id	sid	tid	token	lemma	pos
ejpam-4746	1	1	european	european	PROPN
ejpam-4746	1	2	journal	journal	PROPN
ejpam-4746	1	3	of	of	ADP
ejpam-4746	1	4	pure	pure	ADJ
ejpam-4746	1	5	and	and	CCONJ
ejpam-4746	1	6	applied	apply	VERB
ejpam-4746	1	7	mathematics	mathematic	NOUN
ejpam-4746	1	8	vol	vol	NOUN
ejpam-4746	1	9	.	.	PUNCT
ejpam-4746	2	1	16	16	NUM
ejpam-4746	2	2	,	,	PUNCT
ejpam-4746	2	3	no	no	INTJ
ejpam-4746	2	4	.	.	NOUN
ejpam-4746	2	5	2	2	NUM
ejpam-4746	2	6	,	,	PUNCT
ejpam-4746	2	7	2023	2023	NUM
ejpam-4746	2	8	,	,	PUNCT
ejpam-4746	2	9	1059	1059	NUM
ejpam-4746	2	10	-	-	SYM
ejpam-4746	2	11	1067	1067	NUM
ejpam-4746	2	12	issn	issn	PROPN
ejpam-4746	2	13	1307	1307	NUM
ejpam-4746	2	14	-	-	SYM
ejpam-4746	2	15	5543	5543	NUM
ejpam-4746	2	16	–	–	PUNCT
ejpam-4746	2	17	ejpam.com	ejpam.com	X
ejpam-4746	2	18	published	publish	VERB
ejpam-4746	2	19	by	by	ADP
ejpam-4746	2	20	new	new	PROPN
ejpam-4746	2	21	york	york	PROPN
ejpam-4746	2	22	business	business	PROPN
ejpam-4746	3	1	global	global	PROPN
ejpam-4746	3	2	a	a	DET
ejpam-4746	3	3	hybridization	hybridization	NOUN
ejpam-4746	3	4	of	of	ADP
ejpam-4746	3	5	the	the	DET
ejpam-4746	3	6	hestenes	hestene	NOUN
ejpam-4746	3	7	-	-	PUNCT
ejpam-4746	3	8	stiefel	stiefel	NOUN
ejpam-4746	3	9	and	and	CCONJ
ejpam-4746	3	10	dai	dai	PROPN
ejpam-4746	3	11	-	-	PUNCT
ejpam-4746	3	12	yuan	yuan	PROPN
ejpam-4746	3	13	conjugate	conjugate	ADJ
ejpam-4746	3	14	gradient	gradient	NOUN
ejpam-4746	3	15	methods	method	NOUN
ejpam-4746	3	16	yoksal	yoksal	PROPN
ejpam-4746	3	17	a.	a.	PROPN
ejpam-4746	3	18	laylani1	laylani1	PROPN
ejpam-4746	3	19	,	,	PUNCT
ejpam-4746	3	20	hisham	hisham	PROPN
ejpam-4746	3	21	m.	m.	PROPN
ejpam-4746	3	22	khudhur2,∗	khudhur2,∗	PROPN
ejpam-4746	3	23	,	,	PUNCT
ejpam-4746	3	24	edrees	edree	NOUN
ejpam-4746	3	25	m.	m.	PROPN
ejpam-4746	3	26	nori2	nori2	PROPN
ejpam-4746	3	27	,	,	PUNCT
ejpam-4746	3	28	khalil	khalil	PROPN
ejpam-4746	3	29	k.	k.	PROPN
ejpam-4746	4	1	abbo3	abbo3	PROPN
ejpam-4746	5	1	1	1	NUM
ejpam-4746	5	2	department	department	NOUN
ejpam-4746	5	3	of	of	ADP
ejpam-4746	5	4	mathematics	mathematic	NOUN
ejpam-4746	5	5	,	,	PUNCT
ejpam-4746	5	6	college	college	NOUN
ejpam-4746	5	7	of	of	ADP
ejpam-4746	5	8	sciences	science	NOUN
ejpam-4746	5	9	,	,	PUNCT
ejpam-4746	5	10	university	university	NOUN
ejpam-4746	5	11	of	of	ADP
ejpam-4746	5	12	kirkuk	kirkuk	PROPN
ejpam-4746	5	13	,	,	PUNCT
ejpam-4746	5	14	kirkuk	kirkuk	PROPN
ejpam-4746	5	15	,	,	PUNCT
ejpam-4746	5	16	iraq	iraq	PROPN
ejpam-4746	5	17	2	2	NUM
ejpam-4746	5	18	department	department	NOUN
ejpam-4746	5	19	of	of	ADP
ejpam-4746	5	20	mathematics	mathematic	NOUN
ejpam-4746	5	21	,	,	PUNCT
ejpam-4746	5	22	college	college	NOUN
ejpam-4746	5	23	of	of	ADP
ejpam-4746	5	24	computers	computer	NOUN
ejpam-4746	5	25	sciences	sciences	PROPN
ejpam-4746	5	26	and	and	CCONJ
ejpam-4746	5	27	mathematics	mathematic	NOUN
ejpam-4746	5	28	,	,	PUNCT
ejpam-4746	5	29	university	university	NOUN
ejpam-4746	5	30	of	of	ADP
ejpam-4746	5	31	mosul	mosul	PROPN
ejpam-4746	5	32	,	,	PUNCT
ejpam-4746	5	33	mosul	mosul	PROPN
ejpam-4746	5	34	,	,	PUNCT
ejpam-4746	5	35	iraq	iraq	PROPN
ejpam-4746	5	36	3	3	NUM
ejpam-4746	5	37	department	department	NOUN
ejpam-4746	5	38	of	of	ADP
ejpam-4746	5	39	mathematics	mathematics	PROPN
ejpam-4746	5	40	,	,	PUNCT
ejpam-4746	5	41	college	college	NOUN
ejpam-4746	5	42	of	of	ADP
ejpam-4746	5	43	basic	basic	ADJ
ejpam-4746	5	44	education	education	NOUN
ejpam-4746	5	45	,	,	PUNCT
ejpam-4746	5	46	university	university	NOUN
ejpam-4746	5	47	of	of	ADP
ejpam-4746	5	48	telafer	telafer	PROPN
ejpam-4746	5	49	,	,	PUNCT
ejpam-4746	5	50	tall’afar	tall’afar	ADV
ejpam-4746	5	51	,	,	PUNCT
ejpam-4746	5	52	iraq	iraq	PROPN
ejpam-4746	5	53	abstract	abstract	NOUN
ejpam-4746	5	54	.	.	PUNCT
ejpam-4746	6	1	the	the	DET
ejpam-4746	6	2	paper	paper	NOUN
ejpam-4746	6	3	in	in	ADP
ejpam-4746	6	4	discusses	discusse	NOUN
ejpam-4746	6	5	conjugate	conjugate	ADJ
ejpam-4746	6	6	gradient	gradient	ADJ
ejpam-4746	6	7	methods	method	NOUN
ejpam-4746	6	8	,	,	PUNCT
ejpam-4746	6	9	which	which	PRON
ejpam-4746	6	10	are	be	AUX
ejpam-4746	6	11	often	often	ADV
ejpam-4746	6	12	used	use	VERB
ejpam-4746	6	13	for	for	ADP
ejpam-4746	6	14	unconstrained	unconstrained	ADJ
ejpam-4746	6	15	optimization	optimization	NOUN
ejpam-4746	6	16	and	and	CCONJ
ejpam-4746	6	17	are	be	AUX
ejpam-4746	6	18	the	the	DET
ejpam-4746	6	19	subject	subject	NOUN
ejpam-4746	6	20	of	of	ADP
ejpam-4746	6	21	this	this	DET
ejpam-4746	6	22	discussion	discussion	NOUN
ejpam-4746	6	23	.	.	PUNCT
ejpam-4746	7	1	in	in	ADP
ejpam-4746	7	2	the	the	DET
ejpam-4746	7	3	process	process	NOUN
ejpam-4746	7	4	of	of	ADP
ejpam-4746	7	5	studying	study	VERB
ejpam-4746	7	6	and	and	CCONJ
ejpam-4746	7	7	implementing	implement	VERB
ejpam-4746	7	8	conjugate	conjugate	ADJ
ejpam-4746	7	9	gradient	gradient	ADJ
ejpam-4746	7	10	algorithms	algorithm	NOUN
ejpam-4746	7	11	,	,	PUNCT
ejpam-4746	7	12	it	it	PRON
ejpam-4746	7	13	is	be	AUX
ejpam-4746	7	14	standard	standard	ADJ
ejpam-4746	7	15	practice	practice	NOUN
ejpam-4746	7	16	to	to	PART
ejpam-4746	7	17	assume	assume	VERB
ejpam-4746	7	18	that	that	SCONJ
ejpam-4746	7	19	the	the	DET
ejpam-4746	7	20	descent	descent	NOUN
ejpam-4746	7	21	condition	condition	NOUN
ejpam-4746	7	22	is	be	AUX
ejpam-4746	7	23	true	true	ADJ
ejpam-4746	7	24	.	.	PUNCT
ejpam-4746	8	1	despite	despite	SCONJ
ejpam-4746	8	2	the	the	DET
ejpam-4746	8	3	fact	fact	NOUN
ejpam-4746	8	4	that	that	SCONJ
ejpam-4746	8	5	this	this	DET
ejpam-4746	8	6	sort	sort	NOUN
ejpam-4746	8	7	of	of	ADP
ejpam-4746	8	8	approach	approach	NOUN
ejpam-4746	8	9	very	very	ADV
ejpam-4746	8	10	seldom	seldom	ADV
ejpam-4746	8	11	results	result	VERB
ejpam-4746	8	12	in	in	ADP
ejpam-4746	8	13	search	search	NOUN
ejpam-4746	8	14	routes	route	NOUN
ejpam-4746	8	15	that	that	PRON
ejpam-4746	8	16	slope	slope	VERB
ejpam-4746	8	17	in	in	ADP
ejpam-4746	8	18	a	a	DET
ejpam-4746	8	19	downward	downward	ADJ
ejpam-4746	8	20	direction	direction	NOUN
ejpam-4746	8	21	,	,	PUNCT
ejpam-4746	8	22	this	this	DET
ejpam-4746	8	23	assumption	assumption	NOUN
ejpam-4746	8	24	is	be	AUX
ejpam-4746	8	25	made	make	VERB
ejpam-4746	8	26	routinely	routinely	ADV
ejpam-4746	8	27	.	.	PUNCT
ejpam-4746	9	1	as	as	ADP
ejpam-4746	9	2	a	a	DET
ejpam-4746	9	3	result	result	NOUN
ejpam-4746	9	4	of	of	ADP
ejpam-4746	9	5	this	this	DET
ejpam-4746	9	6	research	research	NOUN
ejpam-4746	9	7	,	,	PUNCT
ejpam-4746	9	8	we	we	PRON
ejpam-4746	9	9	propose	propose	VERB
ejpam-4746	9	10	a	a	DET
ejpam-4746	9	11	revised	revise	VERB
ejpam-4746	9	12	method	method	NOUN
ejpam-4746	9	13	known	know	VERB
ejpam-4746	9	14	as	as	ADP
ejpam-4746	9	15	the	the	DET
ejpam-4746	9	16	improved	improve	VERB
ejpam-4746	9	17	hybrid	hybrid	ADJ
ejpam-4746	9	18	conjugate	conjugate	ADJ
ejpam-4746	9	19	gradient	gradient	NOUN
ejpam-4746	9	20	technique	technique	NOUN
ejpam-4746	9	21	.	.	PUNCT
ejpam-4746	10	1	this	this	DET
ejpam-4746	10	2	method	method	NOUN
ejpam-4746	10	3	is	be	AUX
ejpam-4746	10	4	a	a	DET
ejpam-4746	10	5	convex	convex	ADJ
ejpam-4746	10	6	combination	combination	NOUN
ejpam-4746	10	7	of	of	ADP
ejpam-4746	10	8	the	the	DET
ejpam-4746	10	9	dai	dai	PROPN
ejpam-4746	10	10	-	-	PUNCT
ejpam-4746	10	11	yuan	yuan	PROPN
ejpam-4746	10	12	and	and	CCONJ
ejpam-4746	10	13	hestenes	hestene	NOUN
ejpam-4746	10	14	-	-	PUNCT
ejpam-4746	10	15	stiefel	stiefel	NOUN
ejpam-4746	10	16	methodologies	methodology	NOUN
ejpam-4746	10	17	.	.	PUNCT
ejpam-4746	11	1	the	the	DET
ejpam-4746	11	2	descending	descend	VERB
ejpam-4746	11	3	property	property	NOUN
ejpam-4746	11	4	and	and	CCONJ
ejpam-4746	11	5	global	global	ADJ
ejpam-4746	11	6	convergence	convergence	NOUN
ejpam-4746	11	7	are	be	AUX
ejpam-4746	11	8	both	both	PRON
ejpam-4746	11	9	exhibited	exhibit	VERB
ejpam-4746	11	10	by	by	ADP
ejpam-4746	11	11	the	the	DET
ejpam-4746	11	12	wolfe	wolfe	PROPN
ejpam-4746	11	13	line	line	PROPN
ejpam-4746	11	14	search	search	NOUN
ejpam-4746	11	15	.	.	PUNCT
ejpam-4746	12	1	the	the	DET
ejpam-4746	12	2	numerical	numerical	PROPN
ejpam-4746	12	3	data	data	PROPN
ejpam-4746	12	4	demonstrates	demonstrate	VERB
ejpam-4746	12	5	that	that	SCONJ
ejpam-4746	12	6	the	the	DET
ejpam-4746	12	7	strategy	strategy	NOUN
ejpam-4746	12	8	that	that	PRON
ejpam-4746	12	9	was	be	AUX
ejpam-4746	12	10	presented	present	VERB
ejpam-4746	12	11	is	be	AUX
ejpam-4746	12	12	an	an	DET
ejpam-4746	12	13	efficient	efficient	ADJ
ejpam-4746	12	14	one	one	NUM
ejpam-4746	12	15	.	.	PUNCT
ejpam-4746	13	1	2020	2020	NUM
ejpam-4746	13	2	mathematics	mathematic	NOUN
ejpam-4746	13	3	subject	subject	NOUN
ejpam-4746	13	4	classifications	classification	NOUN
ejpam-4746	13	5	:	:	PUNCT
ejpam-4746	13	6	90c30	90c30	NUM
ejpam-4746	13	7	,	,	PUNCT
ejpam-4746	13	8	65k05	65k05	NUM
ejpam-4746	13	9	,	,	PUNCT
ejpam-4746	13	10	49m37	49m37	NUM
ejpam-4746	13	11	key	key	ADJ
ejpam-4746	13	12	words	word	NOUN
ejpam-4746	13	13	and	and	CCONJ
ejpam-4746	13	14	phrases	phrase	NOUN
ejpam-4746	13	15	:	:	PUNCT
ejpam-4746	13	16	optimization	optimization	NOUN
ejpam-4746	13	17	,	,	PUNCT
ejpam-4746	13	18	conjugate	conjugate	ADJ
ejpam-4746	13	19	gradient	gradient	NOUN
ejpam-4746	13	20	,	,	PUNCT
ejpam-4746	13	21	numerical	numerical	ADJ
ejpam-4746	13	22	results	result	NOUN
ejpam-4746	13	23	1	1	NUM
ejpam-4746	13	24	.	.	PUNCT
ejpam-4746	14	1	introduction	introduction	NOUN
ejpam-4746	14	2	the	the	DET
ejpam-4746	14	3	following	following	ADJ
ejpam-4746	14	4	unconstrained	unconstrained	ADJ
ejpam-4746	14	5	optimization	optimization	NOUN
ejpam-4746	14	6	problems	problem	NOUN
ejpam-4746	14	7	are	be	AUX
ejpam-4746	14	8	dealt	deal	VERB
ejpam-4746	14	9	with	with	ADP
ejpam-4746	14	10	in	in	ADP
ejpam-4746	14	11	this	this	DET
ejpam-4746	14	12	paper	paper	NOUN
ejpam-4746	14	13	:	:	PUNCT
ejpam-4746	14	14	minf(x	minf(x	NOUN
ejpam-4746	14	15	)	)	PUNCT
ejpam-4746	14	16	,	,	PUNCT
ejpam-4746	14	17	x	x	PROPN
ejpam-4746	14	18	∈	∈	PROPN
ejpam-4746	14	19	rn	rn	PROPN
ejpam-4746	14	20	(	(	PUNCT
ejpam-4746	14	21	1	1	NUM
ejpam-4746	14	22	)	)	PUNCT
ejpam-4746	14	23	where	where	SCONJ
ejpam-4746	14	24	f	f	PROPN
ejpam-4746	14	25	:	:	PUNCT
ejpam-4746	14	26	rn	rn	PROPN
ejpam-4746	14	27	→	→	SYM
ejpam-4746	14	28	r	r	NOUN
ejpam-4746	14	29	is	be	AUX
ejpam-4746	14	30	a	a	DET
ejpam-4746	14	31	continuously	continuously	ADV
ejpam-4746	14	32	differentiable	differentiable	ADJ
ejpam-4746	14	33	function	function	NOUN
ejpam-4746	14	34	that	that	PRON
ejpam-4746	14	35	is	be	AUX
ejpam-4746	14	36	bounded	bound	VERB
ejpam-4746	14	37	from	from	ADP
ejpam-4746	14	38	below	below	ADV
ejpam-4746	14	39	.	.	PUNCT
ejpam-4746	15	1	from	from	ADP
ejpam-4746	15	2	an	an	DET
ejpam-4746	15	3	initial	initial	ADJ
ejpam-4746	15	4	guess	guess	NOUN
ejpam-4746	15	5	,	,	PUNCT
ejpam-4746	15	6	a	a	DET
ejpam-4746	15	7	non	non	ADJ
ejpam-4746	15	8	linear	linear	ADJ
ejpam-4746	15	9	conjugate	conjugate	ADJ
ejpam-4746	15	10	gradient	gradient	NOUN
ejpam-4746	15	11	(	(	PUNCT
ejpam-4746	15	12	cg	cg	NOUN
ejpam-4746	15	13	)	)	PUNCT
ejpam-4746	15	14	algorithm	algorithm	NOUN
ejpam-4746	15	15	generates	generate	VERB
ejpam-4746	15	16	a	a	DET
ejpam-4746	15	17	sequence	sequence	NOUN
ejpam-4746	15	18	of	of	ADP
ejpam-4746	15	19	points	point	NOUN
ejpam-4746	15	20	{	{	PUNCT
ejpam-4746	15	21	xk	xk	NOUN
ejpam-4746	15	22	}	}	PUNCT
ejpam-4746	15	23	,	,	PUNCT
ejpam-4746	15	24	according	accord	VERB
ejpam-4746	15	25	to	to	ADP
ejpam-4746	15	26	the	the	DET
ejpam-4746	15	27	formula	formula	NOUN
ejpam-4746	15	28	for	for	ADP
ejpam-4746	15	29	recurrence	recurrence	NOUN
ejpam-4746	15	30	[	[	X
ejpam-4746	15	31	6	6	NUM
ejpam-4746	15	32	,	,	PUNCT
ejpam-4746	15	33	7	7	NUM
ejpam-4746	15	34	]	]	PUNCT
ejpam-4746	15	35	xk+1	xk+1	PROPN
ejpam-4746	16	1	=	=	SYM
ejpam-4746	16	2	xk	xk	PROPN
ejpam-4746	17	1	+	+	NUM
ejpam-4746	17	2	αkdk	αkdk	NOUN
ejpam-4746	17	3	(	(	PUNCT
ejpam-4746	17	4	2	2	NUM
ejpam-4746	17	5	)	)	PUNCT
ejpam-4746	17	6	∗corresponding	∗corresponde	VERB
ejpam-4746	17	7	author	author	NOUN
ejpam-4746	17	8	.	.	PUNCT
ejpam-4746	18	1	doi	doi	NOUN
