejpam-6377	121	12	the	the	DET
ejpam-6377	121	13	new	new	ADJ
ejpam-6377	121	14	conjugate	conjugate	ADJ
ejpam-6377	121	15	gradient	gradient	NOUN
ejpam-6377	121	16	method	method	NOUN
ejpam-6377	121	17	is	be	AUX
ejpam-6377	121	18	superior	superior	ADJ
ejpam-6377	121	19	to	to	ADP
ejpam-6377	121	20	the	the	DET
ejpam-6377	121	21	standard	standard	ADJ
ejpam-6377	121	22	conjugate	conjugate	ADJ
ejpam-6377	121	23	gradient	gradient	NOUN
ejpam-6377	121	24	(	(	PUNCT
ejpam-6377	121	25	hs	hs	NOUN
ejpam-6377	121	26	)	)	PUNCT
ejpam-6377	121	27	method	method	NOUN
ejpam-6377	121	28	concerning	concern	VERB
ejpam-6377	121	29	the	the	DET
ejpam-6377	121	30	noi	noi	PROPN
ejpam-6377	121	31	and	and	CCONJ
ejpam-6377	121	32	nof	nof	PROPN
ejpam-6377	121	33	.	.	PUNCT
ejpam-6377	122	1	the	the	DET
ejpam-6377	122	2	performance	performance	NOUN
ejpam-6377	122	3	results	result	NOUN
ejpam-6377	122	4	are	be	AUX
ejpam-6377	122	5	shown	show	VERB
ejpam-6377	122	6	in	in	ADP
ejpam-6377	122	7	figures	figure	NOUN
ejpam-6377	122	8	1	1	NUM
ejpam-6377	122	9	and	and	CCONJ
ejpam-6377	122	10	2	2	NUM
ejpam-6377	122	11	,	,	PUNCT
ejpam-6377	122	12	using	use	VERB
ejpam-6377	122	13	the	the	DET
ejpam-6377	122	14	performance	performance	NOUN
ejpam-6377	122	15	profile	profile	NOUN
ejpam-6377	122	16	introduced	introduce	VERB
ejpam-6377	122	17	by	by	ADP
ejpam-6377	122	18	dolan	dolan	PROPN
ejpam-6377	122	19	and	and	CCONJ
ejpam-6377	122	20	more	more	ADJ
ejpam-6377	122	21	(	(	PUNCT
ejpam-6377	122	22	2002)[21	2002)[21	NOUN
ejpam-6377	122	23	]	]	PUNCT
ejpam-6377	122	24	.	.	PUNCT
ejpam-6377	123	1	a.	a.	PROPN
ejpam-6377	123	2	a.	a.	PROPN
ejpam-6377	123	3	mustafa	mustafa	PROPN
ejpam-6377	123	4	,	,	PUNCT
ejpam-6377	123	5	h.	h.	PROPN
ejpam-6377	123	6	a.	a.	PROPN
ejpam-6377	123	7	khatab	khatab	PROPN
ejpam-6377	123	8	/	/	SYM
ejpam-6377	123	9	eur	eur	PROPN
ejpam-6377	123	10	.	.	PUNCT
ejpam-6377	124	1	j.	j.	PROPN
ejpam-6377	124	2	pure	pure	PROPN
ejpam-6377	124	3	appl	appl	PROPN
ejpam-6377	124	4	.	.	PROPN
ejpam-6377	124	5	math	math	PROPN
ejpam-6377	124	6	,	,	PUNCT
ejpam-6377	124	7	18	18	NUM
ejpam-6377	124	8	(	(	PUNCT
ejpam-6377	124	9	3	3	NUM
ejpam-6377	124	10	)	)	PUNCT
ejpam-6377	124	11	(	(	PUNCT
ejpam-6377	124	12	2025	2025	NUM
ejpam-6377	124	13	)	)	PUNCT
ejpam-6377	124	14	,	,	PUNCT
ejpam-6377	124	15	6377	6377	NUM
ejpam-6377	124	16	9	9	NUM
ejpam-6377	124	17	of	of	ADP
ejpam-6377	124	18	12	12	NUM
ejpam-6377	124	19	table	table	NOUN
ejpam-6377	124	20	1	1	NUM
ejpam-6377	124	21	:	:	PUNCT
ejpam-6377	124	22	comparative	comparative	ADJ
ejpam-6377	124	23	performance	performance	NOUN
ejpam-6377	124	24	of	of	ADP
ejpam-6377	124	25	the	the	DET
ejpam-6377	124	26	two	two	NUM
ejpam-6377	124	27	algorithms	algorithm	NOUN
ejpam-6377	124	28	(	(	PUNCT
ejpam-6377	124	29	hs	hs	X
ejpam-6377	124	30	and	and	CCONJ
ejpam-6377	124	31	new	new	ADJ
ejpam-6377	124	32	method	method	NOUN
ejpam-6377	124	33	)	)	PUNCT
ejpam-6377	124	34	no	no	DET
ejpam-6377	124	35	test	test	NOUN
ejpam-6377	124	36	function	function	NOUN
ejpam-6377	124	37	n	n	PROPN
ejpam-6377	124	38	noi	noi	PROPN
ejpam-6377	124	39	(	(	PUNCT
ejpam-6377	124	40	hs	hs	PROPN
ejpam-6377	124	41	)	)	PUNCT
ejpam-6377	124	42	nof	nof	PROPN
ejpam-6377	124	43	(	(	PUNCT
ejpam-6377	124	44	hs	hs	PROPN
ejpam-6377	124	45	)	)	PUNCT
ejpam-6377	124	46	noi	noi	PROPN
ejpam-6377	124	47	(	(	PUNCT
ejpam-6377	124	48	new	new	ADJ
ejpam-6377	124	49	)	)	PUNCT
ejpam-6377	124	50	nof	nof	NOUN
ejpam-6377	124	51	(	(	PUNCT
ejpam-6377	124	52	new	new	ADJ
ejpam-6377	124	53	)	)	PUNCT
ejpam-6377	124	54	1	1	NUM
ejpam-6377	124	55	wood	wood	NOUN
ejpam-6377	124	56	10	10	NUM
ejpam-6377	124	57	30	30	NUM
ejpam-6377	124	58	68	68	NUM
ejpam-6377	124	59	30	30	NUM
ejpam-6377	124	60	68	68	NUM
ejpam-6377	124	61	300	300	NUM
ejpam-6377	124	62	30	30	NUM
ejpam-6377	124	63	68	68	NUM
ejpam-6377	124	64	26	26	NUM
ejpam-6377	124	65	60	60	NUM
ejpam-6377	124	66	1000	1000	NUM
ejpam-6377	124	67	30	30	NUM
ejpam-6377	124	68	68	68	NUM
ejpam-6377	124	69	31	31	NUM
ejpam-6377	124	70	71	71	NUM
ejpam-6377	124	71	4000	4000	NUM
ejpam-6377	124	72	30	30	NUM
ejpam-6377	124	73	68	68	NUM
ejpam-6377	124	74	24	24	NUM
ejpam-6377	124	75	57	57	NUM
ejpam-6377	124	76	2	2	NUM
ejpam-6377	124	77	osp	osp	NOUN
ejpam-6377	124	78	10	10	NUM
ejpam-6377	124	79	13	13	NUM
ejpam-6377	124	80	58	58	NUM
ejpam-6377	124	81	13	13	NUM
ejpam-6377	124	82	58	58	NUM
ejpam-6377	124	83	300	300	NUM
ejpam-6377	124	84	88	88	NUM
ejpam-6377	124	85	290	290	NUM
ejpam-6377	124	86	79	79	NUM
ejpam-6377	124	87	251	251	NUM
ejpam-6377	124	88	1000	1000	NUM
ejpam-6377	124	89	156	156	NUM
ejpam-6377	124	90	473	473	NUM
ejpam-6377	124	91	140	140	NUM
ejpam-6377	124	92	419	419	NUM
ejpam-6377	124	93	4000	4000	NUM
ejpam-6377	124	94	230	230	NUM
ejpam-6377	124	95	700	700	NUM
ejpam-6377	124	96	228	228	NUM
ejpam-6377	124	97	678	678	NUM
ejpam-6377	124	98	3	3	NUM
ejpam-6377	124	99	powell	powell	PROPN
ejpam-6377	124	100	10	10	NUM
ejpam-6377	124	101	38	38	NUM
ejpam-6377	124	102	108	108	NUM
ejpam-6377	124	103	39	39	NUM
ejpam-6377	124	104	119	119	NUM
ejpam-6377	124	105	300	300	NUM
ejpam-6377	124	106	40	40	NUM
ejpam-6377	124	107	122	122	NUM
ejpam-6377	124	108	34	34	NUM
ejpam-6377	124	109	109	109	NUM
ejpam-6377	124	110	1000	1000	NUM
ejpam-6377	124	111	41	41	NUM
ejpam-6377	124	112	124	124	NUM
ejpam-6377	124	113	30	30	NUM
ejpam-6377	124	114	92	92	NUM
ejpam-6377	124	115	4000	4000	NUM
ejpam-6377	124	116	41	41	NUM
ejpam-6377	125	1	124	124	NUM
ejpam-6377	125	2	44	44	NUM
ejpam-6377	125	3	115	115	NUM
ejpam-6377	125	4	4	4	NUM
ejpam-6377	125	5	miele	miele	NOUN
ejpam-6377	125	6	10	10	NUM
ejpam-6377	125	7	31	31	NUM
ejpam-6377	125	8	102	102	NUM
ejpam-6377	125	9	31	31	NUM
ejpam-6377	125	10	102	102	NUM
ejpam-6377	125	11	300	300	NUM
ejpam-6377	125	12	40	40	NUM
ejpam-6377	125	13	146	146	NUM
ejpam-6377	125	14	40	40	NUM
ejpam-6377	125	15	147	147	NUM
ejpam-6377	125	16	1000	1000	NUM
ejpam-6377	125	17	46	46	NUM
ejpam-6377	125	18	176	176	NUM
ejpam-6377	125	19	39	39	NUM
ejpam-6377	125	20	139	139	NUM
ejpam-6377	125	21	4000	4000	NUM
ejpam-6377	125	22	54	54	NUM
ejpam-6377	125	23	211	211	NUM
ejpam-6377	125	24	35	35	NUM
ejpam-6377	125	25	122	122	NUM
ejpam-6377	125	26	5	5	NUM
ejpam-6377	125	27	g	g	NOUN
ejpam-6377	125	28	-	-	PUNCT
ejpam-6377	125	29	central	central	ADJ
ejpam-6377	125	30	10	10	NUM
ejpam-6377	125	31	22	22	NUM
ejpam-6377	125	32	159	159	NUM
ejpam-6377	125	33	22	22	NUM
ejpam-6377	125	34	159	159	NUM
ejpam-6377	125	35	300	300	NUM
ejpam-6377	125	36	23	23	NUM
ejpam-6377	125	37	171	171	NUM
ejpam-6377	125	38	23	23	NUM
ejpam-6377	125	39	170	170	NUM
ejpam-6377	125	40	1000	1000	NUM
ejpam-6377	125	41	23	23	NUM
ejpam-6377	125	42	171	171	NUM
ejpam-6377	125	43	22	22	NUM
ejpam-6377	125	44	164	164	NUM
ejpam-6377	125	45	4000	4000	NUM
ejpam-6377	125	46	28	28	NUM
ejpam-6377	125	47	248	248	NUM
ejpam-6377	125	48	31	31	NUM
ejpam-6377	125	49	269	269	NUM
ejpam-6377	125	50	6	6	NUM
ejpam-6377	125	51	shallow	shallow	ADJ
ejpam-6377	125	52	10	10	NUM
ejpam-6377	125	53	8	8	NUM
ejpam-6377	125	54	21	21	NUM
ejpam-6377	125	55	8	8	NUM
ejpam-6377	125	56	21	21	NUM
ejpam-6377	125	57	300	300	NUM
ejpam-6377	125	58	8	8	NUM
ejpam-6377	125	59	21	21	NUM
ejpam-6377	125	60	8	8	NUM
ejpam-6377	125	61	21	21	NUM
ejpam-6377	125	62	1000	1000	NUM
ejpam-6377	125	63	9	9	NUM
ejpam-6377	125	64	24	24	NUM
ejpam-6377	125	65	8	8	NUM
ejpam-6377	125	66	21	21	NUM
ejpam-6377	125	67	4000	4000	NUM
ejpam-6377	125	68	9	9	NUM
ejpam-6377	125	69	24	24	NUM
ejpam-6377	125	70	8	8	NUM
ejpam-6377	125	71	21	21	NUM
ejpam-6377	125	72	7	7	NUM
ejpam-6377	125	73	beal	beal	NOUN
ejpam-6377	125	74	10	10	NUM
ejpam-6377	125	75	11	11	NUM
ejpam-6377	125	76	28	28	NUM
ejpam-6377	125	77	11	11	NUM
ejpam-6377	125	78	28	28	NUM
ejpam-6377	125	79	300	300	NUM
ejpam-6377	125	80	12	12	NUM
ejpam-6377	125	81	30	30	NUM
ejpam-6377	125	82	11	11	NUM
ejpam-6377	125	83	28	28	NUM
ejpam-6377	125	84	1000	1000	NUM
ejpam-6377	125	85	12	12	NUM
ejpam-6377	125	86	30	30	NUM
ejpam-6377	125	87	9	9	NUM
ejpam-6377	125	88	25	25	NUM
ejpam-6377	125	89	4000	4000	NUM
ejpam-6377	125	90	12	12	NUM
ejpam-6377	125	91	30	30	NUM
ejpam-6377	125	92	13	13	NUM
ejpam-6377	125	93	33	33	NUM
ejpam-6377	125	94	8	8	NUM
ejpam-6377	125	95	sum	sum	NOUN
ejpam-6377	125	96	10	10	NUM
ejpam-6377	125	97	6	6	NUM
ejpam-6377	125	98	34	34	NUM
ejpam-6377	125	99	6	6	NUM
ejpam-6377	125	100	34	34	NUM
ejpam-6377	125	101	300	300	NUM
ejpam-6377	125	102	19	19	NUM
ejpam-6377	125	103	105	105	NUM
ejpam-6377	125	104	19	19	NUM
ejpam-6377	125	105	105	105	NUM
ejpam-6377	125	106	1000	1000	NUM
ejpam-6377	125	107	23	23	NUM
ejpam-6377	125	108	128	128	NUM
ejpam-6377	125	109	23	23	NUM
ejpam-6377	125	110	128	128	NUM
ejpam-6377	125	111	4000	4000	NUM
ejpam-6377	125	112	32	32	NUM
ejpam-6377	125	113	142	142	NUM
ejpam-6377	125	114	31	31	NUM
ejpam-6377	125	115	128	128	NUM
ejpam-6377	125	116	9	9	NUM
ejpam-6377	125	117	wolfe	wolfe	PROPN
ejpam-6377	125	118	10	10	NUM
ejpam-6377	125	119	32	32	NUM
ejpam-6377	125	120	65	65	NUM
ejpam-6377	125	121	32	32	NUM
ejpam-6377	125	122	65	65	NUM
ejpam-6377	125	123	300	300	NUM
ejpam-6377	125	124	48	48	NUM
ejpam-6377	125	125	97	97	NUM
ejpam-6377	125	126	44	44	NUM
ejpam-6377	125	127	89	89	NUM
ejpam-6377	125	128	1000	1000	NUM
ejpam-6377	125	129	70	70	NUM
ejpam-6377	125	130	141	141	NUM
ejpam-6377	125	131	45	45	NUM
ejpam-6377	125	132	93	93	NUM
ejpam-6377	125	133	4000	4000	NUM
ejpam-6377	125	134	169	169	NUM
ejpam-6377	125	135	355	355	NUM
ejpam-6377	125	136	55	55	NUM
ejpam-6377	125	137	115	115	NUM
ejpam-6377	125	138	10	10	NUM
ejpam-6377	125	139	cubic	cubic	ADJ
ejpam-6377	125	140	10	10	NUM
ejpam-6377	125	141	13	13	NUM
ejpam-6377	125	142	37	37	NUM
ejpam-6377	125	143	13	13	NUM
ejpam-6377	125	144	37	37	NUM
ejpam-6377	125	145	300	300	NUM
ejpam-6377	125	146	13	13	NUM
ejpam-6377	125	147	37	37	NUM
ejpam-6377	125	148	13	13	NUM
ejpam-6377	125	149	37	37	NUM
ejpam-6377	125	150	1000	1000	NUM
ejpam-6377	125	151	13	13	NUM
ejpam-6377	125	152	37	37	NUM
ejpam-6377	125	153	13	13	NUM
ejpam-6377	125	154	37	37	NUM
ejpam-6377	125	155	4000	4000	NUM
ejpam-6377	125	156	13	13	NUM
ejpam-6377	125	157	37	37	NUM
ejpam-6377	125	158	13	13	NUM
ejpam-6377	125	159	37	37	NUM
ejpam-6377	125	160	11	11	NUM
ejpam-6377	125	161	non	non	ADJ
ejpam-6377	125	162	-	-	ADJ
ejpam-6377	125	163	diagonal	diagonal	ADJ
ejpam-6377	125	164	10	10	NUM
ejpam-6377	125	165	26	26	NUM
ejpam-6377	125	166	72	72	NUM
ejpam-6377	125	167	26	26	NUM
ejpam-6377	125	168	72	72	NUM
ejpam-6377	125	169	300	300	NUM
ejpam-6377	125	170	29	29	NUM
ejpam-6377	125	171	79	79	NUM
ejpam-6377	125	172	30	30	NUM
ejpam-6377	125	173	81	81	NUM
ejpam-6377	125	174	1000	1000	NUM
ejpam-6377	125	175	29	29	NUM
ejpam-6377	125	176	79	79	NUM
ejpam-6377	125	177	27	27	NUM
ejpam-6377	125	178	77	77	NUM
ejpam-6377	125	179	4000	4000	NUM
ejpam-6377	126	1	f	f	NOUN