ejpam-4746	18	2	:	:	PUNCT
ejpam-4746	18	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4746	https://doi.org/10.29020/nybg.ejpam.v16i2.4746	PRON
ejpam-4746	18	4	email	email	NOUN
ejpam-4746	18	5	addresses	address	NOUN
ejpam-4746	18	6	:	:	PUNCT
ejpam-4746	18	7	yuksel@uokirkuk.edu.iq	yuksel@uokirkuk.edu.iq	NOUN
ejpam-4746	18	8	(	(	PUNCT
ejpam-4746	18	9	y.	y.	NOUN
ejpam-4746	18	10	a.	a.	NOUN
ejpam-4746	18	11	laylani	laylani	PROPN
ejpam-4746	18	12	)	)	PUNCT
ejpam-4746	18	13	,	,	PUNCT
ejpam-4746	18	14	hisham892020@uomosul.edu.iq	hisham892020@uomosul.edu.iq	NOUN
ejpam-4746	18	15	(	(	PUNCT
ejpam-4746	18	16	h.	h.	PROPN
ejpam-4746	18	17	m.	m.	PROPN
ejpam-4746	18	18	khudhur	khudhur	PROPN
ejpam-4746	18	19	)	)	PUNCT
ejpam-4746	18	20	,	,	PUNCT
ejpam-4746	18	21	edreesnori@uomosul.edu.iq	edreesnori@uomosul.edu.iq	NOUN
ejpam-4746	18	22	(	(	PUNCT
ejpam-4746	18	23	e.	e.	PROPN
ejpam-4746	18	24	m.	m.	PROPN
ejpam-4746	18	25	nori	nori	PROPN
ejpam-4746	18	26	)	)	PUNCT
ejpam-4746	18	27	,	,	PUNCT
ejpam-4746	18	28	dr.khalil-khuder@uotelafer.edu.iq	dr.khalil-khuder@uotelafer.edu.iq	PROPN
ejpam-4746	18	29	(	(	PUNCT
ejpam-4746	18	30	k.	k.	PROPN
ejpam-4746	18	31	k.	k.	PROPN
ejpam-4746	18	32	abbo	abbo	PROPN
ejpam-4746	18	33	)	)	PUNCT
ejpam-4746	18	34	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4746	18	35	1059	1059	NUM
ejpam-4746	19	1	©	©	PROPN
ejpam-4746	19	2	2023	2023	NUM
ejpam-4746	19	3	ejpam	ejpam	NOUN
ejpam-4746	19	4	all	all	DET
ejpam-4746	19	5	rights	right	NOUN
ejpam-4746	19	6	reserved	reserve	VERB
ejpam-4746	19	7	.	.	PUNCT
ejpam-4746	20	1	h.	h.	PROPN
ejpam-4746	20	2	m.	m.	PROPN
ejpam-4746	20	3	khudhur	khudhur	PROPN
ejpam-4746	20	4	et	et	PROPN
ejpam-4746	20	5	al	al	PROPN
ejpam-4746	20	6	.	.	PUNCT
ejpam-4746	20	7	/	/	SYM
ejpam-4746	20	8	eur	eur	PROPN
ejpam-4746	20	9	.	.	PUNCT
ejpam-4746	21	1	j.	j.	PROPN
ejpam-4746	21	2	pure	pure	PROPN
ejpam-4746	21	3	appl	appl	PROPN
ejpam-4746	21	4	.	.	PROPN
ejpam-4746	21	5	math	math	PROPN
ejpam-4746	21	6	,	,	PUNCT
ejpam-4746	21	7	16	16	NUM
ejpam-4746	21	8	(	(	PUNCT
ejpam-4746	21	9	2	2	NUM
ejpam-4746	21	10	)	)	PUNCT
ejpam-4746	21	11	(	(	PUNCT
ejpam-4746	21	12	2023	2023	NUM
ejpam-4746	21	13	)	)	PUNCT
ejpam-4746	21	14	,	,	PUNCT
ejpam-4746	21	15	1059	1059	NUM
ejpam-4746	21	16	-	-	SYM
ejpam-4746	21	17	1067	1067	NUM
ejpam-4746	21	18	1060	1060	NUM
ejpam-4746	22	1	where	where	SCONJ
ejpam-4746	22	2	dk	dk	PROPN
ejpam-4746	22	3	∈	∈	PROPN
ejpam-4746	22	4	rn	rn	PROPN
ejpam-4746	22	5	search	search	NOUN
ejpam-4746	22	6	direction	direction	NOUN
ejpam-4746	22	7	and	and	CCONJ
ejpam-4746	22	8	αk	αk	ADP
ejpam-4746	22	9	∈	∈	NOUN
ejpam-4746	22	10	r	r	NOUN
ejpam-4746	22	11	is	be	AUX
ejpam-4746	22	12	a	a	DET
ejpam-4746	22	13	step	step	NOUN
ejpam-4746	22	14	length	length	NOUN
ejpam-4746	22	15	that	that	PRON
ejpam-4746	22	16	is	be	AUX
ejpam-4746	22	17	normally	normally	ADV
ejpam-4746	22	18	obtained	obtain	VERB
ejpam-4746	22	19	using	use	VERB
ejpam-4746	22	20	the	the	DET
ejpam-4746	22	21	wolfe	wolfe	PROPN
ejpam-4746	22	22	method	method	NOUN
ejpam-4746	22	23	.	.	PUNCT
ejpam-4746	23	1	[	[	X
ejpam-4746	23	2	16	16	NUM
ejpam-4746	23	3	,	,	PUNCT
ejpam-4746	23	4	19	19	NUM
ejpam-4746	23	5	]	]	PUNCT
ejpam-4746	23	6	and	and	CCONJ
ejpam-4746	23	7	,	,	PUNCT
ejpam-4746	23	8	the	the	DET
ejpam-4746	23	9	standard	standard	ADJ
ejpam-4746	23	10	wofle	wofle	ADJ
ejpam-4746	23	11	condition	condition	NOUN
ejpam-4746	23	12	(	(	PUNCT
ejpam-4746	23	13	swc	swc	NOUN
ejpam-4746	23	14	)	)	PUNCT
ejpam-4746	23	15	f	f	PROPN
ejpam-4746	23	16	(	(	PUNCT
ejpam-4746	23	17	xk	xk	PROPN
ejpam-4746	24	1	+	+	CCONJ
ejpam-4746	24	2	αkdk)−	αkdk)−	PROPN
ejpam-4746	24	3	f	f	PROPN
ejpam-4746	24	4	(	(	PUNCT
ejpam-4746	24	5	xk	xk	PROPN
ejpam-4746	24	6	)	)	PUNCT
ejpam-4746	24	7	≤	≤	NOUN
ejpam-4746	24	8	ραkg	ραkg	NOUN
ejpam-4746	24	9	t	t	PROPN
ejpam-4746	24	10	k	k	PROPN
ejpam-4746	24	11	dk	dk	PROPN
ejpam-4746	24	12	(	(	PUNCT
ejpam-4746	24	13	3	3	NUM
ejpam-4746	24	14	)	)	PUNCT
ejpam-4746	24	15	gtk+1dk	gtk+1dk	PROPN
ejpam-4746	24	16	≥	≥	PROPN
ejpam-4746	24	17	σgtk	σgtk	NOUN
ejpam-4746	24	18	dk	dk	X
ejpam-4746	24	19	(	(	PUNCT
ejpam-4746	24	20	4	4	NUM
ejpam-4746	24	21	)	)	PUNCT
ejpam-4746	24	22	with	with	ADP
ejpam-4746	24	23	0	0	NUM
ejpam-4746	24	24	<	<	X
ejpam-4746	24	25	ρ	ρ	X
ejpam-4746	24	26	<	<	X
ejpam-4746	24	27	σ	σ	X
ejpam-4746	24	28	<	<	X
ejpam-4746	24	29	1	1	NUM
ejpam-4746	24	30	,	,	PUNCT
ejpam-4746	24	31	or	or	CCONJ
ejpam-4746	24	32	by	by	ADP
ejpam-4746	24	33	strong	strong	ADJ
ejpam-4746	24	34	wolfe	wolfe	PROPN
ejpam-4746	24	35	condition(stwc	condition(stwc	PROPN
ejpam-4746	24	36	)	)	PUNCT
ejpam-4746	25	1	f(xk	f(xk	PROPN
ejpam-4746	25	2	+	+	CCONJ
ejpam-4746	25	3	αkdk)−	αkdk)−	NUM
ejpam-4746	25	4	f(xk	f(xk	NOUN
ejpam-4746	25	5	)	)	PUNCT
ejpam-4746	25	6	≤	≤	NUM
ejpam-4746	25	7	ραkg	ραkg	NOUN
ejpam-4746	25	8	t	t	PROPN
ejpam-4746	25	9	k	k	PROPN
ejpam-4746	25	10	dk	dk	PROPN
ejpam-4746	25	11	(	(	PUNCT
ejpam-4746	25	12	5)∣∣gtk+1dk	5)∣∣gtk+1dk	PROPN
ejpam-4746	25	13	∣∣	∣∣	NUM
ejpam-4746	25	14	≤	≤	NUM
ejpam-4746	25	15	−σgtk	−σgtk	NOUN
ejpam-4746	25	16	dk	dk	X
ejpam-4746	25	17	,	,	PUNCT
ejpam-4746	25	18	(	(	PUNCT
ejpam-4746	25	19	6	6	NUM
ejpam-4746	25	20	)	)	PUNCT
ejpam-4746	25	21	and	and	CCONJ
ejpam-4746	25	22	compute	compute	VERB
ejpam-4746	25	23	the	the	DET
ejpam-4746	25	24	search	search	NOUN
ejpam-4746	25	25	direction	direction	NOUN
ejpam-4746	25	26	from	from	ADP
ejpam-4746	25	27	the	the	DET
ejpam-4746	25	28	following	follow	VERB
ejpam-4746	25	29	equation	equation	NOUN
ejpam-4746	25	30	dk+1	dk+1	NOUN
ejpam-4746	25	31	=	=	SYM
ejpam-4746	25	32	−gk+1	−gk+1	PROPN
ejpam-4746	25	33	+	+	CCONJ
ejpam-4746	25	34	βksk	βksk	ADJ
ejpam-4746	25	35	,	,	PUNCT
ejpam-4746	25	36	d0	d0	NOUN
ejpam-4746	25	37	=	=	SYM
ejpam-4746	25	38	−g0	−g0	PROPN
ejpam-4746	25	39	(	(	PUNCT
ejpam-4746	25	40	7	7	NUM
ejpam-4746	25	41	)	)	PUNCT
ejpam-4746	25	42	here	here	ADV
ejpam-4746	25	43	βk	βk	ADP
ejpam-4746	25	44	the	the	DET
ejpam-4746	25	45	conjugate	conjugate	ADJ
ejpam-4746	25	46	gradient	gradient	NOUN
ejpam-4746	25	47	parameter	parameter	NOUN
ejpam-4746	25	48	which	which	PRON
ejpam-4746	25	49	is	be	AUX
ejpam-4746	25	50	a	a	DET
ejpam-4746	25	51	scalar	scalar	ADJ
ejpam-4746	25	52	known	know	VERB
ejpam-4746	25	53	as	as	ADP
ejpam-4746	25	54	gk	gk	PROPN
ejpam-4746	25	55	=	=	SYM
ejpam-4746	25	56	∇f(xk	∇f(xk	NOUN
ejpam-4746	25	57	)	)	PUNCT
ejpam-4746	25	58	and	and	CCONJ
ejpam-4746	25	59	sk	sk	VERB
ejpam-4746	25	60	=	=	SYM
ejpam-4746	25	61	xk+1	xk+1	PROPN
ejpam-4746	25	62	−	−	PROPN
ejpam-4746	25	63	xk	xk	PROPN
ejpam-4746	25	64	.	.	PUNCT
ejpam-4746	25	65	different	different	ADJ
ejpam-4746	25	66	conjugate	conjugate	ADJ
ejpam-4746	25	67	gradient	gradient	NOUN
ejpam-4746	25	68	algorithms	algorithm	NOUN
ejpam-4746	25	69	corresponding	correspond	VERB
ejpam-4746	25	70	to	to	ADP
ejpam-4746	25	71	various	various	ADJ
ejpam-4746	25	72	parameter	parameter	NOUN
ejpam-4746	25	73	choices	choice	NOUN
ejpam-4746	25	74	βk	βk	ADV
ejpam-4746	25	75	see	see	VERB
ejpam-4746	25	76	[	[	X
ejpam-4746	25	77	3	3	NUM
ejpam-4746	25	78	,	,	PUNCT
ejpam-4746	25	79	11	11	NUM
ejpam-4746	25	80	,	,	PUNCT
ejpam-4746	25	81	13	13	NUM
ejpam-4746	25	82	,	,	PUNCT
ejpam-4746	25	83	17	17	NUM
ejpam-4746	25	84	,	,	PUNCT
ejpam-4746	25	85	18	18	NUM
ejpam-4746	25	86	,	,	PUNCT
ejpam-4746	25	87	20	20	NUM
ejpam-4746	25	88	,	,	PUNCT
ejpam-4746	25	89	23	23	NUM
ejpam-4746	25	90	]	]	PUNCT
ejpam-4746	25	91	.	.	PUNCT
ejpam-4746	26	1	as	as	ADP
ejpam-4746	26	2	a	a	DET
ejpam-4746	26	3	consequence	consequence	NOUN
ejpam-4746	26	4	,	,	PUNCT
ejpam-4746	26	5	every	every	DET
ejpam-4746	26	6	conjugate	conjugate	ADJ
ejpam-4746	26	7	gradient	gradient	ADJ
ejpam-4746	26	8	algorithm	algorithm	NOUN
ejpam-4746	26	9	formula	formula	NOUN
ejpam-4746	26	10	definition	definition	NOUN
ejpam-4746	26	11	would	would	AUX
ejpam-4746	26	12	be	be	AUX
ejpam-4746	26	13	the	the	DET
ejpam-4746	26	14	same	same	ADJ
ejpam-4746	26	15	is	be	AUX
ejpam-4746	26	16	crucial	crucial	ADJ
ejpam-4746	26	17	βk	βk	ADP
ejpam-4746	26	18	the	the	DET
ejpam-4746	26	19	formulas	formula	NOUN
ejpam-4746	26	20	are	be	AUX
ejpam-4746	26	21	well	well	ADV
ejpam-4746	26	22	-	-	PUNCT
ejpam-4746	26	23	known	know	VERB
ejpam-4746	26	24	.	.	PUNCT
ejpam-4746	27	1	βk	βk	PROPN
ejpam-4746	27	2	are	be	AUX
ejpam-4746	27	3	as	as	SCONJ
ejpam-4746	27	4	follows	follow	VERB
ejpam-4746	27	5	;	;	PUNCT
ejpam-4746	27	6	βfr	βfr	PROPN
ejpam-4746	27	7	k	k	NOUN
ejpam-4746	27	8	=	=	SYM
ejpam-4746	27	9	gtk+1gk+1	gtk+1gk+1	NOUN
ejpam-4746	27	10	gtk	gtk	NOUN
ejpam-4746	27	11	gk	gk	PROPN
ejpam-4746	27	12	,	,	PUNCT
ejpam-4746	27	13	βdy	βdy	NOUN
ejpam-4746	27	14	k	k	PROPN
ejpam-4746	28	1	=	=	PRON
ejpam-4746	28	2	∥gk+1∥2	∥gk+1∥2	PROPN
ejpam-4746	28	3	ytk	ytk	NOUN
ejpam-4746	28	4	sk	sk	NOUN
ejpam-4746	28	5	,	,	PUNCT
ejpam-4746	28	6	βcd	βcd	NOUN
ejpam-4746	28	7	k	k	NOUN
ejpam-4746	29	1	=	=	PRON
ejpam-4746	30	1	gtk+1gk+1	gtk+1gk+1	NOUN
ejpam-4746	31	1	−dtk	−dtk	NOUN
ejpam-4746	32	1	gk	gk	PROPN
ejpam-4746	33	1	βpr	βpr	NOUN
ejpam-4746	34	1	k	k	NOUN
ejpam-4746	35	1	=	=	PUNCT
ejpam-4746	35	2	ytk	ytk	NOUN
ejpam-4746	35	3	gk+1	gk+1	NUM
ejpam-4746	35	4	gtk	gtk	NOUN
ejpam-4746	35	5	gk	gk	PROPN
ejpam-4746	35	6	,	,	PUNCT
ejpam-4746	35	7	βhs	βhs	NOUN
ejpam-4746	35	8	k	k	PROPN
ejpam-4746	35	9	=	=	PUNCT
ejpam-4746	35	10	ytk	ytk	PROPN
ejpam-4746	35	11	gk+1	gk+1	NUM
ejpam-4746	35	12	ytk	ytk	NOUN
ejpam-4746	35	13	dk	dk	PROPN
ejpam-4746	35	14	,	,	PUNCT
ejpam-4746	35	15	βls	βls	VERB
ejpam-4746	35	16	k	k	X
ejpam-4746	36	1	=	=	PUNCT
ejpam-4746	37	1	ytk	ytk	NUM
ejpam-4746	37	2	gk+1	gk+1	NOUN
ejpam-4746	37	3	−dtk	−dtk	NOUN
ejpam-4746	37	4	gk	gk	PROPN
ejpam-4746	37	5	fr	fr	PROPN
ejpam-4746	37	6	denotes	denotes	PROPN
ejpam-4746	37	7	fletcher	fletcher	PROPN
ejpam-4746	37	8	and	and	CCONJ
ejpam-4746	37	9	reeves	reeves	PROPN
ejpam-4746	37	10	[	[	X
ejpam-4746	37	11	10	10	NUM
ejpam-4746	37	12	]	]	PUNCT
ejpam-4746	37	13	,	,	PUNCT
ejpam-4746	37	14	hs	hs	PROPN
ejpam-4746	37	15	denotes	denote	VERB
ejpam-4746	37	16	hestenes	hestene	NOUN
ejpam-4746	37	17	and	and	CCONJ
ejpam-4746	37	18	steifel	steifel	NOUN
ejpam-4746	37	19	[	[	X
ejpam-4746	37	20	13	13	NUM
ejpam-4746	37	21	]	]	PUNCT
ejpam-4746	37	22	,	,	PUNCT
ejpam-4746	37	23	pr	pr	PROPN
ejpam-4746	37	24	denotes	denote	NOUN
ejpam-4746	37	25	polak	polak	PROPN
ejpam-4746	37	26	and	and	CCONJ
ejpam-4746	37	27	ribiere	ribiere	X
ejpam-4746	38	1	[	[	X
ejpam-4746	38	2	19	19	NUM
ejpam-4746	38	3	]	]	PUNCT
ejpam-4746	38	4	,	,	PUNCT
ejpam-4746	38	5	dy	dy	NOUN
ejpam-4746	38	6	denotes	denote	NOUN
ejpam-4746	38	7	dai	dai	PROPN
ejpam-4746	38	8	and	and	CCONJ
ejpam-4746	38	9	yuan	yuan	PROPN
ejpam-4746	39	1	[	[	X
ejpam-4746	39	2	8	8	NUM
ejpam-4746	39	3	]	]	PUNCT
ejpam-4746	39	4	and	and	CCONJ
ejpam-4746	39	5	ls	ls	PROPN
ejpam-4746	39	6	denotes	denote	NOUN
ejpam-4746	39	7	liu	liu	PROPN
ejpam-4746	39	8	and	and	CCONJ
ejpam-4746	39	9	storey	storey	NOUN
ejpam-4746	39	10	.	.	PUNCT
ejpam-4746	40	1	it	it	PRON
ejpam-4746	40	2	’s	’	VERB
ejpam-4746	40	3	worth	worth	ADJ
ejpam-4746	40	4	noting	note	VERB
ejpam-4746	40	5	that	that	SCONJ
ejpam-4746	40	6	these	these	DET
ejpam-4746	40	7	formulas	formula	NOUN
ejpam-4746	40	8	for	for	ADP
ejpam-4746	40	9	βk	βk	ADV
ejpam-4746	40	10	they	they	PRON
ejpam-4746	40	11	are	be	AUX
ejpam-4746	40	12	similar	similar	ADJ
ejpam-4746	40	13	when	when	SCONJ
ejpam-4746	40	14	the	the	DET
ejpam-4746	40	15	objective	objective	ADJ
ejpam-4746	40	16	function	function	NOUN
ejpam-4746	40	17	is	be	AUX
ejpam-4746	40	18	a	a	DET
ejpam-4746	40	19	strictly	strictly	ADV
ejpam-4746	40	20	convex	convex	ADJ
ejpam-4746	40	21	quadratic	quadratic	ADJ
ejpam-4746	40	22	function	function	NOUN
ejpam-4746	40	23	,	,	PUNCT
ejpam-4746	40	24	and	and	CCONJ
ejpam-4746	40	25	αk	αk	PRON
ejpam-4746	40	26	is	be	AUX
ejpam-4746	40	27	an	an	DET
ejpam-4746	40	28	exact	exact	ADJ
ejpam-4746	40	29	one	one	NUM
ejpam-4746	40	30	-	-	PUNCT
ejpam-4746	40	31	dimensional	dimensional	ADJ
ejpam-4746	40	32	minimizer	minimizer	NOUN
ejpam-4746	40	33	[	[	X
ejpam-4746	40	34	9	9	NUM
ejpam-4746	40	35	]	]	PUNCT
ejpam-4746	40	36	.	.	PUNCT
ejpam-4746	41	1	the	the	DET
ejpam-4746	41	2	following	follow	VERB
ejpam-4746	41	3	is	be	AUX
ejpam-4746	41	4	the	the	DET
ejpam-4746	41	5	outline	outline	NOUN
ejpam-4746	41	6	of	of	ADP
ejpam-4746	41	7	the	the	DET
ejpam-4746	41	8	document	document	NOUN
ejpam-4746	41	9	.	.	PUNCT
ejpam-4746	42	1	section	section	NOUN
ejpam-4746	42	2	2	2	NUM
ejpam-4746	42	3	introduces	introduce	NOUN
ejpam-4746	42	4	and	and	CCONJ
ejpam-4746	42	5	demonstrates	demonstrate	VERB
ejpam-4746	42	6	our	our	PRON
ejpam-4746	42	7	proposed	propose	VERB
ejpam-4746	42	8	method	method	NOUN
ejpam-4746	42	9	(	(	PUNCT
ejpam-4746	42	10	hkye	hkye	NOUN
ejpam-4746	42	11	)	)	PUNCT
ejpam-4746	42	12	for	for	ADP
ejpam-4746	42	13	generating	generate	VERB
ejpam-4746	42	14	descent	descent	NOUN
ejpam-4746	42	15	directions	direction	NOUN
ejpam-4746	42	16	.	.	PUNCT
ejpam-4746	43	1	its	its	PRON
ejpam-4746	43	2	convergence	convergence	NOUN
ejpam-4746	43	3	analysis	analysis	NOUN
ejpam-4746	43	4	is	be	AUX
ejpam-4746	43	5	seen	see	VERB
ejpam-4746	43	6	in	in	ADP
ejpam-4746	43	7	section	section	NOUN
ejpam-4746	43	8	3	3	NUM
ejpam-4746	43	9	.	.	PUNCT
ejpam-4746	44	1	in	in	ADP
ejpam-4746	44	2	section	section	NOUN
ejpam-4746	44	3	4	4	NUM
ejpam-4746	44	4	,	,	PUNCT
ejpam-4746	44	5	you	you	PRON
ejpam-4746	44	6	’ll	’ll	AUX
ejpam-4746	44	7	find	find	VERB
ejpam-4746	44	8	some	some	DET
ejpam-4746	44	9	numerical	numerical	ADJ
ejpam-4746	44	10	experiments	experiment	NOUN
ejpam-4746	44	11	.	.	PUNCT
ejpam-4746	45	1	2	2	X
ejpam-4746	45	2	.	.	X
ejpam-4746	45	3	hybrid	hybrid	ADJ
ejpam-4746	45	4	conjugate	conjugate	ADJ
ejpam-4746	45	5	gradient	gradient	NOUN
ejpam-4746	45	6	method	method	NOUN
ejpam-4746	45	7	the	the	DET
ejpam-4746	45	8	traditional	traditional	ADJ
ejpam-4746	45	9	numerator	numerator	NOUN
ejpam-4746	45	10	conjugate	conjugate	ADJ
ejpam-4746	45	11	gradient	gradient	ADJ
ejpam-4746	45	12	methods	method	NOUN
ejpam-4746	45	13	∥gk+1∥2	∥gk+1∥2	VERB
ejpam-4746	45	14	in	in	ADP
ejpam-4746	45	15	relation	relation	NOUN
ejpam-4746	45	16	to	to	ADP
ejpam-4746	45	17	the	the	DET
ejpam-4746	45	18	update	update	NOUN
ejpam-4746	45	19	parameter	parameter	NOUN
ejpam-4746	45	20	βk	βk	ADP
ejpam-4746	45	21	(	(	PUNCT
ejpam-4746	45	22	fr	fr	PROPN
ejpam-4746	45	23	,	,	PUNCT
ejpam-4746	45	24	dy	dy	X
ejpam-4746	45	25	,	,	PUNCT
ejpam-4746	45	26	cd	cd	PROPN
ejpam-4746	45	27	)	)	PUNCT
ejpam-4746	45	28	although	although	SCONJ
ejpam-4746	45	29	they	they	PRON
ejpam-4746	45	30	have	have	VERB
ejpam-4746	45	31	good	good	ADJ
ejpam-4746	45	32	convergence	convergence	NOUN
ejpam-4746	45	33	properties	property	NOUN
ejpam-4746	45	34	,	,	PUNCT
ejpam-4746	45	35	their	their	PRON
ejpam-4746	45	36	functional	functional	ADJ
ejpam-4746	45	37	performance	performance	NOUN
ejpam-4746	45	38	is	be	AUX
ejpam-4746	45	39	limited	limit	VERB
ejpam-4746	45	40	.	.	PUNCT
ejpam-4746	46	1	while	while	SCONJ
ejpam-4746	46	2	the	the	DET
ejpam-4746	46	3	methods	method	NOUN
ejpam-4746	46	4	with	with	ADP
ejpam-4746	46	5	numerator	numerator	NOUN
ejpam-4746	46	6	gtk+1yksuch	gtk+1yksuch	PROPN
ejpam-4746	46	7	as	as	ADP
ejpam-4746	46	8	(	(	PUNCT
ejpam-4746	46	9	pr	pr	NOUN
ejpam-4746	46	10	,	,	PUNCT
ejpam-4746	46	11	hs	hs	X
ejpam-4746	46	12	,	,	PUNCT
ejpam-4746	46	13	ls)often	ls)often	VERB
ejpam-4746	46	14	have	have	VERB
ejpam-4746	46	15	better	well	ADJ
ejpam-4746	46	16	computation	computation	NOUN
ejpam-4746	46	17	performance	performance	NOUN
ejpam-4746	46	18	,	,	PUNCT
ejpam-4746	46	19	but	but	CCONJ
ejpam-4746	46	20	they	they	PRON
ejpam-4746	46	21	may	may	AUX
ejpam-4746	46	22	not	not	PART
ejpam-4746	46	23	generally	generally	ADV
ejpam-4746	46	24	be	be	AUX
ejpam-4746	46	25	convergent	convergent	ADJ
ejpam-4746	46	26	.	.	PUNCT
ejpam-4746	47	1	in	in	ADP
ejpam-4746	47	2	this	this	DET
ejpam-4746	47	3	section	section	NOUN
ejpam-4746	47	4	we	we	PRON
ejpam-4746	47	5	try	try	VERB
ejpam-4746	47	6	to	to	PART
ejpam-4746	47	7	introduce	introduce	VERB
ejpam-4746	47	8	a	a	DET
ejpam-4746	47	9	new	new	ADJ
ejpam-4746	47	10	hybrid	hybrid	ADJ
ejpam-4746	47	11	conjugate	conjugate	ADJ
ejpam-4746	47	12	gradient	gradient	NOUN
ejpam-4746	47	13	method	method	NOUN
ejpam-4746	47	14	as	as	SCONJ
ejpam-4746	47	15	follows	follow	VERB
ejpam-4746	47	16	:	:	PUNCT
ejpam-4746	47	17	consider	consider	VERB
ejpam-4746	47	18	the	the	DET
ejpam-4746	47	19	following	follow	VERB
ejpam-4746	47	20	search	search	NOUN
ejpam-4746	47	21	direction	direction	NOUN
ejpam-4746	47	22	defined	define	VERB
ejpam-4746	47	23	by	by	ADP
ejpam-4746	47	24	dk+1	dk+1	NOUN
ejpam-4746	47	25	=	=	SYM
ejpam-4746	47	26	−	−	NOUN
ejpam-4746	47	27	gk+1	gk+1	NOUN
ejpam-4746	48	1	+	+	CCONJ
ejpam-4746	49	1	[	[	X
ejpam-4746	49	2	(	(	PUNCT
ejpam-4746	49	3	1−	1−	NUM
ejpam-4746	49	4	θk)β	θk)β	PROPN
ejpam-4746	49	5	hs	hs	PROPN
ejpam-4746	49	6	k	k	PROPN
ejpam-4746	49	7	+	+	CCONJ
ejpam-4746	49	8	θβdy	θβdy	ADJ
ejpam-4746	49	9	k	k	PROPN
ejpam-4746	49	10	]	]	X
ejpam-4746	49	11	sk	sk	X
ejpam-4746	49	12	(	(	PUNCT
ejpam-4746	49	13	8)	8)	NUM
ejpam-4746	49	14	h.	h.	PROPN
ejpam-4746	49	15	m.	m.	NOUN
ejpam-4746	49	16	khudhur	khudhur	PROPN
ejpam-4746	49	17	et	et	PROPN
ejpam-4746	49	18	al	al	PROPN
ejpam-4746	49	19	.	.	PUNCT
ejpam-4746	49	20	/	/	SYM
ejpam-4746	49	21	eur	eur	PROPN
ejpam-4746	49	22	.	.	PUNCT
ejpam-4746	50	1	j.	j.	PROPN
ejpam-4746	50	2	pure	pure	PROPN
ejpam-4746	50	3	appl	appl	PROPN
ejpam-4746	50	4	.	.	PROPN
ejpam-4746	50	5	math	math	PROPN
ejpam-4746	50	6	,	,	PUNCT
ejpam-4746	50	7	16	16	NUM
ejpam-4746	50	8	(	(	PUNCT
ejpam-4746	50	9	2	2	NUM
ejpam-4746	50	10	)	)	PUNCT
ejpam-4746	50	11	(	(	PUNCT
ejpam-4746	50	12	2023	2023	NUM
ejpam-4746	50	13	)	)	PUNCT
ejpam-4746	50	14	,	,	PUNCT
ejpam-4746	50	15	1059	1059	NUM
ejpam-4746	50	16	-	-	SYM
ejpam-4746	50	17	1067	1067	NUM
ejpam-4746	50	18	1061	1061	NUM
ejpam-4746	50	19	by	by	ADP
ejpam-4746	50	20	using	use	VERB
ejpam-4746	50	21	the	the	DET
ejpam-4746	50	22	conjugacy	conjugacy	ADJ
ejpam-4746	50	23	condition	condition	NOUN
ejpam-4746	50	24	(	(	PUNCT
ejpam-4746	50	25	dai	dai	PROPN
ejpam-4746	50	26	-	-	PUNCT
ejpam-4746	50	27	liao	liao	PROPN
ejpam-4746	50	28	)	)	PUNCT
ejpam-4746	50	29	dtk+1yk	dtk+1yk	PROPN
ejpam-4746	50	30	=	=	SYM
ejpam-4746	50	31	−tgtk+1sk	−tgtk+1sk	PROPN
ejpam-4746	50	32	and	and	CCONJ
ejpam-4746	50	33	let	let	VERB
ejpam-4746	50	34	t	t	NOUN
ejpam-4746	50	35	=	=	PUNCT
ejpam-4746	50	36	(	(	PUNCT
ejpam-4746	50	37	stk	stk	PROPN
ejpam-4746	50	38	gk+1	gk+1	NOUN
ejpam-4746	50	39	)	)	PUNCT
ejpam-4746	50	40	2	2	NUM
ejpam-4746	50	41	(	(	PUNCT
ejpam-4746	50	42	ytk	ytk	NOUN
ejpam-4746	50	43	sk	sk	NOUN
ejpam-4746	50	44	)	)	PUNCT
ejpam-4746	50	45	2	2	NUM
ejpam-4746	51	1	we	we	PRON
ejpam-4746	51	2	get	get	VERB
ejpam-4746	51	3	the	the	DET
ejpam-4746	51	4	equation	equation	NOUN
ejpam-4746	51	5	(	(	PUNCT
ejpam-4746	51	6	9	9	NUM
ejpam-4746	51	7	)	)	PUNCT
ejpam-4746	51	8	θk	θk	NOUN
ejpam-4746	51	9	=	=	SYM
ejpam-4746	51	10	(	(	PUNCT
ejpam-4746	51	11	stk	stk	PROPN
ejpam-4746	51	12	gk+1	gk+1	NOUN
ejpam-4746	51	13	)	)	PUNCT
ejpam-4746	51	14	3	3	NUM
ejpam-4746	51	15	(	(	PUNCT
ejpam-4746	51	16	ytk	ytk	NOUN
ejpam-4746	51	17	sk	sk	NOUN
ejpam-4746	51	18	)	)	PUNCT
ejpam-4746	51	19	2	2	NUM
ejpam-4746	51	20	(	(	PUNCT
ejpam-4746	51	21	9	9	NUM
ejpam-4746	51	22	)	)	PUNCT
ejpam-4746	51	23	note	note	NOUN
ejpam-4746	51	24	that	that	SCONJ
ejpam-4746	51	25	θk	θk	VERB
ejpam-4746	51	26	<	<	X
ejpam-4746	51	27	1	1	NUM
ejpam-4746	51	28	,	,	PUNCT
ejpam-4746	51	29	since	since	SCONJ
ejpam-4746	51	30	stk	stk	PROPN
ejpam-4746	51	31	gk+1	gk+1	X
ejpam-4746	51	32	<	<	X
ejpam-4746	51	33	ytk	ytk	NOUN
ejpam-4746	51	34	sk	sk	NOUN
ejpam-4746	51	35	,	,	PUNCT
ejpam-4746	51	36	but	but	CCONJ
ejpam-4746	51	37	it	it	PRON
ejpam-4746	51	38	may	may	AUX
ejpam-4746	51	39	be	be	AUX
ejpam-4746	51	40	θk	θk	NOUN
ejpam-4746	51	41	<	<	X
ejpam-4746	51	42	0	0	NUM
ejpam-4746	51	43	,	,	PUNCT
ejpam-4746	51	44	to	to	PART
ejpam-4746	51	45	avoid	avoid	VERB
ejpam-4746	51	46	this	this	DET
ejpam-4746	51	47	situation	situation	NOUN
ejpam-4746	51	48	we	we	PRON
ejpam-4746	51	49	take	take	VERB
ejpam-4746	51	50	θ	θ	NOUN
ejpam-4746	51	51	=	=	SYM
ejpam-4746	51	52	0	0	NUM
ejpam-4746	51	53	.	.	PUNCT
ejpam-4746	52	1	therefor	therefor	PROPN
ejpam-4746	52	2	,	,	PUNCT
ejpam-4746	52	3	equation	equation	NOUN
ejpam-4746	52	4	(	(	PUNCT
ejpam-4746	52	5	8)	8)	NUM
ejpam-4746	52	6	becomes	become	VERB
ejpam-4746	52	7	dk+1	dk+1	NOUN
ejpam-4746	52	8	=	=	SYM
ejpam-4746	52	9	−	−	NOUN
ejpam-4746	52	10	gk+1	gk+1	AUX
ejpam-4746	53	1	+	+	CCONJ
ejpam-4746	54	1	[	[	X
ejpam-4746	54	2	βhs	βhs	NOUN
ejpam-4746	54	3	k	k	X
ejpam-4746	54	4	]	]	X
ejpam-4746	54	5	sk	sk	X
ejpam-4746	54	6	(	(	PUNCT
ejpam-4746	54	7	10	10	NUM
ejpam-4746	54	8	)	)	PUNCT
ejpam-4746	54	9	we	we	PRON
ejpam-4746	54	10	call	call	VERB
ejpam-4746	54	11	the	the	DET
ejpam-4746	54	12	method	method	NOUN
ejpam-4746	54	13	defined	define	VERB
ejpam-4746	54	14	by	by	ADP
ejpam-4746	54	15	equation	equation	NOUN
ejpam-4746	54	16	(	(	PUNCT
ejpam-4746	54	17	8)(hkye	8)(hkye	ADJ
ejpam-4746	54	18	)	)	PUNCT
ejpam-4746	54	19	method	method	NOUN
ejpam-4746	54	20	.	.	PUNCT
ejpam-4746	55	1	2.1	2.1	NUM
ejpam-4746	55	2	.	.	PUNCT
ejpam-4746	56	1	new	new	ADJ
ejpam-4746	56	2	algorithms	algorithm	NOUN
ejpam-4746	56	3	step	step	VERB
ejpam-4746	56	4	1	1	NUM
ejpam-4746	56	5	.	.	PUNCT
ejpam-4746	57	1	given	give	VERB
ejpam-4746	57	2	x1	x1	PROPN
ejpam-4746	57	3	∈	∈	PROPN
ejpam-4746	57	4	rn	rn	PROPN
ejpam-4746	57	5	,	,	PUNCT
ejpam-4746	57	6	ε	ε	PROPN
ejpam-4746	57	7	>	>	X
ejpam-4746	57	8	0	0	PROPN
ejpam-4746	57	9	,	,	PUNCT
ejpam-4746	57	10	d1	d1	PROPN
ejpam-4746	57	11	=	=	PUNCT
ejpam-4746	57	12	−g1	−g1	VERB
ejpam-4746	57	13	.	.	PUNCT
ejpam-4746	58	1	step	step	NOUN
ejpam-4746	58	2	2	2	NUM
ejpam-4746	58	3	.	.	PUNCT
ejpam-4746	59	1	if	if	SCONJ
ejpam-4746	59	2	∥gk∥2	∥gk∥2	PROPN
ejpam-4746	59	3	<	<	X
ejpam-4746	59	4	ε	ε	PROPN
ejpam-4746	59	5	then	then	ADV
ejpam-4746	59	6	stop	stop	VERB
ejpam-4746	59	7	.	.	PUNCT
ejpam-4746	60	1	else	else	ADV
ejpam-4746	60	2	go	go	VERB
ejpam-4746	60	3	to	to	ADP
ejpam-4746	60	4	step3	step3	PROPN
ejpam-4746	60	5	.	.	PUNCT
ejpam-4746	61	1	step	step	NOUN
ejpam-4746	61	2	3	3	NUM
ejpam-4746	61	3	.	.	PUNCT
ejpam-4746	61	4	compute	compute	VERB
ejpam-4746	61	5	an	an	DET
ejpam-4746	61	6	αk	αk	NOUN
ejpam-4746	61	7	>	>	X
ejpam-4746	61	8	0satisfying	0satisfying	NUM
ejpam-4746	62	1	(	(	PUNCT
ejpam-4746	62	2	5)and	5)and	NUM
ejpam-4746	62	3	(	(	PUNCT
ejpam-4746	62	4	6	6	NUM
ejpam-4746	62	5	)	)	PUNCT
ejpam-4746	62	6	step	step	NOUN
ejpam-4746	62	7	4	4	NUM
ejpam-4746	62	8	.	.	PUNCT
ejpam-4746	63	1	let	let	VERB
ejpam-4746	63	2	xk+1	xk+1	NOUN
ejpam-4746	63	3	=	=	SYM
ejpam-4746	63	4	xk	xk	PROPN
ejpam-4746	64	1	+	+	CCONJ
ejpam-4746	64	2	αkdk	αkdk	NOUN
ejpam-4746	64	3	.	.	PUNCT
ejpam-4746	65	1	if	if	SCONJ
ejpam-4746	65	2	∥gk+1∥2	∥gk+1∥2	PROPN
ejpam-4746	65	3	<	<	X
ejpam-4746	65	4	ε	ε	PROPN
ejpam-4746	65	5	then	then	ADV
ejpam-4746	65	6	stop	stop	VERB
ejpam-4746	65	7	,	,	PUNCT
ejpam-4746	65	8	else	else	ADV
ejpam-4746	65	9	go	go	VERB
ejpam-4746	65	10	to	to	ADP
ejpam-4746	65	11	step5	step5	PROPN
ejpam-4746	65	12	step	step	NOUN
ejpam-4746	65	13	5	5	NUM
ejpam-4746	65	14	compute	compute	PROPN
ejpam-4746	65	15	θand	θand	NOUN
ejpam-4746	65	16	βk	βk	NOUN
ejpam-4746	65	17	.	.	PUNCT
ejpam-4746	66	1	if	if	SCONJ
ejpam-4746	66	2	θ	θ	PROPN
ejpam-4746	66	3	>	>	X
ejpam-4746	67	1	1or	1or	NUM
ejpam-4746	67	2	θ	θ	X
ejpam-4746	67	3	<	<	X
ejpam-4746	67	4	0then	0then	PUNCT
ejpam-4746	67	5	compute	compute	NOUN
ejpam-4746	67	6	dk+1	dk+1	NOUN
ejpam-4746	67	7	=	=	SYM
ejpam-4746	67	8	−gk+1	−gk+1	PROPN
ejpam-4746	67	9	+	+	CCONJ
ejpam-4746	67	10	βhs	βhs	NOUN
ejpam-4746	67	11	k	k	PROPN
ejpam-4746	67	12	sk	sk	PROPN
ejpam-4746	67	13	else	else	ADV
ejpam-4746	67	14	dk+1	dk+1	X
ejpam-4746	67	15	=	=	SYM
ejpam-4746	67	16	−gk+1	−gk+1	PROPN
ejpam-4746	67	17	+	+	CCONJ