ejpam-6377	127	1	f	f	X
ejpam-6377	127	2	f	f	PROPN
ejpam-6377	128	1	f	f	PROPN
ejpam-6377	128	2	12	12	NUM
ejpam-6377	128	3	rosen	rosen	PROPN
ejpam-6377	128	4	10	10	NUM
ejpam-6377	128	5	30	30	NUM
ejpam-6377	128	6	83	83	NUM
ejpam-6377	128	7	30	30	NUM
ejpam-6377	128	8	83	83	NUM
ejpam-6377	128	9	300	300	NUM
ejpam-6377	128	10	30	30	NUM
ejpam-6377	128	11	83	83	NUM
ejpam-6377	128	12	30	30	NUM
ejpam-6377	128	13	83	83	NUM
ejpam-6377	128	14	1000	1000	NUM
ejpam-6377	128	15	30	30	NUM
ejpam-6377	128	16	83	83	NUM
ejpam-6377	128	17	30	30	NUM
ejpam-6377	128	18	83	83	NUM
ejpam-6377	128	19	4000	4000	NUM
ejpam-6377	128	20	30	30	NUM
ejpam-6377	128	21	83	83	NUM
ejpam-6377	128	22	30	30	NUM
ejpam-6377	128	23	83	83	NUM
ejpam-6377	128	24	13	13	NUM
ejpam-6377	128	25	tri	tri	PROPN
ejpam-6377	128	26	10	10	NUM
ejpam-6377	128	27	f	f	NOUN
ejpam-6377	128	28	f	f	PROPN
ejpam-6377	128	29	9	9	NUM
ejpam-6377	128	30	19	19	NUM
ejpam-6377	128	31	300	300	NUM
ejpam-6377	128	32	148	148	NUM
ejpam-6377	128	33	297	297	NUM
ejpam-6377	128	34	147	147	NUM
ejpam-6377	128	35	295	295	NUM
ejpam-6377	128	36	1000	1000	NUM
ejpam-6377	128	37	288	288	NUM
ejpam-6377	128	38	577	577	NUM
ejpam-6377	128	39	288	288	NUM
ejpam-6377	128	40	577	577	NUM
ejpam-6377	128	41	4000	4000	NUM
ejpam-6377	128	42	600	600	NUM
ejpam-6377	128	43	1201	1201	NUM
ejpam-6377	128	44	600	600	NUM
ejpam-6377	128	45	1201	1201	NUM
ejpam-6377	128	46	14	14	NUM
ejpam-6377	128	47	g	g	NOUN
ejpam-6377	128	48	-	-	PUNCT
ejpam-6377	128	49	dixon	dixon	PROPN
ejpam-6377	128	50	10	10	NUM
ejpam-6377	128	51	21	21	NUM
ejpam-6377	128	52	45	45	NUM
ejpam-6377	128	53	21	21	NUM
ejpam-6377	128	54	45	45	NUM
ejpam-6377	128	55	300	300	NUM
ejpam-6377	128	56	508	508	NUM
ejpam-6377	128	57	1136	1136	NUM
ejpam-6377	128	58	536	536	NUM
ejpam-6377	128	59	1206	1206	NUM
ejpam-6377	128	60	1000	1000	NUM
ejpam-6377	128	61	4005	4005	NUM
ejpam-6377	128	62	8015	8015	NUM
ejpam-6377	128	63	534	534	NUM
ejpam-6377	128	64	1163	1163	NUM
ejpam-6377	128	65	4000	4000	NUM
ejpam-6377	128	66	560	560	NUM
ejpam-6377	128	67	1217	1217	NUM
ejpam-6377	128	68	505	505	NUM
ejpam-6377	128	69	1107	1107	NUM
ejpam-6377	128	70	15	15	NUM
ejpam-6377	128	71	fred	fred	ADJ
ejpam-6377	128	72	10	10	NUM
ejpam-6377	128	73	8	8	NUM
ejpam-6377	128	74	23	23	NUM
ejpam-6377	128	75	8	8	NUM
ejpam-6377	128	76	23	23	NUM
ejpam-6377	128	77	300	300	NUM
ejpam-6377	128	78	8	8	NUM
ejpam-6377	128	79	23	23	NUM
ejpam-6377	128	80	8	8	NUM
ejpam-6377	128	81	23	23	NUM
ejpam-6377	128	82	1000	1000	NUM
ejpam-6377	128	83	8	8	NUM
ejpam-6377	128	84	23	23	NUM
ejpam-6377	128	85	8	8	NUM
ejpam-6377	128	86	23	23	NUM
ejpam-6377	128	87	4000	4000	NUM
ejpam-6377	128	88	8	8	NUM
ejpam-6377	128	89	23	23	NUM
ejpam-6377	128	90	8	8	NUM
ejpam-6377	128	91	23	23	NUM
ejpam-6377	128	92	a.	a.	NOUN
ejpam-6377	128	93	a.	a.	NOUN
ejpam-6377	128	94	mustafa	mustafa	PROPN
ejpam-6377	128	95	,	,	PUNCT
ejpam-6377	128	96	h.	h.	PROPN
ejpam-6377	128	97	a.	a.	PROPN
ejpam-6377	128	98	khatab	khatab	PROPN
ejpam-6377	128	99	/	/	SYM
ejpam-6377	128	100	eur	eur	PROPN
ejpam-6377	128	101	.	.	PUNCT
ejpam-6377	129	1	j.	j.	PROPN
ejpam-6377	129	2	pure	pure	PROPN
ejpam-6377	129	3	appl	appl	PROPN
ejpam-6377	129	4	.	.	PROPN
ejpam-6377	129	5	math	math	PROPN
ejpam-6377	129	6	,	,	PUNCT
ejpam-6377	129	7	18	18	NUM
ejpam-6377	129	8	(	(	PUNCT
ejpam-6377	129	9	3	3	NUM
ejpam-6377	129	10	)	)	PUNCT
ejpam-6377	129	11	(	(	PUNCT
ejpam-6377	129	12	2025	2025	NUM
ejpam-6377	129	13	)	)	PUNCT
ejpam-6377	129	14	,	,	PUNCT
ejpam-6377	129	15	6377	6377	NUM
ejpam-6377	129	16	10	10	NUM
ejpam-6377	129	17	of	of	ADP
ejpam-6377	129	18	12	12	NUM
ejpam-6377	129	19	figure	figure	NOUN
ejpam-6377	129	20	1	1	NUM
ejpam-6377	129	21	:	:	PUNCT
ejpam-6377	129	22	performance	performance	NOUN
ejpam-6377	129	23	profile	profile	NOUN
ejpam-6377	129	24	on	on	ADP
ejpam-6377	129	25	the	the	DET
ejpam-6377	129	26	number	number	NOUN
ejpam-6377	129	27	of	of	ADP
ejpam-6377	129	28	iterations	iteration	NOUN
ejpam-6377	129	29	figure	figure	NOUN
ejpam-6377	129	30	2	2	NUM
ejpam-6377	129	31	:	:	PUNCT
ejpam-6377	129	32	performance	performance	NOUN
ejpam-6377	129	33	profile	profile	NOUN
ejpam-6377	129	34	on	on	ADP
ejpam-6377	129	35	the	the	DET
ejpam-6377	129	36	number	number	NOUN
ejpam-6377	129	37	of	of	ADP
ejpam-6377	129	38	functions	function	NOUN
ejpam-6377	129	39	6	6	NUM
ejpam-6377	129	40	.	.	PUNCT
ejpam-6377	129	41	conclusion	conclusion	NOUN
ejpam-6377	129	42	in	in	ADP
ejpam-6377	129	43	this	this	DET
ejpam-6377	129	44	paper	paper	NOUN
ejpam-6377	129	45	,	,	PUNCT
ejpam-6377	129	46	we	we	PRON
ejpam-6377	129	47	suggested	suggest	VERB
ejpam-6377	129	48	a	a	DET
ejpam-6377	129	49	new	new	ADJ
ejpam-6377	129	50	conjugate	conjugate	ADJ
ejpam-6377	129	51	gradient	gradient	NOUN
ejpam-6377	129	52	method	method	NOUN
ejpam-6377	129	53	for	for	ADP
ejpam-6377	129	54	unconstrained	unconstrained	ADJ
ejpam-6377	129	55	optimization	optimization	NOUN
ejpam-6377	129	56	problems	problem	NOUN
ejpam-6377	129	57	.	.	PUNCT
ejpam-6377	130	1	we	we	PRON
ejpam-6377	130	2	proved	prove	VERB
ejpam-6377	130	3	the	the	DET
ejpam-6377	130	4	conjugacy	conjugacy	ADJ
ejpam-6377	130	5	condition	condition	NOUN
ejpam-6377	130	6	,	,	PUNCT
ejpam-6377	130	7	descent	descent	NOUN
ejpam-6377	130	8	condition	condition	NOUN
ejpam-6377	130	9	,	,	PUNCT
ejpam-6377	130	10	sufficient	sufficient	ADJ
ejpam-6377	130	11	descent	descent	NOUN