ejpam-4746	67	18	{	{	PUNCT
ejpam-4746	67	19	(	(	PUNCT
ejpam-4746	67	20	1−	1−	NUM
ejpam-4746	67	21	θβhs	θβhs	NOUN
ejpam-4746	67	22	k	k	PROPN
ejpam-4746	67	23	+	+	CCONJ
ejpam-4746	67	24	θβdy	θβdy	ADJ
ejpam-4746	67	25	k	k	PROPN
ejpam-4746	67	26	}	}	PUNCT
ejpam-4746	67	27	sk	sk	VERB
ejpam-4746	67	28	2.2	2.2	NUM
ejpam-4746	67	29	.	.	PUNCT
ejpam-4746	68	1	descent	descent	NOUN
ejpam-4746	68	2	property	property	NOUN
ejpam-4746	68	3	and	and	CCONJ
ejpam-4746	68	4	global	global	ADJ
ejpam-4746	68	5	convergence	convergence	NOUN
ejpam-4746	68	6	analysis	analysis	NOUN
ejpam-4746	68	7	next	next	ADV
ejpam-4746	68	8	we	we	PRON
ejpam-4746	68	9	will	will	AUX
ejpam-4746	68	10	show	show	VERB
ejpam-4746	68	11	that	that	SCONJ
ejpam-4746	68	12	our	our	PRON
ejpam-4746	68	13	cg	cg	NOUN
ejpam-4746	68	14	method	method	NOUN
ejpam-4746	68	15	(	(	PUNCT
ejpam-4746	68	16	8)	8)	NUM
ejpam-4746	68	17	satisfies	satisfy	VERB
ejpam-4746	68	18	the	the	DET
ejpam-4746	68	19	descent	descent	NOUN
ejpam-4746	68	20	property	property	NOUN
ejpam-4746	68	21	and	and	CCONJ
ejpam-4746	68	22	global	global	ADJ
ejpam-4746	68	23	converges	converge	NOUN
ejpam-4746	68	24	.	.	PUNCT
ejpam-4746	69	1	theorem	theorem	NOUN
ejpam-4746	69	2	1	1	NUM
ejpam-4746	69	3	.	.	PUNCT
ejpam-4746	70	1	let	let	VERB
ejpam-4746	70	2	{	{	PUNCT
ejpam-4746	70	3	θk	θk	VERB
ejpam-4746	70	4	}	}	PUNCT
ejpam-4746	70	5	and	and	CCONJ
ejpam-4746	70	6	{	{	PUNCT
ejpam-4746	70	7	dk+1	dk+1	NOUN
ejpam-4746	70	8	}	}	PUNCT
ejpam-4746	70	9	be	be	VERB
ejpam-4746	70	10	the	the	DET
ejpam-4746	70	11	sequences	sequence	NOUN
ejpam-4746	70	12	generated	generate	VERB
ejpam-4746	70	13	by	by	ADP
ejpam-4746	70	14	eq	eq	PROPN
ejpam-4746	70	15	.	.	PUNCT
ejpam-4746	71	1	(	(	PUNCT
ejpam-4746	71	2	8)	8)	NUM
ejpam-4746	71	3	and	and	CCONJ
ejpam-4746	71	4	(	(	PUNCT
ejpam-4746	71	5	9	9	NUM
ejpam-4746	71	6	)	)	PUNCT
ejpam-4746	71	7	with	with	ADP
ejpam-4746	71	8	strong	strong	ADJ
ejpam-4746	71	9	wolfe	wolfe	PROPN
ejpam-4746	71	10	conditions	condition	NOUN
ejpam-4746	72	1	and	and	CCONJ
ejpam-4746	72	2	assume	assume	VERB
ejpam-4746	72	3	that	that	SCONJ
ejpam-4746	72	4	gtk+1gk	gtk+1gk	ADJ
ejpam-4746	72	5	≥	≥	PUNCT
ejpam-4746	72	6	0	0	NUM
ejpam-4746	72	7	and	and	CCONJ
ejpam-4746	72	8	σ	σ	NUM
ejpam-4746	72	9	≤	≤	NUM
ejpam-4746	72	10	1	1	NUM
ejpam-4746	72	11	2	2	NUM
ejpam-4746	72	12	.	.	PUNCT
ejpam-4746	73	1	then	then	ADV
ejpam-4746	73	2	the	the	DET
ejpam-4746	73	3	search	search	NOUN
ejpam-4746	73	4	directions	direction	NOUN
ejpam-4746	73	5	dk+1	dk+1	VERB
ejpam-4746	73	6	satisfies	satisfie	NOUN
ejpam-4746	74	1	sufficient	sufficient	ADJ
ejpam-4746	74	2	descent	descent	NOUN
ejpam-4746	74	3	condition	condition	NOUN
ejpam-4746	74	4	gtk+1dk	gtk+1dk	PROPN
ejpam-4746	74	5	≤	≤	NUM
ejpam-4746	74	6	−c	−c	NOUN
ejpam-4746	74	7	∥gk∥	∥gk∥	NOUN
ejpam-4746	74	8	where	where	SCONJ
ejpam-4746	74	9	c	c	NOUN
ejpam-4746	74	10	is	be	AUX
ejpam-4746	74	11	constant	constant	ADJ
ejpam-4746	74	12	.	.	PUNCT
ejpam-4746	75	1	proof	proof	NOUN
ejpam-4746	75	2	.	.	PUNCT
ejpam-4746	76	1	the	the	DET
ejpam-4746	76	2	prove	prove	NOUN
ejpam-4746	76	3	is	be	AUX
ejpam-4746	76	4	by	by	ADP
ejpam-4746	76	5	in	in	ADP
ejpam-4746	76	6	induction	induction	NOUN
ejpam-4746	76	7	that	that	PRON
ejpam-4746	76	8	is	be	AUX
ejpam-4746	76	9	if	if	SCONJ
ejpam-4746	76	10	k	k	PROPN
ejpam-4746	76	11	=	=	PUNCT
ejpam-4746	76	12	0	0	PUNCT
ejpam-4746	77	1	then	then	ADV
ejpam-4746	77	2	d1	d1	PROPN
ejpam-4746	77	3	=	=	PUNCT
ejpam-4746	78	1	−g1	−g1	VERB
ejpam-4746	78	2	and	and	CCONJ
ejpam-4746	78	3	gt1	gt1	NOUN
ejpam-4746	78	4	d1	d1	PROPN
ejpam-4746	79	1	=	=	SYM
ejpam-4746	79	2	−∥g1∥	−∥g1∥	NOUN
ejpam-4746	79	3	assume	assume	VERB
ejpam-4746	79	4	that	that	SCONJ
ejpam-4746	79	5	gtk	gtk	NOUN
ejpam-4746	79	6	dk	dk	PRON
ejpam-4746	79	7	≤	≤	PROPN
ejpam-4746	79	8	−c	−c	NOUN
ejpam-4746	79	9	∥gk∥	∥gk∥	NOUN
ejpam-4746	79	10	to	to	PART
ejpam-4746	79	11	prove	prove	VERB
ejpam-4746	79	12	for	for	ADP
ejpam-4746	79	13	k	k	PROPN
ejpam-4746	79	14	=	=	PUNCT
ejpam-4746	79	15	k	k	PROPN
ejpam-4746	80	1	+	+	CCONJ
ejpam-4746	80	2	1	1	NUM
ejpam-4746	80	3	we	we	PRON
ejpam-4746	80	4	have	have	VERB
ejpam-4746	80	5	ytk	ytk	NUM
ejpam-4746	80	6	sk	sk	ADJ
ejpam-4746	80	7	=	=	PUNCT
ejpam-4746	80	8	gtk+1sk	gtk+1sk	PROPN
ejpam-4746	80	9	−	−	PROPN
ejpam-4746	80	10	gtk	gtk	NOUN
ejpam-4746	80	11	sk	sk	ADP
ejpam-4746	80	12	≥	≥	PROPN
ejpam-4746	80	13	(	(	PUNCT
ejpam-4746	80	14	σ	σ	NOUN
ejpam-4746	80	15	−	−	PROPN
ejpam-4746	80	16	1	1	NUM
ejpam-4746	80	17	)	)	PUNCT
ejpam-4746	80	18	gtk	gtk	NOUN
ejpam-4746	80	19	dk	dk	PROPN
ejpam-4746	80	20	>	>	X
ejpam-4746	80	21	0	0	PUNCT
ejpam-4746	80	22	and	and	CCONJ
ejpam-4746	80	23	θk	θk	NOUN
ejpam-4746	80	24	=	=	SYM
ejpam-4746	80	25	(	(	PUNCT
ejpam-4746	80	26	stk	stk	PROPN
ejpam-4746	80	27	gk+1	gk+1	NOUN
ejpam-4746	80	28	)	)	PUNCT
ejpam-4746	80	29	3	3	NUM
ejpam-4746	80	30	(	(	PUNCT
ejpam-4746	80	31	ytk	ytk	NOUN
ejpam-4746	80	32	sk)2	sk)2	PROPN
ejpam-4746	80	33	<	<	X
ejpam-4746	80	34	1	1	NUM
ejpam-4746	80	35	,	,	PUNCT
ejpam-4746	80	36	if	if	SCONJ
ejpam-4746	80	37	θk	θk	X
ejpam-4746	80	38	<	<	X
ejpam-4746	80	39	0	0	NUM
ejpam-4746	80	40	.	.	PUNCT
ejpam-4746	81	1	we	we	PRON
ejpam-4746	81	2	set	set	VERB
ejpam-4746	81	3	θk	θk	NOUN
ejpam-4746	81	4	=	=	SYM
ejpam-4746	81	5	0	0	NUM
ejpam-4746	82	1	therefor	therefor	ADP
ejpam-4746	82	2	we	we	PRON
ejpam-4746	82	3	assume	assume	VERB
ejpam-4746	82	4	0	0	PUNCT
ejpam-4746	82	5	<	<	X
ejpam-4746	82	6	θk	θk	X
ejpam-4746	82	7	<	<	X
ejpam-4746	82	8	1	1	NUM
ejpam-4746	82	9	.	.	PUNCT
ejpam-4746	82	10	then	then	ADV
ejpam-4746	82	11	dk+1	dk+1	VERB
ejpam-4746	82	12	=	=	SYM
ejpam-4746	82	13	−gk+1	−gk+1	PROPN
ejpam-4746	82	14	+	+	CCONJ
ejpam-4746	82	15	[	[	PUNCT
ejpam-4746	82	16	(	(	PUNCT
ejpam-4746	82	17	1−	1−	NUM
ejpam-4746	82	18	θk	θk	NOUN
ejpam-4746	82	19	)	)	PUNCT
ejpam-4746	82	20	ytk	ytk	PROPN
ejpam-4746	82	21	gk+1	gk+1	NUM
ejpam-4746	82	22	ytk	ytk	NOUN
ejpam-4746	82	23	sk	sk	ADP
ejpam-4746	82	24	−	−	PROPN
ejpam-4746	82	25	θk	θk	NOUN
ejpam-4746	82	26	gtk+1gk+1	gtk+1gk+1	NOUN
ejpam-4746	82	27	ytk	ytk	NOUN
ejpam-4746	82	28	sk	sk	NOUN
ejpam-4746	82	29	]	]	PUNCT
ejpam-4746	82	30	sk	sk	PROPN
ejpam-4746	82	31	h.	h.	PROPN
ejpam-4746	82	32	m.	m.	PROPN
ejpam-4746	83	1	khudhur	khudhur	PROPN
ejpam-4746	83	2	et	et	PROPN
ejpam-4746	83	3	al	al	PROPN
ejpam-4746	83	4	.	.	PUNCT
ejpam-4746	83	5	/	/	SYM
ejpam-4746	83	6	eur	eur	PROPN
ejpam-4746	83	7	.	.	PUNCT
ejpam-4746	84	1	j.	j.	PROPN
ejpam-4746	84	2	pure	pure	PROPN
ejpam-4746	84	3	appl	appl	PROPN
ejpam-4746	84	4	.	.	PROPN
ejpam-4746	84	5	math	math	PROPN
ejpam-4746	84	6	,	,	PUNCT
ejpam-4746	84	7	16	16	NUM
ejpam-4746	84	8	(	(	PUNCT
ejpam-4746	84	9	2	2	NUM
ejpam-4746	84	10	)	)	PUNCT
ejpam-4746	84	11	(	(	PUNCT
ejpam-4746	84	12	2023	2023	NUM
ejpam-4746	84	13	)	)	PUNCT
ejpam-4746	84	14	,	,	PUNCT
ejpam-4746	84	15	1059	1059	NUM
ejpam-4746	84	16	-	-	SYM
ejpam-4746	84	17	1067	1067	NUM
ejpam-4746	84	18	1062	1062	NUM
ejpam-4746	84	19	multiply	multiply	ADP
ejpam-4746	84	20	both	both	DET
ejpam-4746	84	21	sides	side	NOUN
ejpam-4746	84	22	by	by	ADP
ejpam-4746	84	23	gtk+1	gtk+1	NOUN
ejpam-4746	84	24	gtk+1dk+1	gtk+1dk+1	NOUN
ejpam-4746	84	25	=	=	SYM
ejpam-4746	84	26	−gtk+1gk+1	−gtk+1gk+1	PROPN
ejpam-4746	85	1	+	+	CCONJ
ejpam-4746	85	2	[	[	PUNCT
ejpam-4746	85	3	(	(	PUNCT
ejpam-4746	85	4	1−	1−	NUM
ejpam-4746	85	5	θk	θk	NOUN
ejpam-4746	85	6	)	)	PUNCT
ejpam-4746	85	7	ytk	ytk	PROPN
ejpam-4746	85	8	gk+1	gk+1	NUM
ejpam-4746	85	9	ytk	ytk	NOUN
ejpam-4746	85	10	sk	sk	ADP
ejpam-4746	85	11	−	−	PROPN
ejpam-4746	85	12	θk	θk	NOUN
ejpam-4746	85	13	gtk+1gk+1	gtk+1gk+1	NOUN
ejpam-4746	85	14	ytk	ytk	NOUN
ejpam-4746	85	15	sk	sk	NOUN
ejpam-4746	85	16	]	]	PUNCT
ejpam-4746	85	17	gtk+1sk	gtk+1sk	PROPN
ejpam-4746	85	18	≤	≤	PROPN
ejpam-4746	85	19	−gtk+1gk+1	−gtk+1gk+1	PROPN
ejpam-4746	86	1	+	+	CCONJ
ejpam-4746	86	2	[	[	PUNCT
ejpam-4746	86	3	(	(	PUNCT
ejpam-4746	86	4	1−	1−	NUM
ejpam-4746	86	5	θk	θk	NOUN
ejpam-4746	86	6	)	)	PUNCT
ejpam-4746	86	7	ytk	ytk	PROPN
ejpam-4746	86	8	gk+1	gk+1	NOUN
ejpam-4746	86	9	g	g	ADP
ejpam-4746	86	10	t	t	PROPN
ejpam-4746	86	11	k+1sk	k+1sk	X
ejpam-4746	86	12	(	(	PUNCT
ejpam-4746	86	13	σ	σ	NOUN
ejpam-4746	86	14	−	−	PROPN
ejpam-4746	86	15	1	1	NUM
ejpam-4746	86	16	)	)	PUNCT
ejpam-4746	86	17	gtk	gtk	NOUN
ejpam-4746	87	1	dk	dk	PRON
ejpam-4746	87	2	−	−	PROPN
ejpam-4746	87	3	(	(	PUNCT
ejpam-4746	87	4	gtk+1sk	gtk+1sk	PROPN
ejpam-4746	87	5	)	)	PUNCT
ejpam-4746	87	6	4	4	NUM
ejpam-4746	87	7	(	(	PUNCT
ejpam-4746	87	8	ytk	ytk	NOUN
ejpam-4746	87	9	sk	sk	ADP
ejpam-4746	87	10	∗	∗	PROPN
ejpam-4746	87	11	ytk	ytk	PROPN
ejpam-4746	87	12	sk	sk	NOUN
ejpam-4746	87	13	)	)	PUNCT
ejpam-4746	87	14	gtk+1gk+1	gtk+1gk+1	VERB
ejpam-4746	87	15	ytk	ytk	NOUN
ejpam-4746	87	16	sk	sk	INTJ
ejpam-4746	87	17	]	]	PUNCT
ejpam-4746	87	18	since	since	SCONJ
ejpam-4746	87	19	the	the	DET
ejpam-4746	87	20	last	last	ADJ
ejpam-4746	87	21	term	term	NOUN
ejpam-4746	87	22	is	be	AUX
ejpam-4746	87	23	positive	positive	ADJ
ejpam-4746	87	24	∴	∴	NOUN
ejpam-4746	87	25	gtk+1dk+1	gtk+1dk+1	PUNCT
ejpam-4746	87	26	≤	≤	PUNCT
ejpam-4746	88	1	−gtk+1gk+1	−gtk+1gk+1	PROPN
ejpam-4746	89	1	+	+	PROPN
ejpam-4746	90	1	[	[	PUNCT
ejpam-4746	90	2	(	(	PUNCT
ejpam-4746	90	3	1−	1−	NUM
ejpam-4746	90	4	θk	θk	NOUN
ejpam-4746	90	5	)	)	PUNCT
ejpam-4746	90	6	∣∣ytk	∣∣ytk	PROPN
ejpam-4746	90	7	gk+1	gk+1	X
ejpam-4746	90	8	∣∣	∣∣	NUM
ejpam-4746	90	9	∣∣gtk+1sk	∣∣gtk+1sk	X
ejpam-4746	90	10	∣∣	∣∣	NUM
ejpam-4746	90	11	(	(	PUNCT
ejpam-4746	90	12	σ	σ	NOUN
ejpam-4746	90	13	−	−	PROPN
ejpam-4746	90	14	1	1	NUM
ejpam-4746	90	15	)	)	PUNCT
ejpam-4746	90	16	gtk	gtk	NOUN
ejpam-4746	90	17	dk	dk	PROPN
ejpam-4746	90	18	]	]	PUNCT
ejpam-4746	90	19	≤	≤	PROPN
ejpam-4746	90	20	−gtk+1gk+1	−gtk+1gk+1	PROPN
ejpam-4746	90	21	+	+	PROPN
ejpam-4746	90	22	[	[	PUNCT
ejpam-4746	90	23	(	(	PUNCT
ejpam-4746	90	24	1−	1−	NUM
ejpam-4746	90	25	θk	θk	NOUN
ejpam-4746	90	26	)	)	PUNCT
ejpam-4746	90	27	∣∣ytk	∣∣ytk	PROPN
ejpam-4746	90	28	gk+1	gk+1	X
ejpam-4746	90	29	∣∣	∣∣	X
ejpam-4746	90	30	(	(	PUNCT
ejpam-4746	90	31	−σgtk	−σgtk	X
ejpam-4746	90	32	dk	dk	X
ejpam-4746	90	33	)	)	PUNCT
ejpam-4746	90	34	(	(	PUNCT
ejpam-4746	90	35	σ	σ	NOUN
ejpam-4746	90	36	−	−	PROPN
ejpam-4746	90	37	1	1	NUM
ejpam-4746	90	38	)	)	PUNCT
ejpam-4746	90	39	gtk	gtk	NOUN
ejpam-4746	90	40	dk	dk	X
ejpam-4746	90	41	]	]	PUNCT
ejpam-4746	90	42	∴	∴	PROPN
ejpam-4746	90	43	gtk+1dk+1	gtk+1dk+1	X
ejpam-4746	90	44	≤	≤	PUNCT
ejpam-4746	90	45	−gtk+1gk+1	−gtk+1gk+1	PROPN
ejpam-4746	90	46	+	+	PROPN
ejpam-4746	90	47	[	[	PUNCT
ejpam-4746	90	48	(	(	PUNCT
ejpam-4746	90	49	1−	1−	NUM
ejpam-4746	90	50	θk	θk	NOUN
ejpam-4746	90	51	)	)	PUNCT
ejpam-4746	90	52	∣∣ytk	∣∣ytk	PROPN
ejpam-4746	90	53	gk+1	gk+1	X
ejpam-4746	90	54	∣∣	∣∣	X
ejpam-4746	90	55	(	(	PUNCT
ejpam-4746	90	56	−σ	−σ	NOUN
ejpam-4746	90	57	)	)	PUNCT
ejpam-4746	90	58	(	(	PUNCT
ejpam-4746	90	59	σ	σ	NOUN
ejpam-4746	90	60	−	−	PROPN
ejpam-4746	90	61	1	1	NUM
ejpam-4746	90	62	)	)	PUNCT
ejpam-4746	90	63	]	]	PUNCT
ejpam-4746	91	1	=	=	PUNCT
ejpam-4746	92	1	−gtk+1gk+1	−gtk+1gk+1	PROPN
ejpam-4746	92	2	+	+	X
ejpam-4746	92	3	[	[	PUNCT
ejpam-4746	92	4	(	(	PUNCT
ejpam-4746	92	5	1−	1−	NUM
ejpam-4746	92	6	θk	θk	NOUN
ejpam-4746	92	7	)	)	PUNCT
ejpam-4746	92	8	ó	ó	NOUN
ejpam-4746	92	9	∣∣ytk	∣∣ytk	NOUN
ejpam-4746	92	10	gk+1	gk+1	X
ejpam-4746	92	11	∣∣	∣∣	X
ejpam-4746	92	12	(	(	PUNCT
ejpam-4746	92	13	1−	1−	NUM
ejpam-4746	92	14	σ	σ	NUM
ejpam-4746	92	15	)	)	PUNCT
ejpam-4746	92	16	]	]	PUNCT
ejpam-4746	92	17	since	since	SCONJ
ejpam-4746	92	18	gtk+1gk	gtk+1gk	PROPN
ejpam-4746	92	19	≥	≥	NOUN
ejpam-4746	92	20	0	0	NUM
ejpam-4746	92	21	and	and	CCONJ
ejpam-4746	92	22	∣∣ytk	∣∣ytk	PROPN
ejpam-4746	92	23	gk+1	gk+1	X
ejpam-4746	92	24	∣∣	∣∣	NUM
ejpam-4746	92	25	=	=	SYM
ejpam-4746	92	26	∣∣gtk+1	∣∣gtk+1	X
ejpam-4746	92	27	(	(	PUNCT
ejpam-4746	92	28	|gk+1	|gk+1	NOUN
ejpam-4746	92	29	−	−	ADP
ejpam-4746	92	30	gk|	gk|	NOUN
ejpam-4746	92	31	)	)	PUNCT
ejpam-4746	92	32	∣∣	∣∣	NUM
ejpam-4746	92	33	≤	≤	PROPN
ejpam-4746	92	34	||gk+1||2	||gk+1||2	NOUN
ejpam-4746	92	35	∴	∴	NOUN
ejpam-4746	92	36	gtk+1dk+1	gtk+1dk+1	VERB
ejpam-4746	92	37	≤	≤	NUM
ejpam-4746	93	1	−gtk+1gk+1	−gtk+1gk+1	PROPN
ejpam-4746	94	1	+	+	CCONJ
ejpam-4746	94	2	[	[	PUNCT
ejpam-4746	94	3	(	(	PUNCT
ejpam-4746	94	4	1−	1−	NUM
ejpam-4746	94	5	θk	θk	NOUN
ejpam-4746	94	6	)	)	PUNCT
ejpam-4746	94	7	σgtk+1gk+1	σgtk+1gk+1	PUNCT
ejpam-4746	94	8	(	(	PUNCT
ejpam-4746	94	9	1−	1−	NUM
ejpam-4746	94	10	σ	σ	NUM
ejpam-4746	94	11	)	)	PUNCT
ejpam-4746	94	12	]	]	PUNCT
ejpam-4746	95	1	=	=	PUNCT
ejpam-4746	95	2	(	(	PUNCT
ejpam-4746	95	3	−1	−1	NOUN
ejpam-4746	95	4	+	+	PUNCT
ejpam-4746	95	5	[	[	PUNCT
ejpam-4746	95	6	σ	σ	X
ejpam-4746	95	7	(	(	PUNCT
ejpam-4746	95	8	1−	1−	NUM
ejpam-4746	95	9	θk	θk	NOUN
ejpam-4746	95	10	)	)	PUNCT
ejpam-4746	95	11	(	(	PUNCT
ejpam-4746	95	12	1−	1−	NUM
ejpam-4746	95	13	σ	σ	NUM
ejpam-4746	95	14	)	)	PUNCT
ejpam-4746	95	15	]	]	PUNCT
ejpam-4746	95	16	)	)	PUNCT
ejpam-4746	95	17	gtk+1gk+1	gtk+1gk+1	VERB
ejpam-4746	95	18	dtk+1gk+1	dtk+1gk+1	X
ejpam-4746	95	19	≤	≤	NUM
ejpam-4746	95	20	−c	−c	NOUN
ejpam-4746	95	21	∥gk+1∥2	∥gk+1∥2	NOUN
ejpam-4746	95	22	where	where	SCONJ
ejpam-4746	95	23	c	c	NOUN
ejpam-4746	95	24	=	=	SYM
ejpam-4746	95	25	(	(	PUNCT
ejpam-4746	95	26	1−	1−	NUM
ejpam-4746	95	27	σ(1−θ	σ(1−θ	NOUN
ejpam-4746	95	28	)	)	PUNCT
ejpam-4746	95	29	(	(	PUNCT
ejpam-4746	95	30	1−σ	1−σ	NUM
ejpam-4746	95	31	)	)	PUNCT
ejpam-4746	95	32	)	)	PUNCT
ejpam-4746	95	33	,	,	PUNCT
ejpam-4746	95	34	the	the	DET
ejpam-4746	95	35	prove	prove	NOUN
ejpam-4746	95	36	is	be	AUX
ejpam-4746	95	37	complete	complete	ADJ
ejpam-4746	95	38	.	.	PUNCT
ejpam-4746	96	1	the	the	DET
ejpam-4746	96	2	following	follow	VERB
ejpam-4746	96	3	assumptions	assumption	NOUN
ejpam-4746	96	4	are	be	AUX
ejpam-4746	96	5	used	use	VERB
ejpam-4746	96	6	to	to	PART
ejpam-4746	96	7	demonstrate	demonstrate	VERB
ejpam-4746	96	8	the	the	DET
ejpam-4746	96	9	proposed	propose	VERB
ejpam-4746	96	10	algorithm	algorithm	NOUN
ejpam-4746	96	11	’s	’s	PART
ejpam-4746	96	12	global	global	ADJ
ejpam-4746	96	13	convergence	convergence	NOUN
ejpam-4746	96	14	.	.	PUNCT
ejpam-4746	97	1	assumption	assumption	NOUN
ejpam-4746	97	2	1	1	NUM
ejpam-4746	97	3	.	.	NOUN
ejpam-4746	97	4	1	1	NUM
ejpam-4746	97	5	.	.	X
ejpam-4746	98	1	in	in	ADP
ejpam-4746	98	2	the	the	DET
ejpam-4746	98	3	level	level	NOUN
ejpam-4746	98	4	set	set	NOUN
ejpam-4746	98	5	,	,	PUNCT
ejpam-4746	98	6	the	the	DET
ejpam-4746	98	7	objective	objective	ADJ
ejpam-4746	98	8	function	function	NOUN
ejpam-4746	98	9	f(x	f(x	PROPN
ejpam-4746	98	10	)	)	PUNCT
ejpam-4746	98	11	is	be	AUX
ejpam-4746	98	12	bounded	bound	VERB
ejpam-4746	98	13	below	below	ADP
ejpam-4746	98	14	ω	ω	PROPN
ejpam-4746	98	15	=	=	SYM
ejpam-4746	98	16	{	{	PUNCT
ejpam-4746	98	17	x	x	PROPN
ejpam-4746	98	18	∈	∈	PROPN
ejpam-4746	98	19	rn	rn	PROPN
ejpam-4746	98	20	:	:	PUNCT
ejpam-4746	98	21	f(x	f(x	PROPN
ejpam-4746	98	22	)	)	PUNCT
ejpam-4746	98	23	≤	≤	NUM
ejpam-4746	98	24	f(x1	f(x1	NOUN
ejpam-4746	98	25	)	)	PUNCT
ejpam-4746	98	26	}	}	PUNCT
ejpam-4746	98	27	;	;	PUNCT
ejpam-4746	99	1	2	2	X
ejpam-4746	99	2	.	.	X
ejpam-4746	99	3	in	in	ADP
ejpam-4746	99	4	some	some	DET
ejpam-4746	99	5	parts	part	NOUN
ejpam-4746	99	6	of	of	ADP
ejpam-4746	99	7	town	town	NOUN
ejpam-4746	99	8	n	n	PROPN
ejpam-4746	99	9	ofω	ofω	NOUN
ejpam-4746	99	10	,	,	PUNCT
ejpam-4746	99	11	f	f	PROPN
ejpam-4746	99	12	there	there	PRON
ejpam-4746	99	13	exists	exist	VERB
ejpam-4746	99	14	a	a	DET
ejpam-4746	99	15	constant	constant	ADJ
ejpam-4746	99	16	that	that	PRON
ejpam-4746	99	17	is	be	AUX
ejpam-4746	99	18	constantly	constantly	ADV
ejpam-4746	99	19	differentiable	differentiable	ADJ
ejpam-4746	99	20	and	and	CCONJ
ejpam-4746	99	21	has	have	VERB
ejpam-4746	99	22	a	a	DET
ejpam-4746	99	23	lipschitz	lipschitz	NOUN
ejpam-4746	99	24	continuous	continuous	ADJ
ejpam-4746	99	25	gradient	gradient	NOUN
ejpam-4746	99	26	l	l	PROPN
ejpam-4746	99	27	>	>	X
ejpam-4746	99	28	0	0	NUM
ejpam-4746	100	1	such	such	ADJ
ejpam-4746	100	2	that	that	SCONJ
ejpam-4746	100	3	:	:	PUNCT
ejpam-4746	100	4	∥g(x)−	∥g(x)−	X
ejpam-4746	100	5	g(y)∥	g(y)∥	VERB
ejpam-4746	100	6	≤	≤	NUM
ejpam-4746	100	7	l	l	NOUN
ejpam-4746	100	8	∥x−	∥x−	PROPN
ejpam-4746	100	9	y∥	y∥	NOUN
ejpam-4746	100	10	,	,	PUNCT
ejpam-4746	100	11	∀x	∀x	NUM
ejpam-4746	100	12	,	,	PUNCT
ejpam-4746	100	13	y	y	PROPN
ejpam-4746	100	14	∈	∈	PROPN
ejpam-4746	100	15	n	n	CCONJ
ejpam-4746	100	16	(	(	PUNCT
ejpam-4746	100	17	11	11	NUM
ejpam-4746	100	18	)	)	PUNCT
ejpam-4746	100	19	it	it	PRON
ejpam-4746	100	20	’s	’	VERB
ejpam-4746	100	21	worth	worth	ADJ
ejpam-4746	100	22	noting	note	VERB
ejpam-4746	100	23	that	that	SCONJ
ejpam-4746	100	24	these	these	DET
ejpam-4746	100	25	assumptions	assumption	NOUN
ejpam-4746	100	26	suggest	suggest	VERB
ejpam-4746	100	27	the	the	DET
ejpam-4746	100	28	existence	existence	NOUN
ejpam-4746	100	29	of	of	ADP
ejpam-4746	100	30	a	a	DET
ejpam-4746	100	31	constant	constant	ADJ
ejpam-4746	100	32	γ	γ	NOUN
ejpam-4746	100	33	,	,	PUNCT
ejpam-4746	100	34	implying	imply	VERB
ejpam-4746	100	35	that	that	SCONJ
ejpam-4746	100	36	∥gk∥	∥gk∥	ADJ
ejpam-4746	100	37	≤	≤	PROPN
ejpam-4746	100	38	γ	γ	PROPN
ejpam-4746	100	39	,	,	PUNCT
ejpam-4746	100	40	for	for	ADP
ejpam-4746	100	41	any	any	DET
ejpam-4746	100	42	x	x	NOUN
ejpam-4746	100	43	in	in	ADP
ejpam-4746	100	44	the	the	DET
ejpam-4746	100	45	level	level	NOUN
ejpam-4746	100	46	set	set	VERB
ejpam-4746	100	47	ω	ω	NUM
ejpam-4746	100	48	,	,	PUNCT
ejpam-4746	100	49	and	and	CCONJ
ejpam-4746	100	50	∥x∥	∥x∥	NOUN
ejpam-4746	100	51	≤	≤	PROPN
ejpam-4746	100	52	b	b	NOUN
ejpam-4746	100	53	,	,	PUNCT
ejpam-4746	100	54	∀x	∀x	X
ejpam-4746	100	55	∈	∈	PROPN
ejpam-4746	100	56	ω	ω	X
ejpam-4746	100	57	lemma	lemma	PROPN
ejpam-4746	100	58	1	1	NUM
ejpam-4746	100	59	.	.	PUNCT
ejpam-4746	101	1	[	[	X
ejpam-4746	101	2	1	1	NUM
ejpam-4746	101	3	,	,	PUNCT
ejpam-4746	101	4	2	2	NUM
ejpam-4746	101	5	,	,	PUNCT
ejpam-4746	101	6	12	12	NUM
ejpam-4746	101	7	,	,	PUNCT
ejpam-4746	101	8	14	14	NUM
ejpam-4746	101	9	,	,	PUNCT
ejpam-4746	101	10	15	15	NUM
ejpam-4746	101	11	]	]	PUNCT
ejpam-4746	101	12	assume	assume	VERB
ejpam-4746	101	13	that	that	SCONJ
ejpam-4746	101	14	dkis	dki	VERB
ejpam-4746	101	15	a	a	DET
ejpam-4746	101	16	descent	descent	NOUN
ejpam-4746	101	17	direction	direction	NOUN
ejpam-4746	101	18	and	and	CCONJ
ejpam-4746	101	19	gk	gk	NOUN
ejpam-4746	101	20	satisfies	satisfy	VERB
ejpam-4746	101	21	the	the	DET
ejpam-4746	101	22	lipschitz	lipschitz	NOUN
ejpam-4746	101	23	condition∥g(x)−	condition∥g(x)−	PROPN
ejpam-4746	101	24	g(y)∥	g(y)∥	NOUN
ejpam-4746	102	1	≤	≤	NUM
ejpam-4746	102	2	l	l	NOUN
ejpam-4746	103	1	∥x−	∥x−	PROPN
ejpam-4746	103	2	y∥for	y∥for	PROPN
ejpam-4746	103	3	all	all	DET
ejpam-4746	103	4	xon	xon	NOUN
ejpam-4746	103	5	the	the	DET
ejpam-4746	103	6	linking	link	VERB
ejpam-4746	103	7	section	section	NOUN
ejpam-4746	103	8	of	of	ADP
ejpam-4746	103	9	a	a	DET
ejpam-4746	103	10	line	line	NOUN
ejpam-4746	103	11	xk	xk	PROPN
ejpam-4746	103	12	and	and	CCONJ
ejpam-4746	103	13	xk+1	xk+1	NUM
ejpam-4746	103	14	l	l	NOUN
ejpam-4746	103	15	is	be	AUX
ejpam-4746	103	16	the	the	DET
ejpam-4746	103	17	constant	constant	ADJ
ejpam-4746	103	18	in	in	ADP
ejpam-4746	103	19	this	this	DET
ejpam-4746	103	20	equation	equation	NOUN
ejpam-4746	103	21	.	.	PUNCT
ejpam-4746	104	1	if	if	SCONJ
ejpam-4746	104	2	wolfe	wolfe	PROPN
ejpam-4746	104	3	’s	’s	PART
ejpam-4746	104	4	condition	condition	NOUN
ejpam-4746	104	5	is	be	AUX
ejpam-4746	104	6	met	meet	VERB
ejpam-4746	104	7	,	,	PUNCT
ejpam-4746	104	8	the	the	DET
ejpam-4746	104	9	line	line	NOUN
ejpam-4746	104	10	quest	quest	NOUN
ejpam-4746	104	11	is	be	AUX
ejpam-4746	104	12	successful	successful	ADJ
ejpam-4746	104	13	then	then	ADV
ejpam-4746	104	14	αk	αk	CCONJ
ejpam-4746	104	15	≥	≥	NOUN
ejpam-4746	104	16	1−	1−	NUM
ejpam-4746	104	17	σ	σ	NUM
ejpam-4746	104	18	l	l	NOUN
ejpam-4746	104	19	∣∣gtk	∣∣gtk	NUM
ejpam-4746	104	20	dk∣∣	dk∣∣	PROPN
ejpam-4746	105	1	∥dk∥2	∥dk∥2	PROPN
ejpam-4746	105	2	h.	h.	PROPN
ejpam-4746	105	3	m.	m.	PROPN
ejpam-4746	105	4	khudhur	khudhur	PROPN
ejpam-4746	105	5	et	et	PROPN
ejpam-4746	105	6	al	al	PROPN
ejpam-4746	105	7	.	.	PUNCT
ejpam-4746	105	8	/	/	SYM
ejpam-4746	105	9	eur	eur	PROPN
ejpam-4746	105	10	.	.	PUNCT
ejpam-4746	106	1	j.	j.	PROPN
ejpam-4746	106	2	pure	pure	PROPN
ejpam-4746	106	3	appl	appl	PROPN
ejpam-4746	106	4	.	.	PROPN
ejpam-4746	106	5	math	math	PROPN
ejpam-4746	106	6	,	,	PUNCT
ejpam-4746	106	7	16	16	NUM
ejpam-4746	106	8	(	(	PUNCT
ejpam-4746	106	9	2	2	NUM
ejpam-4746	106	10	)	)	PUNCT
ejpam-4746	106	11	(	(	PUNCT
ejpam-4746	106	12	2023	2023	NUM
ejpam-4746	106	13	)	)	PUNCT
ejpam-4746	106	14	,	,	PUNCT
ejpam-4746	106	15	1059	1059	NUM
ejpam-4746	106	16	-	-	SYM
ejpam-4746	106	17	1067	1067	NUM
ejpam-4746	106	18	1063	1063	NUM
ejpam-4746	106	19	lemma	lemma	PROPN
ejpam-4746	106	20	2	2	NUM
ejpam-4746	106	21	.	.	PUNCT
ejpam-4746	107	1	[	[	X
ejpam-4746	107	2	4	4	NUM
ejpam-4746	107	3	,	,	PUNCT
ejpam-4746	107	4	5	5	NUM
ejpam-4746	107	5	,	,	PUNCT
ejpam-4746	107	6	8	8	NUM
ejpam-4746	107	7	,	,	PUNCT
ejpam-4746	107	8	15	15	NUM
ejpam-4746	107	9	,	,	PUNCT
ejpam-4746	107	10	21	21	NUM
ejpam-4746	107	11	,	,	PUNCT
ejpam-4746	107	12	22	22	NUM
ejpam-4746	107	13	]	]	PUNCT
ejpam-4746	107	14	assume	assume	VERB
ejpam-4746	107	15	the	the	DET
ejpam-4746	107	16	assumption	assumption	NOUN
ejpam-4746	107	17	is	be	AUX
ejpam-4746	107	18	right	right	ADJ
ejpam-4746	107	19	.	.	PUNCT
ejpam-4746	108	1	the	the	DET
ejpam-4746	108	2	descent	descent	NOUN
ejpam-4746	108	3	condition	condition	NOUN
ejpam-4746	108	4	is	be	AUX
ejpam-4746	108	5	satisfied	satisfied	ADJ
ejpam-4746	108	6	if	if	SCONJ
ejpam-4746	108	7	the	the	DET
ejpam-4746	108	8	conjugate	conjugate	ADJ
ejpam-4746	108	9	gradient	gradient	NOUN
ejpam-4746	108	10	method	method	NOUN
ejpam-4746	108	11	is	be	AUX
ejpam-4746	108	12	used	use	VERB
ejpam-4746	108	13	.	.	PUNCT
ejpam-4746	109	1	∞∑	∞∑	NUM
ejpam-4746	109	2	k=1	k=1	X
ejpam-4746	109	3	(	(	PUNCT
ejpam-4746	109	4	gtk	gtk	NOUN
ejpam-4746	109	5	dk	dk	PROPN
ejpam-4746	109	6	)	)	PUNCT
ejpam-4746	109	7	2	2	NUM
ejpam-4746	109	8	∥dk∥2	∥dk∥2	NOUN
ejpam-4746	109	9	<	<	X
ejpam-4746	110	1	+	+	ADJ
ejpam-4746	110	2	∞	∞	PROPN
ejpam-4746	110	3	(	(	PUNCT
ejpam-4746	110	4	12	12	NUM
ejpam-4746	110	5	)	)	PUNCT
ejpam-4746	110	6	theorem	theorem	NOUN
ejpam-4746	110	7	2	2	NUM
ejpam-4746	110	8	.	.	X
ejpam-4746	110	9	assume	assume	VERB
ejpam-4746	110	10	the	the	DET
ejpam-4746	110	11	assumption	assumption	NOUN
ejpam-4746	110	12	2.3	2.3	NUM
ejpam-4746	110	13	.	.	PUNCT
ejpam-4746	110	14	is	be	AUX
ejpam-4746	110	15	true	true	ADJ
ejpam-4746	110	16	.	.	PUNCT
ejpam-4746	111	1	let	let	VERB
ejpam-4746	111	2	{	{	PUNCT
ejpam-4746	111	3	gk}and	gk}and	X
ejpam-4746	111	4	{	{	PUNCT
ejpam-4746	111	5	dk	dk	NOUN
ejpam-4746	111	6	}	}	PUNCT
ejpam-4746	111	7	be	be	VERB
ejpam-4746	111	8	the	the	DET
ejpam-4746	111	9	sequence	sequence	NOUN
ejpam-4746	111	10	generated	generate	VERB
ejpam-4746	111	11	by	by	ADP
ejpam-4746	111	12	the	the	DET
ejpam-4746	111	13	algorithm	algorithm	NOUN
ejpam-4746	111	14	(	(	PUNCT
ejpam-4746	111	15	hkye	hkye	NOUN
ejpam-4746	111	16	)	)	PUNCT
ejpam-4746	111	17	when	when	SCONJ
ejpam-4746	111	18	subjected	subject	VERB
ejpam-4746	111	19	to	to	ADP
ejpam-4746	111	20	a	a	DET
ejpam-4746	111	21	strong	strong	ADJ
ejpam-4746	111	22	wolfe	wolfe	PROPN
ejpam-4746	111	23	line	line	NOUN
ejpam-4746	111	24	search	search	NOUN
ejpam-4746	111	25	condition	condition	NOUN
ejpam-4746	111	26	.	.	PUNCT
ejpam-4746	112	1	then	then	ADV
ejpam-4746	112	2	lim	lim	PROPN
ejpam-4746	112	3	inf	inf	PROPN
ejpam-4746	112	4	∥gk∥	∥gk∥	PROPN
ejpam-4746	112	5	k→∞	k→∞	NOUN
ejpam-4746	112	6	=	=	SYM
ejpam-4746	112	7	0	0	NUM
ejpam-4746	112	8	proof	proof	NOUN
ejpam-4746	112	9	.	.	PUNCT
ejpam-4746	113	1	it	it	PRON
ejpam-4746	113	2	follows	follow	VERB
ejpam-4746	113	3	from	from	ADP
ejpam-4746	113	4	assumption	assumption	NOUN
ejpam-4746	113	5	2.3	2.3	NUM
ejpam-4746	113	6	.	.	PUNCT
ejpam-4746	114	1	that	that	SCONJ