ejpam-6377	130	12	condition	condition	NOUN
ejpam-6377	130	13	,	,	PUNCT
ejpam-6377	130	14	and	and	CCONJ
ejpam-6377	130	15	the	the	DET
ejpam-6377	130	16	global	global	ADJ
ejpam-6377	130	17	convergence	convergence	NOUN
ejpam-6377	130	18	of	of	ADP
ejpam-6377	130	19	the	the	DET
ejpam-6377	130	20	new	new	ADJ
ejpam-6377	130	21	method	method	NOUN
ejpam-6377	130	22	.	.	PUNCT
ejpam-6377	131	1	implemented	implement	VERB
ejpam-6377	131	2	and	and	CCONJ
ejpam-6377	131	3	tested	test	VERB
ejpam-6377	131	4	to	to	ADP
ejpam-6377	131	5	a.	a.	PROPN
ejpam-6377	131	6	a.	a.	PROPN
ejpam-6377	131	7	mustafa	mustafa	PROPN
ejpam-6377	131	8	,	,	PUNCT
ejpam-6377	131	9	h.	h.	PROPN
ejpam-6377	131	10	a.	a.	PROPN
ejpam-6377	131	11	khatab	khatab	PROPN
ejpam-6377	131	12	/	/	SYM
ejpam-6377	131	13	eur	eur	PROPN
ejpam-6377	131	14	.	.	PUNCT
ejpam-6377	132	1	j.	j.	PROPN
ejpam-6377	132	2	pure	pure	PROPN
ejpam-6377	132	3	appl	appl	PROPN
ejpam-6377	132	4	.	.	PROPN
ejpam-6377	132	5	math	math	PROPN
ejpam-6377	132	6	,	,	PUNCT
ejpam-6377	132	7	18	18	NUM
ejpam-6377	132	8	(	(	PUNCT
ejpam-6377	132	9	3	3	NUM
ejpam-6377	132	10	)	)	PUNCT
ejpam-6377	132	11	(	(	PUNCT
ejpam-6377	132	12	2025	2025	NUM
ejpam-6377	132	13	)	)	PUNCT
ejpam-6377	132	14	,	,	PUNCT
ejpam-6377	132	15	6377	6377	NUM
ejpam-6377	132	16	11	11	NUM
ejpam-6377	132	17	of	of	ADP
ejpam-6377	132	18	12	12	NUM
ejpam-6377	132	19	some	some	DET
ejpam-6377	132	20	extent	extent	NOUN
ejpam-6377	132	21	.	.	PUNCT
ejpam-6377	133	1	the	the	DET
ejpam-6377	133	2	new	new	ADJ
ejpam-6377	133	3	method	method	NOUN
ejpam-6377	133	4	was	be	AUX
ejpam-6377	133	5	compared	compare	VERB
ejpam-6377	133	6	with	with	ADP
ejpam-6377	133	7	the	the	DET
ejpam-6377	133	8	standard	standard	ADJ
ejpam-6377	133	9	conjugate	conjugate	ADJ
ejpam-6377	133	10	gradient	gradient	NOUN
ejpam-6377	133	11	(	(	PUNCT
ejpam-6377	133	12	hs	hs	NOUN
ejpam-6377	133	13	)	)	PUNCT
ejpam-6377	133	14	method	method	NOUN
ejpam-6377	133	15	.	.	PUNCT
ejpam-6377	134	1	the	the	DET
ejpam-6377	134	2	numerical	numerical	ADJ
ejpam-6377	134	3	tests	test	NOUN
ejpam-6377	134	4	were	be	AUX
ejpam-6377	134	5	carried	carry	VERB
ejpam-6377	134	6	out	out	ADP
ejpam-6377	134	7	on	on	ADP
ejpam-6377	134	8	lowand	lowand	ADJ
ejpam-6377	134	9	high	high	ADJ
ejpam-6377	134	10	-	-	PUNCT
ejpam-6377	134	11	dimensionality	dimensionality	NOUN
ejpam-6377	134	12	problems	problem	NOUN
ejpam-6377	134	13	and	and	CCONJ
ejpam-6377	134	14	comparisons	comparison	NOUN
ejpam-6377	134	15	were	be	AUX
ejpam-6377	134	16	made	make	VERB
ejpam-6377	134	17	amongst	amongst	ADP
ejpam-6377	134	18	different	different	ADJ
ejpam-6377	134	19	test	test	NOUN
ejpam-6377	134	20	functions	function	NOUN
ejpam-6377	134	21	with	with	ADP
ejpam-6377	134	22	inexact	inexact	ADJ
ejpam-6377	134	23	line	line	NOUN
ejpam-6377	134	24	search	search	NOUN
ejpam-6377	134	25	.	.	PUNCT
ejpam-6377	135	1	we	we	PRON
ejpam-6377	135	2	used	use	VERB
ejpam-6377	135	3	fifteen	fifteen	NUM
ejpam-6377	135	4	function	function	NOUN
ejpam-6377	135	5	with	with	ADP
ejpam-6377	135	6	different	different	ADJ
ejpam-6377	135	7	dimensions	dimension	NOUN
ejpam-6377	135	8	(	(	PUNCT
ejpam-6377	135	9	10	10	NUM
ejpam-6377	135	10	,	,	PUNCT
ejpam-6377	135	11	300	300	NUM
ejpam-6377	135	12	,	,	PUNCT
ejpam-6377	135	13	1000	1000	NUM
ejpam-6377	135	14	,	,	PUNCT
ejpam-6377	135	15	and	and	CCONJ
ejpam-6377	135	16	4000	4000	NUM
ejpam-6377	135	17	)	)	PUNCT
ejpam-6377	135	18	.	.	PUNCT
ejpam-6377	136	1	two	two	NUM
ejpam-6377	136	2	important	important	ADJ
ejpam-6377	136	3	measures	measure	NOUN
ejpam-6377	136	4	are	be	AUX
ejpam-6377	136	5	used	use	VERB
ejpam-6377	136	6	to	to	PART
ejpam-6377	136	7	assess	assess	VERB
ejpam-6377	136	8	the	the	DET
ejpam-6377	136	9	approaches	approach	NOUN
ejpam-6377	136	10	’	'	PUNCT
ejpam-6377	136	11	performance	performance	NOUN
ejpam-6377	136	12	:	:	PUNCT
ejpam-6377	136	13	the	the	DET
ejpam-6377	136	14	number	number	NOUN
ejpam-6377	136	15	of	of	ADP
ejpam-6377	136	16	iterations	iteration	NOUN
ejpam-6377	136	17	(	(	PUNCT
ejpam-6377	136	18	noi	noi	PROPN
ejpam-6377	136	19	)	)	PUNCT
ejpam-6377	136	20	and	and	CCONJ
ejpam-6377	136	21	the	the	DET
ejpam-6377	136	22	number	number	NOUN
ejpam-6377	136	23	of	of	ADP
ejpam-6377	136	24	function	function	NOUN
ejpam-6377	136	25	evaluations	evaluation	NOUN
ejpam-6377	136	26	(	(	PUNCT
ejpam-6377	136	27	nof	nof	PROPN
ejpam-6377	136	28	)	)	PUNCT
ejpam-6377	136	29	.	.	PUNCT
ejpam-6377	137	1	the	the	DET
ejpam-6377	137	2	numerical	numerical	ADJ
ejpam-6377	137	3	results	result	NOUN
ejpam-6377	137	4	in	in	ADP
ejpam-6377	137	5	table	table	NOUN
ejpam-6377	137	6	1	1	NUM
ejpam-6377	137	7	and	and	CCONJ
ejpam-6377	137	8	the	the	DET
ejpam-6377	137	9	figures	figure	NOUN
ejpam-6377	137	10	1	1	NUM
ejpam-6377	137	11	and	and	CCONJ
ejpam-6377	137	12	2	2	NUM
ejpam-6377	137	13	demonstrate	demonstrate	VERB
ejpam-6377	137	14	that	that	SCONJ
ejpam-6377	137	15	the	the	DET
ejpam-6377	137	16	proposed	propose	VERB
ejpam-6377	137	17	method	method	NOUN
ejpam-6377	137	18	performs	perform	VERB
ejpam-6377	137	19	effectively	effectively	ADV
ejpam-6377	137	20	.	.	PUNCT
ejpam-6377	138	1	references	reference	NOUN
ejpam-6377	138	2	[	[	X
ejpam-6377	138	3	1	1	NUM
ejpam-6377	138	4	]	]	X
ejpam-6377	138	5	i.	i.	PROPN
ejpam-6377	138	6	ahmed	ahmed	PROPN
ejpam-6377	138	7	and	and	CCONJ
ejpam-6377	138	8	b.	b.	PROPN
ejpam-6377	138	9	mohanty	mohanty	PROPN
ejpam-6377	138	10	.	.	PUNCT