ejpam-4746	114	2	there	there	PRON
ejpam-4746	114	3	is	be	VERB
ejpam-4746	114	4	a	a	DET
ejpam-4746	114	5	positive	positive	ADJ
ejpam-4746	114	6	constant	constant	ADJ
ejpam-4746	114	7	γ	γ	NOUN
ejpam-4746	114	8	>	>	X
ejpam-4746	114	9	0	0	NUM
ejpam-4746	114	10	such	such	ADJ
ejpam-4746	114	11	that	that	SCONJ
ejpam-4746	114	12	∥g(x)∥	∥g(x)∥	PROPN
ejpam-4746	114	13	≤	≤	NOUN
ejpam-4746	114	14	γ	γ	NOUN
ejpam-4746	114	15	for	for	ADP
ejpam-4746	114	16	all	all	DET
ejpam-4746	114	17	x	x	SYM
ejpam-4746	114	18	∈	∈	PROPN
ejpam-4746	114	19	ω	ω	NUM
ejpam-4746	114	20	,	,	PUNCT
ejpam-4746	114	21	and	and	CCONJ
ejpam-4746	114	22	theorem	theorem	VERB
ejpam-4746	114	23	2.1	2.1	NUM
ejpam-4746	114	24	.	.	PUNCT
ejpam-4746	115	1	αk	αk	CCONJ
ejpam-4746	115	2	≥	≥	NOUN
ejpam-4746	115	3	(	(	PUNCT
ejpam-4746	115	4	1−σ	1−σ	NUM
ejpam-4746	115	5	)	)	PUNCT
ejpam-4746	115	6	l	l	NOUN
ejpam-4746	115	7	(	(	PUNCT
ejpam-4746	115	8	gtk	gtk	NOUN
ejpam-4746	115	9	dk	dk	PROPN
ejpam-4746	115	10	)	)	PUNCT
ejpam-4746	115	11	2	2	NUM
ejpam-4746	115	12	∥dk∥2	∥dk∥2	NOUN
ejpam-4746	115	13	=	=	PUNCT
ejpam-4746	115	14	λ	λ	X
ejpam-4746	115	15	if	if	SCONJ
ejpam-4746	115	16	the	the	DET
ejpam-4746	115	17	theorem	theorem	NOUN
ejpam-4746	115	18	is	be	AUX
ejpam-4746	115	19	incorrect	incorrect	ADJ
ejpam-4746	115	20	,	,	PUNCT
ejpam-4746	115	21	then	then	ADV
ejpam-4746	115	22	a	a	DET
ejpam-4746	115	23	positive	positive	ADJ
ejpam-4746	115	24	constant	constant	NOUN
ejpam-4746	115	25	must	must	AUX
ejpam-4746	115	26	exist	exist	VERB
ejpam-4746	115	27	>	>	PUNCT
ejpam-4746	115	28	0	0	NUM
ejpam-4746	115	29	such	such	ADJ
ejpam-4746	115	30	that	that	PRON
ejpam-4746	115	31	is	be	AUX
ejpam-4746	115	32	true	true	ADJ
ejpam-4746	115	33	for	for	ADP
ejpam-4746	115	34	all	all	PRON
ejpam-4746	115	35	k	k	ADV
ejpam-4746	115	36	sufficiently	sufficiently	ADV
ejpam-4746	115	37	large	large	ADJ
ejpam-4746	115	38	∥gk∥	∥gk∥	ADJ
ejpam-4746	115	39	≥	≥	NOUN
ejpam-4746	115	40	µ	µ	X
ejpam-4746	115	41	(	(	PUNCT
ejpam-4746	115	42	13	13	NUM
ejpam-4746	115	43	)	)	PUNCT
ejpam-4746	115	44	by	by	ADP
ejpam-4746	115	45	the	the	DET
ejpam-4746	115	46	eq(6)and	eq(6)and	NOUN
ejpam-4746	115	47	theorem	theorem	VERB
ejpam-4746	115	48	2.1	2.1	NUM
ejpam-4746	115	49	.	.	PUNCT
ejpam-4746	115	50	,	,	PUNCT
ejpam-4746	115	51	it	it	PRON
ejpam-4746	115	52	results	result	VERB
ejpam-4746	115	53	that	that	SCONJ
ejpam-4746	115	54	ytk	ytk	NOUN
ejpam-4746	115	55	sk	sk	NOUN
ejpam-4746	115	56	=	=	PUNCT
ejpam-4746	115	57	gtk+1sk	gtk+1sk	PROPN
ejpam-4746	115	58	−	−	PROPN
ejpam-4746	115	59	gtk	gtk	NOUN
ejpam-4746	115	60	sk	sk	ADP
ejpam-4746	115	61	≥	≥	NOUN
ejpam-4746	115	62	−(1−	−(1−	ADP
ejpam-4746	115	63	σ)gtk	σ)gtk	PROPN
ejpam-4746	115	64	sk	sk	VERB
ejpam-4746	115	65	≥	≥	NOUN
ejpam-4746	115	66	c(1−	c(1−	PART
ejpam-4746	116	1	σ)gk	σ)gk	PROPN
ejpam-4746	116	2	2	2	NUM
ejpam-4746	116	3	(	(	PUNCT
ejpam-4746	116	4	14	14	NUM
ejpam-4746	116	5	)	)	PUNCT
ejpam-4746	116	6	lipschitz	lipschitz	NOUN
ejpam-4746	116	7	continuity	continuity	NOUN
ejpam-4746	116	8	of	of	ADP
ejpam-4746	116	9	the	the	DET
ejpam-4746	116	10	gradient	gradient	NOUN
ejpam-4746	116	11	,	,	PUNCT
ejpam-4746	116	12	gives	give	VERB
ejpam-4746	116	13	yk	yk	NOUN
ejpam-4746	116	14	=	=	PUNCT
ejpam-4746	117	1	gi+1	gi+1	NOUN
ejpam-4746	118	1	−	−	PROPN
ejpam-4746	118	2	gk	gk	PROPN
ejpam-4746	118	3	≤	≤	PROPN
ejpam-4746	118	4	l	l	NOUN
ejpam-4746	118	5	xk+1	xk+1	NUM
ejpam-4746	118	6	−	−	PROPN
ejpam-4746	118	7	xk	xk	PROPN
ejpam-4746	118	8	≤	≤	PROPN
ejpam-4746	118	9	lr	lr	X
ejpam-4746	118	10	(	(	PUNCT
ejpam-4746	118	11	15	15	NUM
ejpam-4746	118	12	)	)	PUNCT
ejpam-4746	118	13	where	where	SCONJ
ejpam-4746	118	14	r	r	NOUN
ejpam-4746	118	15	=	=	NOUN
ejpam-4746	118	16	max{∥x−	max{∥x−	NOUN
ejpam-4746	118	17	y∥	y∥	NOUN
ejpam-4746	118	18	;	;	PUNCT
ejpam-4746	118	19	x	x	X
ejpam-4746	118	20	,	,	PUNCT
ejpam-4746	118	21	y	y	PROPN
ejpam-4746	118	22	∈	∈	PROPN
ejpam-4746	118	23	ω	ω	PROPN
ejpam-4746	118	24	}	}	PUNCT
ejpam-4746	118	25	is	be	AUX
ejpam-4746	118	26	diameter	diameter	NOUN
ejpam-4746	118	27	of	of	ADP
ejpam-4746	118	28	the	the	DET
ejpam-4746	118	29	level	level	NOUN
ejpam-4746	118	30	.	.	PUNCT
ejpam-4746	119	1	now	now	ADV
ejpam-4746	119	2	|βk|	|βk|	NOUN
ejpam-4746	119	3	=	=	PUNCT
ejpam-4746	119	4	∣∣(1−	∣∣(1−	PROPN
ejpam-4746	119	5	θk)β	θk)β	PROPN
ejpam-4746	119	6	hs	hs	PROPN
ejpam-4746	119	7	k	k	PROPN
ejpam-4746	119	8	+	+	CCONJ
ejpam-4746	119	9	θβdy	θβdy	ADJ
ejpam-4746	119	10	k	k	PROPN
ejpam-4746	119	11	∣∣	∣∣	VERB
ejpam-4746	119	12	≤	≤	X
ejpam-4746	119	13	∣∣βhs	∣∣βhs	PROPN
ejpam-4746	119	14	k	k	PROPN
ejpam-4746	119	15	∣∣+	∣∣+	PROPN
ejpam-4746	119	16	∣∣βdy	∣∣βdy	PROPN
ejpam-4746	119	17	k	k	X
ejpam-4746	119	18	∣∣	∣∣	X
ejpam-4746	119	19	=	=	SYM
ejpam-4746	119	20	∣∣αkg	∣∣αkg	PROPN
ejpam-4746	119	21	t	t	PROPN
ejpam-4746	119	22	k	k	PROPN
ejpam-4746	119	23	yk	yk	PROPN
ejpam-4746	119	24	∣∣∣∣ytk	∣∣∣∣ytk	PROPN
ejpam-4746	119	25	sk∣∣	sk∣∣	PROPN
ejpam-4746	119	26	+	+	CCONJ
ejpam-4746	119	27	∣∣αkg	∣∣αkg	PROPN
ejpam-4746	119	28	t	t	PROPN
ejpam-4746	119	29	k+1gk+1	k+1gk+1	NOUN
ejpam-4746	119	30	∣∣∣∣ytk	∣∣∣∣ytk	PROPN
ejpam-4746	119	31	sk∣∣	sk∣∣	NOUN
ejpam-4746	119	32	≤	≤	NOUN
ejpam-4746	119	33	αk	αk	ADP
ejpam-4746	119	34	∥gk+1∥	∥gk+1∥	NUM
ejpam-4746	119	35	∥yk∥	∥yk∥	PRON
ejpam-4746	119	36	c	c	NOUN
ejpam-4746	119	37	∥gk∥	∥gk∥	NOUN
ejpam-4746	120	1	+	+	CCONJ
ejpam-4746	120	2	αk	αk	CCONJ
ejpam-4746	120	3	∥gk+1∥	∥gk+1∥	NUM
ejpam-4746	120	4	c(1−	c(1−	NOUN
ejpam-4746	120	5	σ	σ	NOUN
ejpam-4746	120	6	)	)	PUNCT
ejpam-4746	120	7	∥gk∥	∥gk∥	ADJ
ejpam-4746	120	8	≤	≤	PUNCT
ejpam-4746	120	9	αkγlr	αkγlr	PROPN
ejpam-4746	120	10	c(1−	c(1−	NOUN
ejpam-4746	120	11	σ	σ	PROPN
ejpam-4746	120	12	)	)	PUNCT
ejpam-4746	121	1	+	+	NUM
ejpam-4746	121	2	αkγ	αkγ	NOUN
ejpam-4746	121	3	2	2	NUM
ejpam-4746	121	4	c(1−	c(1−	NOUN
ejpam-4746	121	5	σ)µ2	σ)µ2	PROPN
ejpam-4746	121	6	=	=	SYM
ejpam-4746	121	7	v	v	NOUN
ejpam-4746	121	8	therefor	therefor	ADP
ejpam-4746	121	9	∥dk+1∥	∥dk+1∥	NUM
ejpam-4746	121	10	=	=	SYM
ejpam-4746	121	11	∥gk+1∥+	∥gk+1∥+	NOUN
ejpam-4746	121	12	|βk|	|βk|	NOUN
ejpam-4746	121	13	∥xk+1	∥xk+1	ADP
ejpam-4746	121	14	−	−	PROPN
ejpam-4746	121	15	xk∥	xk∥	PROPN
ejpam-4746	121	16	=	=	SYM
ejpam-4746	121	17	∥gk+1∥+	∥gk+1∥+	NOUN
ejpam-4746	121	18	|βk|∥sk∥	|βk|∥sk∥	NOUN
ejpam-4746	121	19	αk	αk	NOUN
ejpam-4746	121	20	≤	≤	NOUN
ejpam-4746	121	21	γ	γ	X
ejpam-4746	121	22	+	+	NOUN
ejpam-4746	121	23	v	v	NOUN
ejpam-4746	121	24	r	r	NOUN
ejpam-4746	121	25	µ	µ	X
ejpam-4746	121	26	≡	≡	PROPN
ejpam-4746	121	27	q	q	PROPN
ejpam-4746	121	28	(	(	PUNCT
ejpam-4746	121	29	16	16	NUM
ejpam-4746	121	30	)	)	PUNCT
ejpam-4746	121	31	which	which	PRON
ejpam-4746	121	32	gives	give	VERB
ejpam-4746	121	33	∑	∑	PROPN
ejpam-4746	121	34	k≥0	k≥0	PROPN
ejpam-4746	121	35	1	1	NUM
ejpam-4746	121	36	∥dk∥	∥dk∥	NOUN
ejpam-4746	121	37	=	=	SYM
ejpam-4746	121	38	∞	∞	PROPN
ejpam-4746	121	39	(	(	PUNCT
ejpam-4746	121	40	17	17	NUM
ejpam-4746	121	41	)	)	PUNCT
ejpam-4746	121	42	h.	h.	NOUN
ejpam-4746	121	43	m.	m.	NOUN
ejpam-4746	122	1	khudhur	khudhur	PROPN
ejpam-4746	122	2	et	et	PROPN
ejpam-4746	122	3	al	al	PROPN
ejpam-4746	122	4	.	.	PUNCT
ejpam-4746	122	5	/	/	SYM
ejpam-4746	122	6	eur	eur	PROPN
ejpam-4746	122	7	.	.	PUNCT
ejpam-4746	123	1	j.	j.	PROPN
ejpam-4746	123	2	pure	pure	PROPN
ejpam-4746	123	3	appl	appl	PROPN
ejpam-4746	123	4	.	.	PROPN
ejpam-4746	123	5	math	math	PROPN
ejpam-4746	123	6	,	,	PUNCT
ejpam-4746	123	7	16	16	NUM
ejpam-4746	123	8	(	(	PUNCT
ejpam-4746	123	9	2	2	NUM
ejpam-4746	123	10	)	)	PUNCT
ejpam-4746	123	11	(	(	PUNCT
ejpam-4746	123	12	2023	2023	NUM
ejpam-4746	123	13	)	)	PUNCT
ejpam-4746	123	14	,	,	PUNCT
ejpam-4746	123	15	1059	1059	NUM
ejpam-4746	123	16	-	-	SYM
ejpam-4746	123	17	1067	1067	NUM
ejpam-4746	123	18	1064	1064	NUM
ejpam-4746	123	19	theorem	theorem	VERB
ejpam-4746	123	20	2.1	2.1	NUM
ejpam-4746	123	21	.	.	PUNCT
ejpam-4746	124	1	and	and	CCONJ
ejpam-4746	124	2	eq(13	eq(13	PROPN
ejpam-4746	124	3	)	)	PUNCT
ejpam-4746	124	4	and	and	CCONJ
ejpam-4746	124	5	the	the	DET
ejpam-4746	124	6	zoutendijk	zoutendijk	NOUN
ejpam-4746	124	7	condition	condition	NOUN
ejpam-4746	124	8	,	,	PUNCT
ejpam-4746	124	9	on	on	ADP
ejpam-4746	124	10	the	the	DET
ejpam-4746	124	11	other	other	ADJ
ejpam-4746	124	12	hand	hand	NOUN
ejpam-4746	124	13	,	,	PUNCT
ejpam-4746	124	14	result	result	VERB
ejpam-4746	124	15	from	from	ADP
ejpam-4746	124	16	adequate	adequate	ADJ
ejpam-4746	124	17	descent	descent	NOUN
ejpam-4746	124	18	c2γ4	c2γ4	X
ejpam-4746	124	19	∑	∑	PROPN
ejpam-4746	124	20	k≥0	k≥0	PROPN
ejpam-4746	124	21	1	1	NUM
ejpam-4746	124	22	∥dk∥	∥dk∥	NOUN
ejpam-4746	124	23	≤	≤	NOUN
ejpam-4746	124	24	∑	∑	PUNCT
ejpam-4746	125	1	k≥0	k≥0	PROPN
ejpam-4746	125	2	c2	c2	PROPN
ejpam-4746	125	3	∥gk∥4	∥gk∥4	PROPN
ejpam-4746	125	4	∥dk∥2	∥dk∥2	PROPN
ejpam-4746	125	5	≤	≤	NOUN
ejpam-4746	125	6	∑	∑	PUNCT
ejpam-4746	125	7	k≥0	k≥0	PROPN
ejpam-4746	125	8	(	(	PUNCT
ejpam-4746	125	9	gtk	gtk	NOUN
ejpam-4746	125	10	dk	dk	PROPN
ejpam-4746	125	11	)	)	PUNCT
ejpam-4746	125	12	2	2	NUM
ejpam-4746	125	13	∥dk∥2	∥dk∥2	NOUN
ejpam-4746	126	1	=	=	SYM
ejpam-4746	126	2	∞	∞	PROPN
ejpam-4746	126	3	as	as	ADP
ejpam-4746	126	4	a	a	DET
ejpam-4746	126	5	result	result	NOUN
ejpam-4746	126	6	of	of	ADP
ejpam-4746	126	7	the	the	DET
ejpam-4746	126	8	inconsistency	inconsistency	NOUN
ejpam-4746	126	9	with	with	ADP
ejpam-4746	126	10	(	(	PUNCT
ejpam-4746	126	11	17	17	NUM
ejpam-4746	126	12	)	)	PUNCT
ejpam-4746	126	13	,	,	PUNCT
ejpam-4746	126	14	(	(	PUNCT
ejpam-4746	126	15	13	13	NUM
ejpam-4746	126	16	)	)	PUNCT
ejpam-4746	126	17	does	do	AUX
ejpam-4746	126	18	not	not	PART
ejpam-4746	126	19	hold	hold	VERB
ejpam-4746	126	20	,	,	PUNCT
ejpam-4746	126	21	and	and	CCONJ
ejpam-4746	126	22	as	as	ADP
ejpam-4746	126	23	a	a	DET
ejpam-4746	126	24	result	result	NOUN
ejpam-4746	126	25	lim	lim	PROPN
ejpam-4746	126	26	inf	inf	PROPN
ejpam-4746	126	27	∥gk∥	∥gk∥	PROPN
ejpam-4746	126	28	k→∞	k→∞	NOUN
ejpam-4746	126	29	=	=	SYM
ejpam-4746	126	30	0	0	NOUN
ejpam-4746	127	1	the	the	DET
ejpam-4746	127	2	prove	prove	NOUN
ejpam-4746	127	3	is	be	AUX
ejpam-4746	127	4	complete	complete	ADJ
ejpam-4746	127	5	.	.	PUNCT
ejpam-4746	128	1	3	3	X
ejpam-4746	128	2	.	.	X
ejpam-4746	128	3	comparisons	comparison	NOUN
ejpam-4746	128	4	and	and	CCONJ
ejpam-4746	128	5	numerical	numerical	ADJ
ejpam-4746	128	6	results	result	NOUN
ejpam-4746	128	7	the	the	DET
ejpam-4746	128	8	computational	computational	ADJ
ejpam-4746	128	9	output	output	NOUN
ejpam-4746	128	10	of	of	ADP
ejpam-4746	128	11	a	a	DET
ejpam-4746	128	12	fortran	fortran	ADJ
ejpam-4746	128	13	implementation	implementation	NOUN
ejpam-4746	128	14	of	of	ADP
ejpam-4746	128	15	the	the	DET
ejpam-4746	128	16	latest	late	ADJ
ejpam-4746	128	17	suggested	suggest	VERB
ejpam-4746	128	18	(	(	PUNCT
ejpam-4746	128	19	hkye	hkye	NOUN
ejpam-4746	128	20	)	)	PUNCT
ejpam-4746	128	21	algorithm	algorithm	NOUN
ejpam-4746	128	22	on	on	ADP
ejpam-4746	128	23	a	a	DET
ejpam-4746	128	24	set	set	NOUN
ejpam-4746	128	25	of	of	ADP
ejpam-4746	128	26	400	400	NUM
ejpam-4746	128	27	unconstrained	unconstrained	ADJ
ejpam-4746	128	28	optimization	optimization	NOUN
ejpam-4746	128	29	test	test	NOUN
ejpam-4746	128	30	problems	problem	NOUN
ejpam-4746	128	31	is	be	AUX
ejpam-4746	128	32	presented	present	VERB
ejpam-4746	128	33	in	in	ADP
ejpam-4746	128	34	this	this	DET
ejpam-4746	128	35	section	section	NOUN
ejpam-4746	128	36	.	.	PUNCT
ejpam-4746	129	1	the	the	DET
ejpam-4746	129	2	unconstrained	unconstrained	ADJ
ejpam-4746	129	3	optimization	optimization	NOUN
ejpam-4746	129	4	problems	problem	NOUN
ejpam-4746	129	5	are	be	AUX
ejpam-4746	129	6	the	the	DET
ejpam-4746	129	7	test	test	NOUN
ejpam-4746	129	8	problems	problem	NOUN
ejpam-4746	129	9	in	in	ADP
ejpam-4746	129	10	[	[	X
ejpam-4746	129	11	6	6	NUM
ejpam-4746	129	12	]	]	PUNCT
ejpam-4746	129	13	.	.	PUNCT
ejpam-4746	130	1	we	we	PRON
ejpam-4746	130	2	chose	choose	VERB
ejpam-4746	130	3	40	40	NUM
ejpam-4746	130	4	test	test	NOUN
ejpam-4746	130	5	problems	problem	NOUN
ejpam-4746	130	6	that	that	PRON
ejpam-4746	130	7	were	be	AUX
ejpam-4746	130	8	either	either	CCONJ
ejpam-4746	130	9	extended	extended	ADJ
ejpam-4746	130	10	or	or	CCONJ
ejpam-4746	130	11	generalized	generalize	VERB
ejpam-4746	130	12	.	.	PUNCT
ejpam-4746	131	1	each	each	DET
ejpam-4746	131	2	problem	problem	NOUN
ejpam-4746	131	3	is	be	AUX
ejpam-4746	131	4	evaluated	evaluate	VERB
ejpam-4746	131	5	ten	ten	NUM
ejpam-4746	131	6	times	time	NOUN
ejpam-4746	131	7	,	,	PUNCT
ejpam-4746	131	8	with	with	ADP
ejpam-4746	131	9	the	the	DET
ejpam-4746	131	10	number	number	NOUN
ejpam-4746	131	11	of	of	ADP
ejpam-4746	131	12	variables	variable	NOUN
ejpam-4746	131	13	increasingly	increasingly	ADV
ejpam-4746	131	14	increasing	increase	VERB
ejpam-4746	131	15	n=100,200	n=100,200	PROPN
ejpam-4746	131	16	,	,	PUNCT
ejpam-4746	131	17	.	.	PUNCT
ejpam-4746	131	18	.	.	PUNCT
ejpam-4746	132	1	.	.	PUNCT
ejpam-4746	133	1	,	,	PUNCT
ejpam-4746	133	2	1000	1000	NUM
ejpam-4746	133	3	.	.	PUNCT
ejpam-4746	134	1	the	the	DET
ejpam-4746	134	2	code	code	NOUN
ejpam-4746	134	3	for	for	ADP
ejpam-4746	134	4	fortran	fortran	NOUN
ejpam-4746	134	5	from	from	ADP
ejpam-4746	134	6	we	we	PRON
ejpam-4746	134	7	compare	compare	VERB
ejpam-4746	134	8	our	our	PRON
ejpam-4746	134	9	results	result	NOUN
ejpam-4746	134	10	to	to	ADP
ejpam-4746	134	11	those	those	PRON
ejpam-4746	134	12	of	of	ADP
ejpam-4746	134	13	the	the	DET
ejpam-4746	134	14	hs	hs	PROPN
ejpam-4746	134	15	and	and	CCONJ
ejpam-4746	134	16	dy	dy	NOUN
ejpam-4746	134	17	algorithms	algorithm	NOUN
ejpam-4746	134	18	,	,	PUNCT
ejpam-4746	134	19	as	as	ADV
ejpam-4746	134	20	well	well	ADV
ejpam-4746	134	21	as	as	ADP
ejpam-4746	134	22	the	the	DET
ejpam-4746	134	23	dolan	dolan	NOUN
ejpam-4746	134	24	and	and	CCONJ
ejpam-4746	134	25	more	more	ADJ
ejpam-4746	134	26	performance	performance	NOUN
ejpam-4746	134	27	profiles	profile	NOUN
ejpam-4746	134	28	[	[	X
ejpam-4746	134	29	23	23	NUM
ejpam-4746	134	30	]	]	PUNCT
ejpam-4746	134	31	.	.	PUNCT
ejpam-4746	135	1	the	the	DET
ejpam-4746	135	2	strong	strong	ADJ
ejpam-4746	135	3	wolfe	wolfe	PROPN
ejpam-4746	135	4	line	line	NOUN
ejpam-4746	135	5	search	search	NOUN
ejpam-4746	135	6	conditions	condition	NOUN
ejpam-4746	135	7	are	be	AUX
ejpam-4746	135	8	used	use	VERB
ejpam-4746	135	9	in	in	ADP
ejpam-4746	135	10	all	all	DET
ejpam-4746	135	11	algorithms	algorithm	NOUN
ejpam-4746	135	12	withρ	withρ	NOUN
ejpam-4746	135	13	=	=	SYM
ejpam-4746	135	14	0.0001andσ	0.0001andσ	PROPN
ejpam-4746	135	15	=	=	PUNCT
ejpam-4746	135	16	0.4	0.4	NUM
ejpam-4746	135	17	.	.	PUNCT
ejpam-4746	136	1	the	the	DET
ejpam-4746	136	2	same	same	ADJ
ejpam-4746	136	3	criteria	criterion	NOUN
ejpam-4746	136	4	for	for	ADP
ejpam-4746	136	5	stopping	stop	VERB
ejpam-4746	136	6	∥gk∥2	∥gk∥2	PROPN
ejpam-4746	136	7	<	<	X
ejpam-4746	136	8	10−6is	10−6is	PRON
ejpam-4746	136	9	used	use	VERB
ejpam-4746	136	10	.	.	PUNCT
ejpam-4746	137	1	algorithm	algorithm	NOUN
ejpam-4746	137	2	comparisons	comparison	NOUN
ejpam-4746	137	3	are	be	AUX
ejpam-4746	137	4	presented	present	VERB
ejpam-4746	137	5	in	in	ADP
ejpam-4746	137	6	the	the	DET
ejpam-4746	137	7	following	follow	VERB
ejpam-4746	137	8	context	context	NOUN
ejpam-4746	137	9	.	.	PUNCT
ejpam-4746	138	1	let	let	VERB
ejpam-4746	138	2	falg1	falg1	PROPN
ejpam-4746	138	3	i	i	PRON
ejpam-4746	138	4	and	and	CCONJ
ejpam-4746	138	5	faig2	faig2	PROPN
ejpam-4746	138	6	i	i	PRON
ejpam-4746	138	7	to	to	PART
ejpam-4746	138	8	be	be	AUX
ejpam-4746	138	9	the	the	DET
ejpam-4746	138	10	best	good	ADJ
ejpam-4746	138	11	value	value	NOUN
ejpam-4746	138	12	found	find	VERB
ejpam-4746	138	13	by	by	ADP
ejpam-4746	138	14	alg1	alg1	PROPN
ejpam-4746	138	15	andalg2	andalg2	PROPN
ejpam-4746	139	1	for	for	ADP
ejpam-4746	139	2	problem	problem	NOUN
ejpam-4746	139	3	i=1,	i=1,	PROPN
ejpam-4746	139	4	..	..	PROPN
ejpam-4746	139	5	,400	,400	NOUN
ejpam-4746	139	6	,	,	PUNCT
ejpam-4746	139	7	respectively	respectively	ADV
ejpam-4746	139	8	.	.	PUNCT
ejpam-4746	140	1	if	if	SCONJ
ejpam-4746	140	2	the	the	DET
ejpam-4746	140	3	performance	performance	NOUN
ejpam-4746	140	4	of	of	ADP
ejpam-4746	140	5	alg1	alg1	PROPN
ejpam-4746	140	6	was	be	AUX
ejpam-4746	140	7	better	well	ADJ
ejpam-4746	140	8	than	than	ADP
ejpam-4746	140	9	the	the	DET
ejpam-4746	140	10	performance	performance	NOUN
ejpam-4746	140	11	of	of	ADP
ejpam-4746	140	12	alg2	alg2	NOUN
ejpam-4746	140	13	in	in	ADP
ejpam-4746	140	14	the	the	DET
ejpam-4746	140	15	specific	specific	ADJ
ejpam-4746	140	16	problem	problem	NOUN
ejpam-4746	140	17	i	i	PRON
ejpam-4746	140	18	we	we	PRON
ejpam-4746	140	19	can	can	AUX
ejpam-4746	140	20	assume	assume	VERB
ejpam-4746	140	21	that	that	SCONJ
ejpam-4746	140	22	the	the	DET
ejpam-4746	140	23	performance	performance	NOUN
ejpam-4746	140	24	of	of	ADP
ejpam-4746	140	25	alg1	alg1	PROPN
ejpam-4746	140	26	was	be	AUX
ejpam-4746	140	27	better	well	ADJ
ejpam-4746	140	28	than	than	ADP
ejpam-4746	140	29	the	the	DET
ejpam-4746	140	30	performance	performance	NOUN
ejpam-4746	140	31	of	of	ADP
ejpam-4746	140	32	alg2	alg2	PRON
ejpam-4746	140	33	.	.	PUNCT
ejpam-4746	141	1	∣∣falg1	∣∣falg1	VERB
ejpam-4746	141	2	i	i	PRON
ejpam-4746	141	3	−	−	VERB
ejpam-4746	141	4	faig2	faig2	PROPN
ejpam-4746	142	1	i	i	PRON
ejpam-4746	142	2	∣∣	∣∣	X
ejpam-4746	142	3	<	<	X
ejpam-4746	142	4	10−3	10−3	NUM
ejpam-4746	142	5	the	the	DET
ejpam-4746	142	6	number	number	NOUN
ejpam-4746	142	7	of	of	ADP
ejpam-4746	142	8	iterations	iteration	NOUN
ejpam-4746	142	9	(	(	PUNCT
ejpam-4746	142	10	#	#	SYM
ejpam-4746	142	11	ite	ite	NOUN
ejpam-4746	142	12	)	)	PUNCT
ejpam-4746	142	13	,	,	PUNCT
ejpam-4746	142	14	function	function	NOUN
ejpam-4746	142	15	-	-	PUNCT
ejpam-4746	142	16	gradient	gradient	NOUN
ejpam-4746	142	17	evaluations	evaluation	NOUN
ejpam-4746	142	18	(	(	PUNCT
ejpam-4746	142	19	#	#	NOUN
ejpam-4746	142	20	fg	fg	NOUN
ejpam-4746	142	21	)	)	PUNCT
ejpam-4746	142	22	,	,	PUNCT
ejpam-4746	142	23	or	or	CCONJ
ejpam-4746	142	24	cpu	cpu	VERB
ejpam-4746	142	25	time	time	NOUN
ejpam-4746	142	26	corresponding	correspond	VERB
ejpam-4746	142	27	to	to	ADP
ejpam-4746	142	28	alg1	alg1	PROPN
ejpam-4746	142	29	was	be	AUX
ejpam-4746	142	30	less	less	ADJ
ejpam-4746	142	31	than	than	ADP
ejpam-4746	142	32	the	the	DET
ejpam-4746	142	33	number	number	NOUN
ejpam-4746	142	34	of	of	ADP
ejpam-4746	142	35	(	(	PUNCT
ejpam-4746	142	36	#	#	NOUN
ejpam-4746	142	37	ite	ite	NOUN
ejpam-4746	142	38	)	)	PUNCT
ejpam-4746	142	39	,	,	PUNCT
ejpam-4746	142	40	(	(	PUNCT
ejpam-4746	142	41	#	#	NOUN
ejpam-4746	142	42	fg	fg	NOUN
ejpam-4746	142	43	)	)	PUNCT
ejpam-4746	142	44	,	,	PUNCT
ejpam-4746	142	45	or	or	CCONJ
ejpam-4746	142	46	cpu	cpu	VERB
ejpam-4746	142	47	time	time	NOUN
ejpam-4746	142	48	corresponding	correspond	VERB
ejpam-4746	142	49	to	to	ADP
ejpam-4746	142	50	alg2	alg2	PROPN
ejpam-4746	142	51	,	,	PUNCT
ejpam-4746	142	52	respectively	respectively	ADV
ejpam-4746	142	53	.	.	PUNCT
ejpam-4746	143	1	to	to	PART
ejpam-4746	143	2	compare	compare	VERB
ejpam-4746	143	3	the	the	DET
ejpam-4746	143	4	performance	performance	NOUN
ejpam-4746	143	5	of	of	ADP
ejpam-4746	143	6	(	(	PUNCT
ejpam-4746	143	7	hkye	hkye	NOUN
ejpam-4746	143	8	)	)	PUNCT
ejpam-4746	143	9	to	to	ADP
ejpam-4746	143	10	that	that	PRON
ejpam-4746	143	11	of	of	ADP
ejpam-4746	143	12	hs	hs	PROPN
ejpam-4746	143	13	and	and	CCONJ
ejpam-4746	143	14	dy	dy	PROPN
ejpam-4746	143	15	,	,	PUNCT
ejpam-4746	143	16	we	we	PRON
ejpam-4746	143	17	consider	consider	VERB
ejpam-4746	143	18	the	the	DET
ejpam-4746	143	19	number	number	NOUN
ejpam-4746	143	20	of	of	ADP
ejpam-4746	143	21	iterations	iteration	NOUN
ejpam-4746	143	22	(	(	PUNCT
ejpam-4746	143	23	#	#	SYM
ejpam-4746	143	24	ite	ite	NOUN
ejpam-4746	143	25	)	)	PUNCT
ejpam-4746	143	26	in	in	ADP
ejpam-4746	143	27	fig.1	fig.1	PROPN
ejpam-4746	143	28	.	.	PUNCT
ejpam-4746	143	29	figure	figure	NOUN
ejpam-4746	143	30	2	2	NUM
ejpam-4746	143	31	shows	show	VERB
ejpam-4746	143	32	how	how	SCONJ
ejpam-4746	143	33	these	these	DET
ejpam-4746	143	34	algorithms	algorithm	NOUN
ejpam-4746	143	35	perform	perform	VERB
ejpam-4746	143	36	when	when	SCONJ
ejpam-4746	143	37	evaluating	evaluate	VERB
ejpam-4746	143	38	the	the	DET
ejpam-4746	143	39	number	number	NOUN
ejpam-4746	143	40	of	of	ADP
ejpam-4746	143	41	function	function	NOUN
ejpam-4746	143	42	gradients	gradient	NOUN
ejpam-4746	143	43	(	(	PUNCT
ejpam-4746	143	44	#	#	SYM
ejpam-4746	143	45	fg	fg	NOUN
ejpam-4746	143	46	)	)	PUNCT
ejpam-4746	143	47	,	,	PUNCT
ejpam-4746	143	48	while	while	SCONJ
ejpam-4746	143	49	figure	figure	NOUN
ejpam-4746	143	50	3	3	NUM
ejpam-4746	143	51	shows	show	VERB
ejpam-4746	143	52	how	how	SCONJ
ejpam-4746	143	53	they	they	PRON
ejpam-4746	143	54	perform	perform	VERB
ejpam-4746	143	55	when	when	SCONJ
ejpam-4746	143	56	evaluating	evaluate	VERB
ejpam-4746	143	57	cpu	cpu	NOUN
ejpam-4746	143	58	time	time	NOUN
ejpam-4746	143	59	.	.	PUNCT
ejpam-4746	144	1	we	we	PRON
ejpam-4746	144	2	can	can	AUX
ejpam-4746	144	3	see	see	VERB
ejpam-4746	144	4	that	that	PRON
ejpam-4746	144	5	(	(	PUNCT
ejpam-4746	144	6	hkye	hkye	NOUN
ejpam-4746	144	7	)	)	PUNCT
ejpam-4746	144	8	is	be	AUX
ejpam-4746	144	9	the	the	DET
ejpam-4746	144	10	best	good	ADJ
ejpam-4746	144	11	performer	performer	NOUN
ejpam-4746	144	12	.	.	PUNCT
ejpam-4746	145	1	these	these	DET
ejpam-4746	145	2	codes	code	NOUN
ejpam-4746	145	3	vary	vary	VERB
ejpam-4746	145	4	in	in	ADP
ejpam-4746	145	5	their	their	PRON
ejpam-4746	145	6	search	search	NOUN
ejpam-4746	145	7	path	path	NOUN
ejpam-4746	145	8	since	since	SCONJ
ejpam-4746	145	9	they	they	PRON
ejpam-4746	145	10	use	use	VERB
ejpam-4746	145	11	the	the	DET
ejpam-4746	145	12	same	same	ADJ
ejpam-4746	145	13	strong	strong	ADJ
ejpam-4746	145	14	wolfe	wolfe	PROPN
ejpam-4746	145	15	line	line	NOUN
ejpam-4746	145	16	search	search	NOUN
ejpam-4746	145	17	and	and	CCONJ
ejpam-4746	145	18	stopping	stopping	NOUN
ejpam-4746	145	19	criteria	criterion	NOUN
ejpam-4746	145	20	.	.	PUNCT
ejpam-4746	146	1	as	as	ADP
ejpam-4746	146	2	a	a	DET
ejpam-4746	146	3	result	result	NOUN
ejpam-4746	146	4	,	,	PUNCT
ejpam-4746	146	5	it	it	PRON
ejpam-4746	146	6	appears	appear	VERB
ejpam-4746	146	7	that	that	SCONJ
ejpam-4746	146	8	(	(	PUNCT
ejpam-4746	146	9	hkye	hkye	NOUN
ejpam-4746	146	10	)	)	PUNCT
ejpam-4746	146	11	generates	generate	VERB
ejpam-4746	146	12	the	the	DET
ejpam-4746	146	13	best	good	ADJ
ejpam-4746	146	14	search	search	NOUN
ejpam-4746	146	15	direction	direction	NOUN
ejpam-4746	146	16	among	among	ADP
ejpam-4746	146	17	these	these	DET
ejpam-4746	146	18	methods	method	NOUN
ejpam-4746	146	19	.	.	PUNCT
ejpam-4746	147	1	h.	h.	PROPN
ejpam-4746	147	2	m.	m.	PROPN
ejpam-4746	147	3	khudhur	khudhur	PROPN
ejpam-4746	147	4	et	et	PROPN
ejpam-4746	147	5	al	al	PROPN
ejpam-4746	147	6	.	.	PUNCT
ejpam-4746	147	7	/	/	SYM
ejpam-4746	147	8	eur	eur	PROPN
ejpam-4746	147	9	.	.	PUNCT
ejpam-4746	148	1	j.	j.	PROPN
ejpam-4746	148	2	pure	pure	PROPN
ejpam-4746	148	3	appl	appl	PROPN
ejpam-4746	148	4	.	.	PROPN
ejpam-4746	148	5	math	math	PROPN
ejpam-4746	148	6	,	,	PUNCT
ejpam-4746	148	7	16	16	NUM
ejpam-4746	148	8	(	(	PUNCT
ejpam-4746	148	9	2	2	NUM
ejpam-4746	148	10	)	)	PUNCT
ejpam-4746	148	11	(	(	PUNCT
ejpam-4746	148	12	2023	2023	NUM
ejpam-4746	148	13	)	)	PUNCT
ejpam-4746	148	14	,	,	PUNCT
ejpam-4746	148	15	1059	1059	NUM
ejpam-4746	148	16	-	-	SYM
ejpam-4746	148	17	1067	1067	NUM
ejpam-4746	148	18	1065	1065	NUM
ejpam-4746	148	19	figure	figure	NOUN
ejpam-4746	148	20	1	1	NUM
ejpam-4746	148	21	:	:	PUNCT
ejpam-4746	148	22	iteration	iteration	NOUN
ejpam-4746	148	23	-	-	PUNCT
ejpam-4746	148	24	based	base	VERB
ejpam-4746	148	25	efficiency	efficiency	NOUN
ejpam-4746	148	26	figure	figure	NOUN
ejpam-4746	148	27	2	2	NUM
ejpam-4746	148	28	:	:	PUNCT
ejpam-4746	148	29	performance	performance	NOUN
ejpam-4746	148	30	by	by	ADP
ejpam-4746	148	31	function	function	NOUN
ejpam-4746	148	32	figure	figure	NOUN
ejpam-4746	148	33	3	3	NUM
ejpam-4746	148	34	:	:	PUNCT
ejpam-4746	148	35	time	time	NOUN
ejpam-4746	148	36	-	-	PUNCT