ejpam-6377	139	1	recent	recent	ADJ
ejpam-6377	139	2	advances	advance	NOUN
ejpam-6377	139	3	in	in	ADP
ejpam-6377	139	4	nonlinear	nonlinear	ADJ
ejpam-6377	139	5	optimization	optimization	NOUN
ejpam-6377	139	6	methods	method	NOUN
ejpam-6377	139	7	for	for	ADP
ejpam-6377	139	8	machine	machine	NOUN
ejpam-6377	139	9	learning	learning	NOUN
ejpam-6377	139	10	models	model	NOUN
ejpam-6377	139	11	.	.	PUNCT
ejpam-6377	140	1	applied	apply	VERB
ejpam-6377	140	2	intelligence	intelligence	NOUN
ejpam-6377	140	3	,	,	PUNCT
ejpam-6377	140	4	53:1587–1603	53:1587–1603	NUM
ejpam-6377	140	5	,	,	PUNCT
ejpam-6377	140	6	2023	2023	NUM
ejpam-6377	140	7	.	.	PUNCT
ejpam-6377	141	1	[	[	X
ejpam-6377	141	2	2	2	NUM
ejpam-6377	141	3	]	]	X
ejpam-6377	141	4	r.	r.	PROPN
ejpam-6377	141	5	bakar	bakar	PROPN
ejpam-6377	141	6	and	and	CCONJ
ejpam-6377	141	7	z.	z.	PROPN
ejpam-6377	141	8	j.	j.	PROPN
ejpam-6377	141	9	weng	weng	PROPN
ejpam-6377	141	10	.	.	PUNCT
ejpam-6377	142	1	an	an	DET
ejpam-6377	142	2	adaptive	adaptive	ADJ
ejpam-6377	142	3	conjugate	conjugate	ADJ
ejpam-6377	142	4	gradient	gradient	NOUN
ejpam-6377	142	5	method	method	NOUN
ejpam-6377	142	6	with	with	ADP
ejpam-6377	142	7	descent	descent	NOUN
ejpam-6377	142	8	property	property	NOUN
ejpam-6377	142	9	.	.	PUNCT
ejpam-6377	143	1	numerical	numerical	ADJ
ejpam-6377	143	2	algorithms	algorithms	PROPN
ejpam-6377	143	3	,	,	PUNCT
ejpam-6377	143	4	94:107–129	94:107–129	PROPN
ejpam-6377	143	5	,	,	PUNCT
ejpam-6377	143	6	2023	2023	NUM
ejpam-6377	143	7	.	.	PUNCT
ejpam-6377	144	1	[	[	X
ejpam-6377	144	2	3	3	X
ejpam-6377	144	3	]	]	X
ejpam-6377	144	4	h.	h.	PROPN
ejpam-6377	144	5	chen	chen	PROPN
ejpam-6377	144	6	and	and	CCONJ
ejpam-6377	144	7	j.	j.	PROPN
ejpam-6377	144	8	zhang	zhang	PROPN
ejpam-6377	144	9	.	.	PUNCT
ejpam-6377	145	1	three	three	NUM
ejpam-6377	145	2	-	-	PUNCT
ejpam-6377	145	3	term	term	NOUN
ejpam-6377	145	4	conjugate	conjugate	ADJ
ejpam-6377	145	5	gradient	gradient	NOUN
ejpam-6377	145	6	algorithms	algorithm	NOUN
ejpam-6377	145	7	with	with	ADP
ejpam-6377	145	8	inexact	inexact	ADJ
ejpam-6377	145	9	line	line	NOUN
ejpam-6377	145	10	search	search	NOUN
ejpam-6377	145	11	for	for	ADP
ejpam-6377	145	12	large	large	ADJ
ejpam-6377	145	13	-	-	PUNCT
ejpam-6377	145	14	scale	scale	NOUN
ejpam-6377	145	15	optimization	optimization	NOUN
ejpam-6377	145	16	.	.	PUNCT
ejpam-6377	146	1	optimization	optimization	NOUN
ejpam-6377	146	2	letters	letter	NOUN
ejpam-6377	146	3	,	,	PUNCT
ejpam-6377	146	4	16(8):2315–2333	16(8):2315–2333	ADV
ejpam-6377	146	5	,	,	PUNCT
ejpam-6377	146	6	2022	2022	NUM
ejpam-6377	146	7	.	.	PUNCT
ejpam-6377	147	1	[	[	X
ejpam-6377	147	2	4	4	NUM
ejpam-6377	147	3	]	]	PUNCT
ejpam-6377	147	4	a.	a.	NOUN
ejpam-6377	147	5	k.	k.	PROPN
ejpam-6377	147	6	hussein	hussein	PROPN
ejpam-6377	147	7	and	and	CCONJ
ejpam-6377	147	8	s.	s.	PROPN
ejpam-6377	147	9	g.	g.	PROPN
ejpam-6377	147	10	shareef	shareef	PROPN
ejpam-6377	147	11	.	.	PUNCT
ejpam-6377	148	1	a	a	DET
ejpam-6377	148	2	new	new	ADJ
ejpam-6377	148	3	parameter	parameter	NOUN
ejpam-6377	148	4	conjugate	conjugate	ADJ
ejpam-6377	148	5	gradient	gradient	NOUN
ejpam-6377	148	6	method	method	NOUN
ejpam-6377	148	7	based	base	VERB
ejpam-6377	148	8	on	on	ADP
ejpam-6377	148	9	three	three	NUM
ejpam-6377	148	10	terms	term	NOUN
ejpam-6377	148	11	unconstrained	unconstraine	VERB
ejpam-6377	148	12	optimization	optimization	NOUN
ejpam-6377	148	13	.	.	PUNCT
ejpam-6377	149	1	general	general	ADJ
ejpam-6377	149	2	letters	letter	NOUN
ejpam-6377	149	3	in	in	ADP
ejpam-6377	149	4	mathematics	mathematic	NOUN
ejpam-6377	149	5	,	,	PUNCT
ejpam-6377	149	6	7(1):39	7(1):39	NUM
ejpam-6377	149	7	–	–	PUNCT
ejpam-6377	149	8	44	44	NUM
ejpam-6377	149	9	,	,	PUNCT
ejpam-6377	149	10	2019	2019	NUM
ejpam-6377	149	11	.	.	PUNCT
ejpam-6377	150	1	[	[	X
ejpam-6377	150	2	5	5	X
ejpam-6377	150	3	]	]	X
ejpam-6377	150	4	y.	y.	PROPN
ejpam-6377	150	5	h.	h.	PROPN
ejpam-6377	150	6	dai	dai	PROPN
ejpam-6377	150	7	,	,	PUNCT
ejpam-6377	150	8	j.	j.	PROPN
ejpam-6377	150	9	y.	y.	PROPN
ejpam-6377	150	10	han	han	PROPN
ejpam-6377	150	11	,	,	PUNCT
ejpam-6377	150	12	g.	g.	PROPN
ejpam-6377	150	13	h.	h.	PROPN
ejpam-6377	150	14	liu	liu	PROPN
ejpam-6377	150	15	,	,	PUNCT
ejpam-6377	150	16	d.	d.	PROPN
ejpam-6377	150	17	f.	f.	PROPN
ejpam-6377	150	18	sun	sun	PROPN
ejpam-6377	150	19	,	,	PUNCT
ejpam-6377	150	20	h.	h.	PROPN
ejpam-6377	150	21	x.	x.	PROPN
ejpam-6377	150	22	yin	yin	PROPN
ejpam-6377	150	23	,	,	PUNCT
ejpam-6377	150	24	and	and	CCONJ
ejpam-6377	150	25	y.	y.	PROPN
ejpam-6377	150	26	x.	x.	PROPN
ejpam-6377	150	27	yuan	yuan	PROPN
ejpam-6377	150	28	.	.	PUNCT
ejpam-6377	151	1	convergence	convergence	NOUN
ejpam-6377	151	2	properties	property	NOUN
ejpam-6377	151	3	of	of	ADP
ejpam-6377	151	4	nonlinear	nonlinear	ADJ
ejpam-6377	151	5	conjugate	conjugate	ADJ
ejpam-6377	151	6	gradient	gradient	ADJ
ejpam-6377	151	7	methods	method	NOUN
ejpam-6377	151	8	.	.	PUNCT
ejpam-6377	152	1	siam	siam	PROPN
ejpam-6377	152	2	journal	journal	PROPN
ejpam-6377	152	3	on	on	ADP
ejpam-6377	152	4	optimization	optimization	NOUN
ejpam-6377	152	5	,	,	PUNCT
ejpam-6377	152	6	10:348–358	10:348–358	PROPN
ejpam-6377	152	7	,	,	PUNCT
ejpam-6377	152	8	1999	1999	NUM
ejpam-6377	152	9	.	.	PUNCT
ejpam-6377	153	1	[	[	X
ejpam-6377	153	2	6	6	NUM
ejpam-6377	153	3	]	]	PUNCT
ejpam-6377	153	4	a.	a.	NOUN
ejpam-6377	153	5	a.	a.	PROPN
ejpam-6377	153	6	mustafa	mustafa	PROPN
ejpam-6377	153	7	.	.	PUNCT
ejpam-6377	154	1	new	new	ADJ
ejpam-6377	154	2	spectral	spectral	ADJ
ejpam-6377	154	3	ls	ls	ADJ
ejpam-6377	154	4	conjugate	conjugate	ADJ
ejpam-6377	154	5	gradient	gradient	NOUN
ejpam-6377	154	6	method	method	NOUN
ejpam-6377	154	7	for	for	ADP
ejpam-6377	154	8	nonlinear	nonlinear	ADJ
ejpam-6377	154	9	unconstrained	unconstrained	ADJ
ejpam-6377	154	10	optimization	optimization	NOUN
ejpam-6377	154	11	.	.	PUNCT
ejpam-6377	155	1	international	international	ADJ
ejpam-6377	155	2	journal	journal	PROPN
ejpam-6377	155	3	of	of	ADP
ejpam-6377	155	4	computer	computer	NOUN
ejpam-6377	155	5	mathematics	mathematic	NOUN
ejpam-6377	155	6	,	,	PUNCT
ejpam-6377	155	7	100(4):838–846	100(4):838–846	NUM
ejpam-6377	155	8	,	,	PUNCT
ejpam-6377	155	9	2023	2023	NUM
ejpam-6377	155	10	.	.	PUNCT
ejpam-6377	156	1	[	[	X
ejpam-6377	156	2	7	7	X
ejpam-6377	156	3	]	]	PUNCT
ejpam-6377	156	4	a.	a.	NOUN
ejpam-6377	156	5	a.	a.	PROPN
ejpam-6377	156	6	mustafa	mustafa	PROPN
ejpam-6377	156	7	.	.	PUNCT
ejpam-6377	157	1	a	a	DET
ejpam-6377	157	2	new	new	ADJ
ejpam-6377	157	3	algorithm	algorithm	NOUN
ejpam-6377	157	4	for	for	ADP
ejpam-6377	157	5	spectral	spectral	ADJ
ejpam-6377	157	6	conjugate	conjugate	ADJ
ejpam-6377	157	7	gradient	gradient	NOUN
ejpam-6377	157	8	in	in	ADP
ejpam-6377	157	9	nonlinear	nonlinear	ADJ
ejpam-6377	157	10	optimization	optimization	NOUN
ejpam-6377	157	11	.	.	PUNCT
ejpam-6377	158	1	mathematics	mathematic	NOUN
ejpam-6377	158	2	and	and	CCONJ
ejpam-6377	158	3	statistics	statistic	NOUN
ejpam-6377	158	4	,	,	PUNCT
ejpam-6377	158	5	10(2):293–300	10(2):293–300	NUM
ejpam-6377	158	6	,	,	PUNCT
ejpam-6377	158	7	2022	2022	NUM
ejpam-6377	158	8	.	.	PUNCT
ejpam-6377	159	1	[	[	X
ejpam-6377	159	2	8	8	NUM
ejpam-6377	159	3	]	]	X
ejpam-6377	159	4	y.	y.	PROPN
ejpam-6377	159	5	liu	liu	PROPN
ejpam-6377	159	6	and	and	CCONJ
ejpam-6377	159	7	h.	h.	PROPN
ejpam-6377	159	8	wang	wang	PROPN
ejpam-6377	159	9	.	.	PUNCT
ejpam-6377	160	1	spectral	spectral	ADJ
ejpam-6377	160	2	-	-	PUNCT
ejpam-6377	160	3	type	type	NOUN
ejpam-6377	160	4	cg	cg	NOUN
ejpam-6377	160	5	methods	method	NOUN
ejpam-6377	160	6	for	for	ADP
ejpam-6377	160	7	deep	deep	ADJ
ejpam-6377	160	8	learning	learn	VERB
ejpam-6377	160	9	optimization	optimization	NOUN
ejpam-6377	160	10	.	.	PUNCT
ejpam-6377	161	1	journal	journal	NOUN
ejpam-6377	161	2	of	of	ADP
ejpam-6377	161	3	computational	computational	ADJ
ejpam-6377	161	4	mathematics	mathematic	NOUN
ejpam-6377	161	5	,	,	PUNCT
ejpam-6377	161	6	43(1):45–67	43(1):45–67	NUM
ejpam-6377	161	7	,	,	PUNCT
ejpam-6377	161	8	2024	2024	NUM
ejpam-6377	161	9	.	.	PUNCT
ejpam-6377	162	1	[	[	X
ejpam-6377	162	2	9	9	NUM
ejpam-6377	162	3	]	]	PUNCT
ejpam-6377	162	4	a.	a.	NOUN
ejpam-6377	162	5	k.	k.	PROPN
ejpam-6377	162	6	mohammed	mohammed	PROPN
ejpam-6377	162	7	and	and	CCONJ
ejpam-6377	162	8	s.	s.	PROPN
ejpam-6377	162	9	r.	r.	PROPN
ejpam-6377	162	10	al	al	PROPN
ejpam-6377	162	11	-	-	PUNCT
ejpam-6377	162	12	taie	taie	PROPN
ejpam-6377	162	13	.	.	PUNCT
ejpam-6377	163	1	global	global	ADJ
ejpam-6377	163	2	convergence	convergence	NOUN
ejpam-6377	163	3	of	of	ADP
ejpam-6377	163	4	parameterized	parameterized	ADJ
ejpam-6377	163	5	conjugate	conjugate	ADJ
ejpam-6377	163	6	gradient	gradient	ADJ
ejpam-6377	163	7	algorithms	algorithm	NOUN
ejpam-6377	163	8	.	.	PUNCT
ejpam-6377	164	1	mathematics	mathematic	NOUN
ejpam-6377	164	2	,	,	PUNCT
ejpam-6377	164	3	12(3):389–404	12(3):389–404	PROPN
ejpam-6377	164	4	,	,	PUNCT
ejpam-6377	164	5	2024	2024	NUM
ejpam-6377	164	6	.	.	PUNCT
ejpam-6377	165	1	[	[	X
ejpam-6377	165	2	10	10	NUM
ejpam-6377	165	3	]	]	X
ejpam-6377	165	4	f.	f.	PROPN
ejpam-6377	165	5	zhang	zhang	PROPN
ejpam-6377	165	6	and	and	CCONJ
ejpam-6377	165	7	c.	c.	PROPN
ejpam-6377	165	8	li	li	PROPN
ejpam-6377	165	9	.	.	PROPN
ejpam-6377	165	10	sufficient	sufficient	ADJ
ejpam-6377	165	11	descent	descent	NOUN
ejpam-6377	165	12	and	and	CCONJ
ejpam-6377	165	13	global	global	ADJ
ejpam-6377	165	14	convergence	convergence	NOUN
ejpam-6377	165	15	in	in	ADP
ejpam-6377	165	16	nonlinear	nonlinear	ADJ
ejpam-6377	165	17	cg	cg	NOUN
ejpam-6377	165	18	methods	method	NOUN
ejpam-6377	165	19	with	with	ADP
ejpam-6377	165	20	modified	modified	ADJ
ejpam-6377	165	21	β	β	NOUN
ejpam-6377	165	22	-	-	NOUN
ejpam-6377	165	23	updates	update	NOUN
ejpam-6377	165	24	.	.	PUNCT
ejpam-6377	166	1	journal	journal	NOUN
ejpam-6377	166	2	of	of	ADP
ejpam-6377	166	3	optimization	optimization	NOUN
ejpam-6377	166	4	theory	theory	NOUN
ejpam-6377	166	5	and	and	CCONJ
ejpam-6377	166	6	applications	application	NOUN
ejpam-6377	166	7	,	,	PUNCT
ejpam-6377	166	8	195:623	195:623	NUM
ejpam-6377	166	9	–	–	PUNCT
ejpam-6377	166	10	647	647	NUM
ejpam-6377	166	11	,	,	PUNCT
ejpam-6377	166	12	2025	2025	NUM
ejpam-6377	166	13	.	.	PUNCT
ejpam-6377	167	1	[	[	X
ejpam-6377	167	2	11	11	NUM
ejpam-6377	167	3	]	]	PUNCT
ejpam-6377	167	4	r.	r.	PROPN
ejpam-6377	167	5	fletcher	fletcher	PROPN
ejpam-6377	167	6	and	and	CCONJ
ejpam-6377	167	7	c.	c.	PROPN
ejpam-6377	167	8	m.	m.	PROPN
ejpam-6377	167	9	reeves	reeves	PROPN
ejpam-6377	167	10	.	.	PUNCT
ejpam-6377	168	1	function	function	NOUN
ejpam-6377	168	2	minimization	minimization	NOUN
ejpam-6377	168	3	by	by	ADP
ejpam-6377	168	4	conjugate	conjugate	ADJ
ejpam-6377	168	5	gradients	gradient	NOUN
ejpam-6377	168	6	.	.	PUNCT
ejpam-6377	169	1	the	the	DET
ejpam-6377	169	2	computer	computer	NOUN
ejpam-6377	169	3	journal	journal	NOUN
ejpam-6377	169	4	,	,	PUNCT
ejpam-6377	169	5	7(2):149–154	7(2):149–154	NUM
ejpam-6377	169	6	,	,	PUNCT
ejpam-6377	169	7	1964	1964	NUM
ejpam-6377	169	8	.	.	PUNCT
ejpam-6377	170	1	[	[	X
ejpam-6377	170	2	12	12	NUM
ejpam-6377	170	3	]	]	X
ejpam-6377	170	4	y.	y.	PROPN
ejpam-6377	170	5	h.	h.	PROPN
ejpam-6377	170	6	dai	dai	PROPN
ejpam-6377	170	7	and	and	CCONJ
ejpam-6377	170	8	y.	y.	PROPN
ejpam-6377	170	9	yuan	yuan	PROPN
ejpam-6377	170	10	.	.	PUNCT
ejpam-6377	171	1	a	a	DET
ejpam-6377	171	2	nonlinear	nonlinear	ADJ
ejpam-6377	171	3	conjugate	conjugate	ADJ
ejpam-6377	171	4	gradient	gradient	NOUN
ejpam-6377	171	5	method	method	NOUN
ejpam-6377	171	6	with	with	ADP
ejpam-6377	171	7	a	a	DET
ejpam-6377	171	8	strong	strong	ADJ
ejpam-6377	171	9	global	global	ADJ
ejpam-6377	171	10	convergence	convergence	NOUN
ejpam-6377	171	11	property	property	NOUN
ejpam-6377	171	12	.	.	PUNCT
ejpam-6377	172	1	siam	siam	PROPN
ejpam-6377	172	2	journal	journal	PROPN
ejpam-6377	172	3	on	on	ADP
ejpam-6377	172	4	optimization	optimization	NOUN
ejpam-6377	172	5	,	,	PUNCT
ejpam-6377	172	6	10:177–182	10:177–182	PROPN
ejpam-6377	172	7	,	,	PUNCT
ejpam-6377	172	8	1999	1999	NUM
ejpam-6377	172	9	.	.	PUNCT
ejpam-6377	173	1	[	[	X
ejpam-6377	173	2	13	13	NUM
ejpam-6377	173	3	]	]	PUNCT
ejpam-6377	173	4	m.	m.	NOUN
ejpam-6377	173	5	r.	r.	PROPN
ejpam-6377	173	6	hestenes	hestenes	PROPN
ejpam-6377	173	7	and	and	CCONJ
ejpam-6377	173	8	e.	e.	PROPN
ejpam-6377	173	9	stiefel	stiefel	PROPN
ejpam-6377	173	10	.	.	PUNCT
ejpam-6377	174	1	methods	method	NOUN
ejpam-6377	174	2	of	of	ADP
ejpam-6377	174	3	conjugate	conjugate	ADJ
ejpam-6377	174	4	gradients	gradient	NOUN
ejpam-6377	174	5	for	for	ADP
ejpam-6377	174	6	solving	solve	VERB
ejpam-6377	174	7	linear	linear	NOUN
ejpam-6377	174	8	systems	system	NOUN
ejpam-6377	174	9	.	.	PUNCT
ejpam-6377	175	1	journal	journal	PROPN
ejpam-6377	175	2	of	of	ADP
ejpam-6377	175	3	research	research	NOUN
ejpam-6377	175	4	of	of	ADP
ejpam-6377	175	5	the	the	DET
ejpam-6377	175	6	national	national	PROPN
ejpam-6377	175	7	bureau	bureau	PROPN
ejpam-6377	175	8	of	of	ADP
ejpam-6377	175	9	standards	standard	NOUN
ejpam-6377	175	10	,	,	PUNCT
ejpam-6377	175	11	49(6):409–436	49(6):409–436	NOUN
ejpam-6377	175	12	,	,	PUNCT
ejpam-6377	175	13	1952	1952	NUM
ejpam-6377	175	14	.	.	PUNCT
ejpam-6377	176	1	[	[	X
ejpam-6377	176	2	14	14	NUM
ejpam-6377	176	3	]	]	X
ejpam-6377	176	4	e.	e.	PROPN
ejpam-6377	176	5	polak	polak	PROPN
ejpam-6377	176	6	and	and	CCONJ
ejpam-6377	176	7	g.	g.	PROPN
ejpam-6377	176	8	ribière	ribière	PROPN
ejpam-6377	176	9	.	.	PUNCT
ejpam-6377	177	1	note	note	VERB
ejpam-6377	177	2	sur	sur	PROPN
ejpam-6377	177	3	la	la	X
ejpam-6377	177	4	convergence	convergence	NOUN
ejpam-6377	177	5	de	de	X
ejpam-6377	177	6	méthodes	méthodes	X
ejpam-6377	177	7	de	de	PROPN
ejpam-6377	177	8	directions	direction	NOUN
ejpam-6377	177	9	conjuguées	conjuguées	PROPN
ejpam-6377	177	10	.	.	PUNCT
ejpam-6377	178	1	revue	revue	PROPN
ejpam-6377	178	2	française	française	PROPN
ejpam-6377	178	3	d’informatique	d’informatique	NOUN
ejpam-6377	178	4	et	et	X
ejpam-6377	178	5	de	de	X
ejpam-6377	178	6	recherche	recherche	X
ejpam-6377	178	7	opérationnelle	opérationnelle	PROPN
ejpam-6377	178	8	,	,	PUNCT
ejpam-6377	178	9	16:35–43	16:35–43	NUM
ejpam-6377	178	10	,	,	PUNCT
ejpam-6377	178	11	1969	1969	NUM
ejpam-6377	178	12	.	.	PUNCT
ejpam-6377	179	1	a.	a.	NOUN
ejpam-6377	179	2	a.	a.	PROPN
ejpam-6377	179	3	mustafa	mustafa	PROPN
ejpam-6377	179	4	,	,	PUNCT
ejpam-6377	179	5	h.	h.	PROPN
ejpam-6377	179	6	a.	a.	PROPN
ejpam-6377	179	7	khatab	khatab	PROPN
ejpam-6377	179	8	/	/	SYM
ejpam-6377	179	9	eur	eur	PROPN
ejpam-6377	179	10	.	.	PUNCT
ejpam-6377	180	1	j.	j.	PROPN
ejpam-6377	180	2	pure	pure	PROPN
ejpam-6377	180	3	appl	appl	PROPN
ejpam-6377	180	4	.	.	PROPN
ejpam-6377	180	5	math	math	PROPN
ejpam-6377	180	6	,	,	PUNCT
ejpam-6377	180	7	18	18	NUM
ejpam-6377	180	8	(	(	PUNCT
ejpam-6377	180	9	3	3	NUM
ejpam-6377	180	10	)	)	PUNCT
ejpam-6377	180	11	(	(	PUNCT
ejpam-6377	180	12	2025	2025	NUM
ejpam-6377	180	13	)	)	PUNCT
ejpam-6377	180	14	,	,	PUNCT
ejpam-6377	180	15	6377	6377	NUM
ejpam-6377	180	16	12	12	NUM
ejpam-6377	180	17	of	of	ADP
ejpam-6377	180	18	12	12	NUM
ejpam-6377	181	1	[	[	SYM
ejpam-6377	181	2	15	15	NUM
ejpam-6377	181	3	]	]	X
ejpam-6377	181	4	r.	r.	PROPN
ejpam-6377	181	5	fletcher	fletcher	PROPN
ejpam-6377	181	6	.	.	PUNCT
ejpam-6377	182	1	practical	practical	ADJ
ejpam-6377	182	2	methods	method	NOUN
ejpam-6377	182	3	of	of	ADP
ejpam-6377	182	4	optimization	optimization	NOUN
ejpam-6377	182	5	.	.	PUNCT
ejpam-6377	183	1	wiley	wiley	PROPN
ejpam-6377	183	2	,	,	PUNCT
ejpam-6377	183	3	new	new	PROPN
ejpam-6377	183	4	york	york	PROPN
ejpam-6377	183	5	,	,	PUNCT
ejpam-6377	183	6	2	2	NUM
ejpam-6377	183	7	edition	edition	NOUN
ejpam-6377	183	8	,	,	PUNCT
ejpam-6377	183	9	1987	1987	NUM
ejpam-6377	183	10	.	.	PUNCT
ejpam-6377	184	1	[	[	X
ejpam-6377	184	2	16	16	X
ejpam-6377	184	3	]	]	X
ejpam-6377	184	4	y.	y.	PROPN
ejpam-6377	184	5	liu	liu	PROPN
ejpam-6377	184	6	and	and	CCONJ
ejpam-6377	184	7	c.	c.	PROPN
ejpam-6377	184	8	storey	storey	PROPN
ejpam-6377	184	9	.	.	PUNCT
ejpam-6377	185	1	efficient	efficient	ADJ
ejpam-6377	185	2	generalized	generalize	VERB
ejpam-6377	185	3	conjugate	conjugate	ADJ
ejpam-6377	185	4	gradient	gradient	ADJ
ejpam-6377	185	5	algorithms	algorithm	NOUN
ejpam-6377	185	6	,	,	PUNCT
ejpam-6377	185	7	part	part	NOUN
ejpam-6377	185	8	1	1	NUM
ejpam-6377	185	9	:	:	PUNCT
ejpam-6377	185	10	theory	theory	NOUN
ejpam-6377	185	11	.	.	PUNCT
ejpam-6377	186	1	journal	journal	NOUN
ejpam-6377	186	2	of	of	ADP
ejpam-6377	186	3	optimization	optimization	NOUN
ejpam-6377	186	4	theory	theory	NOUN
ejpam-6377	186	5	and	and	CCONJ
ejpam-6377	186	6	applications	application	NOUN
ejpam-6377	186	7	,	,	PUNCT
ejpam-6377	186	8	69:129–137	69:129–137	NUM
ejpam-6377	186	9	,	,	PUNCT
ejpam-6377	186	10	1991	1991	NUM
ejpam-6377	186	11	.	.	PUNCT
ejpam-6377	187	1	[	[	X
ejpam-6377	187	2	17	17	NUM
ejpam-6377	187	3	]	]	X
ejpam-6377	187	4	g.	g.	PROPN
ejpam-6377	187	5	zoutendijk	zoutendijk	PROPN
ejpam-6377	187	6	.	.	PUNCT
ejpam-6377	188	1	nonlinear	nonlinear	ADJ
ejpam-6377	188	2	programming	programming	NOUN
ejpam-6377	188	3	,	,	PUNCT
ejpam-6377	188	4	computational	computational	ADJ
ejpam-6377	188	5	methods	method	NOUN
ejpam-6377	188	6	.	.	PUNCT
ejpam-6377	189	1	in	in	ADP
ejpam-6377	189	2	j.	j.	PROPN
ejpam-6377	189	3	abadie	abadie	PROPN
ejpam-6377	189	4	,	,	PUNCT
ejpam-6377	189	5	editor	editor	NOUN
ejpam-6377	189	6	,	,	PUNCT
ejpam-6377	189	7	integer	integer	NOUN
ejpam-6377	189	8	and	and	CCONJ
ejpam-6377	189	9	nonlinear	nonlinear	ADJ
ejpam-6377	189	10	programming	programming	NOUN
ejpam-6377	189	11	,	,	PUNCT
ejpam-6377	189	12	pages	page	NOUN
ejpam-6377	189	13	37–86	37–86	NUM
ejpam-6377	189	14	.	.	PUNCT
ejpam-6377	190	1	north	north	NOUN
ejpam-6377	190	2	-	-	PUNCT
ejpam-6377	190	3	holland	holland	PROPN
ejpam-6377	190	4	,	,	PUNCT
ejpam-6377	190	5	1970	1970	NUM
ejpam-6377	190	6	.	.	PUNCT
ejpam-6377	191	1	[	[	X
ejpam-6377	191	2	18	18	NUM
ejpam-6377	191	3	]	]	PUNCT
ejpam-6377	191	4	a.	a.	PROPN
ejpam-6377	191	5	al	al	PROPN
ejpam-6377	191	6	-	-	PUNCT
ejpam-6377	191	7	baali	baali	PROPN
ejpam-6377	191	8	.	.	PUNCT
ejpam-6377	192	1	descent	descent	NOUN
ejpam-6377	192	2	property	property	NOUN
ejpam-6377	192	3	and	and	CCONJ
ejpam-6377	192	4	global	global	ADJ
ejpam-6377	192	5	convergence	convergence	NOUN
ejpam-6377	192	6	of	of	ADP
ejpam-6377	192	7	the	the	DET
ejpam-6377	192	8	fletcher	fletcher	PROPN
ejpam-6377	192	9	-	-	PUNCT
ejpam-6377	192	10	reeves	reeves	PROPN
ejpam-6377	192	11	method	method	NOUN
ejpam-6377	192	12	with	with	ADP
ejpam-6377	192	13	inexact	inexact	ADJ
ejpam-6377	192	14	line	line	NOUN
ejpam-6377	192	15	search	search	NOUN
ejpam-6377	192	16	.	.	PUNCT
ejpam-6377	193	1	i	i	PRON
ejpam-6377	193	2	m	m	VERB
ejpam-6377	193	3	a	a	DET
ejpam-6377	193	4	journal	journal	NOUN
ejpam-6377	193	5	of	of	ADP
ejpam-6377	193	6	numerical	numerical	ADJ
ejpam-6377	193	7	analysis	analysis	NOUN
ejpam-6377	193	8	,	,	PUNCT
ejpam-6377	193	9	5:121–124	5:121–124	NUM
ejpam-6377	193	10	,	,	PUNCT
ejpam-6377	193	11	1985	1985	NUM
ejpam-6377	193	12	.	.	PUNCT
ejpam-6377	194	1	[	[	X
ejpam-6377	194	2	19	19	NUM
ejpam-6377	194	3	]	]	PUNCT
ejpam-6377	194	4	w.	w.	PROPN
ejpam-6377	194	5	w.	w.	PROPN
ejpam-6377	194	6	hager	hager	PROPN
ejpam-6377	194	7	and	and	CCONJ
ejpam-6377	194	8	h.	h.	PROPN
ejpam-6377	194	9	zhang	zhang	PROPN
ejpam-6377	194	10	.	.	PUNCT
ejpam-6377	195	1	a	a	DET
ejpam-6377	195	2	new	new	ADJ
ejpam-6377	195	3	conjugate	conjugate	ADJ
ejpam-6377	195	4	gradient	gradient	NOUN
ejpam-6377	195	5	method	method	NOUN
ejpam-6377	195	6	with	with	ADP
ejpam-6377	195	7	guaranteed	guarantee	VERB
ejpam-6377	195	8	descent	descent	NOUN
ejpam-6377	195	9	and	and	CCONJ
ejpam-6377	195	10	an	an	DET
ejpam-6377	195	11	efficient	efficient	ADJ
ejpam-6377	195	12	line	line	NOUN
ejpam-6377	195	13	search	search	NOUN
ejpam-6377	195	14	.	.	PUNCT
ejpam-6377	196	1	siam	siam	PROPN
ejpam-6377	196	2	journal	journal	PROPN
ejpam-6377	196	3	on	on	ADP
ejpam-6377	196	4	optimization	optimization	NOUN
ejpam-6377	196	5	,	,	PUNCT
ejpam-6377	196	6	16(1):170–192	16(1):170–192	NUM
ejpam-6377	196	7	,	,	PUNCT
ejpam-6377	196	8	2005	2005	NUM
ejpam-6377	196	9	.	.	PUNCT
ejpam-6377	197	1	[	[	X
ejpam-6377	197	2	20	20	NUM
ejpam-6377	197	3	]	]	PUNCT
ejpam-6377	197	4	s.	s.	PROPN
ejpam-6377	197	5	g.	g.	PROPN
ejpam-6377	197	6	hussein	hussein	PROPN
ejpam-6377	197	7	and	and	CCONJ
ejpam-6377	197	8	a.	a.	PROPN
ejpam-6377	197	9	k.	k.	PROPN
ejpam-6377	197	10	hussein	hussein	PROPN
ejpam-6377	197	11	.	.	PUNCT
ejpam-6377	198	1	general	general	ADJ
ejpam-6377	198	2	letters	letter	NOUN
ejpam-6377	198	3	in	in	ADP
ejpam-6377	198	4	mathematics	mathematic	NOUN
ejpam-6377	198	5	,	,	PUNCT
ejpam-6377	198	6	9(2	9(2	NUM
ejpam-6377	198	7	)	)	PUNCT
ejpam-6377	198	8	,	,	PUNCT
ejpam-6377	198	9	2020	2020	NUM
ejpam-6377	198	10	.	.	PUNCT
ejpam-6377	199	1	[	[	X
ejpam-6377	199	2	21	21	NUM
ejpam-6377	199	3	]	]	X
ejpam-6377	199	4	e.	e.	PROPN
ejpam-6377	199	5	d.	d.	PROPN
ejpam-6377	199	6	dolan	dolan	PROPN
ejpam-6377	199	7	and	and	CCONJ
ejpam-6377	199	8	j.	j.	PROPN
ejpam-6377	199	9	j.	j.	PROPN
ejpam-6377	199	10	moré.	moré.	PROPN
ejpam-6377	199	11	benchmarking	benchmarke	VERB
ejpam-6377	199	12	optimization	optimization	NOUN
ejpam-6377	199	13	software	software	NOUN
ejpam-6377	199	14	with	with	ADP
ejpam-6377	199	15	performance	performance	NOUN
ejpam-6377	199	16	profiles	profile	NOUN
ejpam-6377	199	17	.	.	PUNCT
ejpam-6377	200	1	mathematical	mathematical	ADJ
ejpam-6377	200	2	programming	programming	NOUN
ejpam-6377	200	3	,	,	PUNCT
ejpam-6377	200	4	91(2):201–213	91(2):201–213	PROPN
ejpam-6377	200	5	,	,	PUNCT
ejpam-6377	200	6	2002	2002	NUM
ejpam-6377	200	7	.	.	PUNCT