ejpam-4746	148	37	based	base	VERB
ejpam-4746	148	38	performance	performance	NOUN
ejpam-4746	148	39	references	reference	NOUN
ejpam-4746	148	40	1066	1066	NUM
ejpam-4746	148	41	4	4	NUM
ejpam-4746	148	42	.	.	PUNCT
ejpam-4746	149	1	conclusion	conclusion	NOUN
ejpam-4746	149	2	we	we	PRON
ejpam-4746	149	3	presented	present	VERB
ejpam-4746	149	4	in	in	ADP
ejpam-4746	149	5	this	this	DET
ejpam-4746	149	6	research	research	NOUN
ejpam-4746	149	7	a	a	DET
ejpam-4746	149	8	new	new	ADJ
ejpam-4746	149	9	type	type	NOUN
ejpam-4746	149	10	of	of	ADP
ejpam-4746	149	11	conjugate	conjugate	ADJ
ejpam-4746	149	12	gradient	gradient	NOUN
ejpam-4746	149	13	technique	technique	NOUN
ejpam-4746	149	14	for	for	ADP
ejpam-4746	149	15	solving	solve	VERB
ejpam-4746	149	16	unconstrained	unconstrained	ADJ
ejpam-4746	149	17	optimization	optimization	NOUN
ejpam-4746	149	18	problems	problem	NOUN
ejpam-4746	149	19	,	,	PUNCT
ejpam-4746	149	20	and	and	CCONJ
ejpam-4746	149	21	the	the	DET
ejpam-4746	149	22	proposed	propose	VERB
ejpam-4746	149	23	algorithm	algorithm	NOUN
ejpam-4746	149	24	has	have	AUX
ejpam-4746	149	25	shown	show	VERB
ejpam-4746	149	26	high	high	ADJ
ejpam-4746	149	27	efficiency	efficiency	NOUN
ejpam-4746	149	28	in	in	ADP
ejpam-4746	149	29	solving	solve	VERB
ejpam-4746	149	30	these	these	DET
ejpam-4746	149	31	problems	problem	NOUN
ejpam-4746	149	32	with	with	ADP
ejpam-4746	149	33	the	the	DET
ejpam-4746	149	34	least	least	ADJ
ejpam-4746	149	35	number	number	NOUN
ejpam-4746	149	36	of	of	ADP
ejpam-4746	149	37	iterations	iteration	NOUN
ejpam-4746	149	38	and	and	CCONJ
ejpam-4746	149	39	higher	high	ADJ
ejpam-4746	149	40	accuracy	accuracy	NOUN
ejpam-4746	149	41	in	in	ADP
ejpam-4746	149	42	reaching	reach	VERB
ejpam-4746	149	43	the	the	DET
ejpam-4746	149	44	approximate	approximate	ADJ
ejpam-4746	149	45	solution	solution	NOUN
ejpam-4746	149	46	of	of	ADP
ejpam-4746	149	47	the	the	DET
ejpam-4746	149	48	function	function	NOUN
ejpam-4746	149	49	.	.	PUNCT
ejpam-4746	150	1	references	reference	NOUN
ejpam-4746	150	2	[	[	X
ejpam-4746	150	3	1	1	NUM
ejpam-4746	150	4	]	]	PUNCT
ejpam-4746	150	5	k	k	PROPN
ejpam-4746	150	6	k	k	PROPN
ejpam-4746	150	7	abbo	abbo	PROPN
ejpam-4746	150	8	and	and	CCONJ
ejpam-4746	150	9	h	h	PROPN
ejpam-4746	150	10	m	m	PROPN
ejpam-4746	150	11	khudhur	khudhur	PROPN
ejpam-4746	150	12	.	.	PUNCT
ejpam-4746	151	1	new	new	ADJ
ejpam-4746	151	2	a	a	DET
ejpam-4746	151	3	hybrid	hybrid	ADJ
ejpam-4746	151	4	conjugate	conjugate	ADJ
ejpam-4746	151	5	gradient	gradient	NOUN
ejpam-4746	151	6	fletcher	fletcher	PROPN
ejpam-4746	151	7	-	-	PUNCT
ejpam-4746	151	8	reeves	reeves	PROPN
ejpam-4746	151	9	and	and	CCONJ
ejpam-4746	151	10	polak	polak	PROPN
ejpam-4746	151	11	-	-	PUNCT
ejpam-4746	151	12	ribiere	ribiere	NOUN
ejpam-4746	151	13	algorithm	algorithm	NOUN
ejpam-4746	151	14	for	for	ADP
ejpam-4746	151	15	unconstrained	unconstrained	ADJ
ejpam-4746	151	16	optimization	optimization	NOUN
ejpam-4746	151	17	.	.	PUNCT
ejpam-4746	152	1	tikrit	tikrit	PROPN
ejpam-4746	152	2	journal	journal	NOUN
ejpam-4746	152	3	of	of	ADP
ejpam-4746	152	4	pure	pure	ADJ
ejpam-4746	152	5	science	science	NOUN
ejpam-4746	152	6	,	,	PUNCT
ejpam-4746	152	7	21:124–129	21:124–129	PROPN
ejpam-4746	152	8	,	,	PUNCT
ejpam-4746	152	9	2016	2016	NUM
ejpam-4746	152	10	.	.	PUNCT
ejpam-4746	153	1	[	[	X
ejpam-4746	153	2	2	2	NUM
ejpam-4746	153	3	]	]	PUNCT
ejpam-4746	153	4	k	k	PROPN
ejpam-4746	153	5	k	k	PROPN
ejpam-4746	153	6	abbo	abbo	PROPN
ejpam-4746	153	7	and	and	CCONJ
ejpam-4746	153	8	h	h	PROPN
ejpam-4746	153	9	m	m	PROPN
ejpam-4746	153	10	khudhur	khudhur	PROPN
ejpam-4746	153	11	.	.	PUNCT
ejpam-4746	154	1	new	new	ADJ
ejpam-4746	154	2	a	a	DET
ejpam-4746	154	3	hybrid	hybrid	ADJ
ejpam-4746	154	4	hestenes	hestene	NOUN
ejpam-4746	154	5	-	-	PUNCT
ejpam-4746	154	6	stiefel	stiefel	NOUN
ejpam-4746	154	7	and	and	CCONJ
ejpam-4746	154	8	dai	dai	PROPN
ejpam-4746	154	9	-	-	PUNCT
ejpam-4746	154	10	yuan	yuan	PROPN
ejpam-4746	154	11	conjugate	conjugate	ADJ
ejpam-4746	154	12	gradient	gradient	NOUN
ejpam-4746	154	13	algorithms	algorithm	NOUN
ejpam-4746	154	14	for	for	ADP
ejpam-4746	154	15	unconstrained	unconstrained	ADJ
ejpam-4746	154	16	optimization	optimization	NOUN
ejpam-4746	154	17	.	.	PUNCT
ejpam-4746	155	1	tikrit	tikrit	PROPN
ejpam-4746	155	2	journal	journal	NOUN
ejpam-4746	155	3	of	of	ADP
ejpam-4746	155	4	pure	pure	ADJ
ejpam-4746	155	5	science	science	NOUN
ejpam-4746	155	6	,	,	PUNCT
ejpam-4746	155	7	21:118–123	21:118–123	PROPN
ejpam-4746	155	8	,	,	PUNCT
ejpam-4746	155	9	2016	2016	NUM
ejpam-4746	155	10	.	.	PUNCT
ejpam-4746	156	1	[	[	X
ejpam-4746	156	2	3	3	X
ejpam-4746	156	3	]	]	X
ejpam-4746	156	4	k	k	PROPN
ejpam-4746	156	5	k	k	PROPN
ejpam-4746	156	6	abbo	abbo	PROPN
ejpam-4746	156	7	,	,	PUNCT
ejpam-4746	156	8	y	y	PROPN
ejpam-4746	156	9	a	a	DET
ejpam-4746	156	10	laylani	laylani	NOUN
ejpam-4746	156	11	,	,	PUNCT
ejpam-4746	156	12	and	and	CCONJ
ejpam-4746	156	13	h	h	PROPN
ejpam-4746	156	14	m	m	PROPN
ejpam-4746	156	15	khudhur	khudhur	PROPN
ejpam-4746	156	16	.	.	PROPN
ejpam-4746	156	17	proposed	propose	VERB
ejpam-4746	156	18	new	new	ADJ
ejpam-4746	156	19	scaled	scale	VERB
ejpam-4746	156	20	conjugate	conjugate	ADJ
ejpam-4746	156	21	gradient	gradient	ADJ
ejpam-4746	156	22	algorithm	algorithm	NOUN
ejpam-4746	156	23	for	for	ADP
ejpam-4746	156	24	unconstrained	unconstrained	ADJ
ejpam-4746	156	25	optimization	optimization	NOUN
ejpam-4746	156	26	.	.	PUNCT
ejpam-4746	157	1	int	int	NOUN
ejpam-4746	157	2	.	.	PUNCT
ejpam-4746	158	1	j.	j.	PROPN
ejpam-4746	158	2	enhanc	enhanc	PROPN
ejpam-4746	158	3	.	.	PUNCT
ejpam-4746	159	1	res	re	NOUN
ejpam-4746	159	2	.	.	PUNCT
ejpam-4746	160	1	sci	sci	PROPN
ejpam-4746	160	2	.	.	PROPN
ejpam-4746	160	3	technol	technol	PROPN
ejpam-4746	160	4	.	.	PUNCT
ejpam-4746	161	1	eng	eng	PROPN
ejpam-4746	161	2	,	,	PUNCT
ejpam-4746	161	3	5:269–276	5:269–276	NUM
ejpam-4746	161	4	,	,	PUNCT
ejpam-4746	161	5	2016	2016	NUM
ejpam-4746	161	6	.	.	PUNCT
ejpam-4746	162	1	[	[	X
ejpam-4746	162	2	4	4	NUM
ejpam-4746	162	3	]	]	X
ejpam-4746	162	4	k	k	PROPN
ejpam-4746	162	5	k	k	PROPN
ejpam-4746	162	6	abbo	abbo	PROPN
ejpam-4746	162	7	,	,	PUNCT
ejpam-4746	162	8	y	y	PROPN
ejpam-4746	162	9	a	a	DET
ejpam-4746	162	10	laylani	laylani	NOUN
ejpam-4746	162	11	,	,	PUNCT
ejpam-4746	162	12	and	and	CCONJ
ejpam-4746	162	13	h	h	PROPN
ejpam-4746	162	14	m	m	PROPN
ejpam-4746	162	15	khudhur	khudhur	PROPN
ejpam-4746	162	16	.	.	PUNCT
ejpam-4746	163	1	a	a	DET
ejpam-4746	163	2	new	new	ADJ
ejpam-4746	163	3	spectral	spectral	ADJ
ejpam-4746	163	4	conjugate	conjugate	ADJ
ejpam-4746	163	5	gradient	gradient	ADJ
ejpam-4746	163	6	algorithm	algorithm	NOUN
ejpam-4746	163	7	for	for	ADP
ejpam-4746	163	8	unconstrained	unconstrained	ADJ
ejpam-4746	163	9	optimization	optimization	NOUN
ejpam-4746	163	10	.	.	PUNCT
ejpam-4746	164	1	int	int	NOUN
ejpam-4746	164	2	.	.	PUNCT
ejpam-4746	165	1	j.	j.	PROPN
ejpam-4746	165	2	math	math	PROPN
ejpam-4746	165	3	.	.	PUNCT
ejpam-4746	166	1	comput	comput	PROPN
ejpam-4746	166	2	.	.	PUNCT
ejpam-4746	167	1	appl	appl	PROPN
ejpam-4746	167	2	.	.	PUNCT
ejpam-4746	168	1	res	re	NOUN
ejpam-4746	168	2	,	,	PUNCT
ejpam-4746	168	3	8:1–9	8:1–9	NUM
ejpam-4746	168	4	,	,	PUNCT
ejpam-4746	168	5	2018	2018	NUM
ejpam-4746	168	6	.	.	PUNCT
ejpam-4746	169	1	[	[	X
ejpam-4746	169	2	5	5	NUM
ejpam-4746	169	3	]	]	X
ejpam-4746	169	4	z	z	NOUN
ejpam-4746	169	5	m	m	VERB
ejpam-4746	169	6	abdullah	abdullah	PROPN
ejpam-4746	169	7	,	,	PUNCT
ejpam-4746	169	8	m	m	NOUN
ejpam-4746	169	9	hameed	hameed	NOUN
ejpam-4746	169	10	,	,	PUNCT
ejpam-4746	169	11	h	h	PROPN
ejpam-4746	169	12	m	m	PROPN
ejpam-4746	169	13	khudhur	khudhur	PROPN
ejpam-4746	169	14	,	,	PUNCT
ejpam-4746	169	15	and	and	CCONJ
ejpam-4746	169	16	m	m	PROPN
ejpam-4746	169	17	a	a	DET
ejpam-4746	169	18	khaleel	khaleel	NOUN
ejpam-4746	169	19	.	.	PUNCT
ejpam-4746	170	1	modified	modify	VERB
ejpam-4746	170	2	new	new	ADJ
ejpam-4746	170	3	conjugate	conjugate	ADJ
ejpam-4746	170	4	gradient	gradient	NOUN
ejpam-4746	170	5	method	method	NOUN
ejpam-4746	170	6	for	for	ADP
ejpam-4746	170	7	unconstrained	unconstrained	ADJ
ejpam-4746	170	8	optimization	optimization	NOUN
ejpam-4746	170	9	.	.	PUNCT
ejpam-4746	171	1	tikrit	tikrit	PROPN
ejpam-4746	171	2	journal	journal	NOUN
ejpam-4746	171	3	of	of	ADP
ejpam-4746	171	4	pure	pure	ADJ
ejpam-4746	171	5	science	science	NOUN
ejpam-4746	171	6	,	,	PUNCT
ejpam-4746	171	7	24:86–90	24:86–90	NUM
ejpam-4746	171	8	,	,	PUNCT
ejpam-4746	171	9	2019	2019	NUM
ejpam-4746	171	10	.	.	PUNCT
ejpam-4746	172	1	[	[	X
ejpam-4746	172	2	6	6	NUM
ejpam-4746	172	3	]	]	PUNCT
ejpam-4746	172	4	n	n	DET
ejpam-4746	172	5	andrei	andrei	NOUN
ejpam-4746	172	6	.	.	PUNCT
ejpam-4746	173	1	an	an	DET
ejpam-4746	173	2	unconstrained	unconstrained	ADJ
ejpam-4746	173	3	optimization	optimization	NOUN
ejpam-4746	173	4	test	test	NOUN
ejpam-4746	173	5	functions	function	NOUN
ejpam-4746	173	6	collection	collection	NOUN
ejpam-4746	173	7	.	.	PUNCT
ejpam-4746	174	1	adv	adv	PROPN
ejpam-4746	174	2	.	.	PUNCT
ejpam-4746	174	3	model	model	PROPN
ejpam-4746	174	4	.	.	PUNCT
ejpam-4746	175	1	optim	optim	ADJ
ejpam-4746	175	2	,	,	PUNCT
ejpam-4746	175	3	10:147–161	10:147–161	NUM
ejpam-4746	175	4	,	,	PUNCT
ejpam-4746	175	5	2008	2008	NUM
ejpam-4746	175	6	.	.	PUNCT
ejpam-4746	176	1	[	[	X
ejpam-4746	176	2	7	7	X
ejpam-4746	176	3	]	]	X
ejpam-4746	176	4	y	y	PROPN
ejpam-4746	176	5	dai	dai	PROPN
ejpam-4746	176	6	and	and	CCONJ
ejpam-4746	176	7	l	l	PROPN
ejpam-4746	176	8	liao	liao	PROPN
ejpam-4746	176	9	.	.	PUNCT
ejpam-4746	177	1	new	new	ADJ
ejpam-4746	177	2	conjugacy	conjugacy	ADJ
ejpam-4746	177	3	conditions	condition	NOUN
ejpam-4746	177	4	and	and	CCONJ
ejpam-4746	177	5	related	relate	VERB
ejpam-4746	177	6	non	non	ADJ
ejpam-4746	177	7	-	-	ADJ
ejpam-4746	177	8	linear	linear	ADJ
ejpam-4746	177	9	cg	cg	NOUN
ejpam-4746	177	10	methods	method	NOUN
ejpam-4746	177	11	’	'	PUNCT
ejpam-4746	177	12	appl	appl	PROPN
ejpam-4746	177	13	.	.	PUNCT
ejpam-4746	178	1	math	math	PROPN
ejpam-4746	178	2	optim	optim	PROPN
ejpam-4746	178	3	.	.	PUNCT
ejpam-4746	178	4	,(43	,(43	PUNCT
ejpam-4746	178	5	)	)	PUNCT
ejpam-4746	178	6	.	.	PUNCT
ejpam-4746	179	1	spring	spring	NOUN
ejpam-4746	179	2	-	-	PUNCT
ejpam-4746	179	3	verlag	verlag	PROPN
ejpam-4746	179	4	,	,	PUNCT
ejpam-4746	179	5	new	new	PROPN
ejpam-4746	179	6	york	york	PROPN
ejpam-4746	179	7	,	,	PUNCT
ejpam-4746	179	8	2001	2001	NUM
ejpam-4746	179	9	.	.	PUNCT
ejpam-4746	180	1	[	[	X
ejpam-4746	180	2	8	8	NUM
ejpam-4746	180	3	]	]	X
ejpam-4746	180	4	y	y	PROPN
ejpam-4746	180	5	h	h	PROPN
ejpam-4746	180	6	dai	dai	PROPN
ejpam-4746	180	7	and	and	CCONJ
ejpam-4746	180	8	y	y	PROPN
ejpam-4746	180	9	yuan	yuan	PROPN
ejpam-4746	180	10	.	.	PUNCT
ejpam-4746	181	1	a	a	DET
ejpam-4746	181	2	nonlinear	nonlinear	ADJ
ejpam-4746	181	3	conjugate	conjugate	ADJ
ejpam-4746	181	4	gradient	gradient	NOUN
ejpam-4746	181	5	method	method	NOUN
ejpam-4746	181	6	with	with	ADP
ejpam-4746	181	7	a	a	DET
ejpam-4746	181	8	strong	strong	ADJ
ejpam-4746	181	9	global	global	ADJ
ejpam-4746	181	10	convergence	convergence	NOUN
ejpam-4746	181	11	property	property	NOUN
ejpam-4746	181	12	.	.	PUNCT
ejpam-4746	182	1	siam	siam	PROPN
ejpam-4746	182	2	journal	journal	PROPN
ejpam-4746	182	3	on	on	ADP
ejpam-4746	182	4	optimization	optimization	NOUN
ejpam-4746	182	5	,	,	PUNCT
ejpam-4746	182	6	10:177–182	10:177–182	PROPN
ejpam-4746	182	7	,	,	PUNCT
ejpam-4746	182	8	1999	1999	NUM
ejpam-4746	182	9	.	.	PUNCT
ejpam-4746	183	1	[	[	X
ejpam-4746	183	2	9	9	NUM
ejpam-4746	183	3	]	]	X
ejpam-4746	183	4	r	r	NOUN
ejpam-4746	183	5	fletcher	fletcher	NOUN
ejpam-4746	183	6	.	.	PUNCT
ejpam-4746	184	1	practical	practical	ADJ
ejpam-4746	184	2	methods	method	NOUN
ejpam-4746	184	3	of	of	ADP
ejpam-4746	184	4	optimization	optimization	NOUN
ejpam-4746	184	5	.	.	PUNCT
ejpam-4746	185	1	john	john	PROPN
ejpam-4746	185	2	wiley	wiley	PROPN
ejpam-4746	185	3	&	&	CCONJ
ejpam-4746	185	4	sons	son	NOUN
ejpam-4746	185	5	,	,	PUNCT
ejpam-4746	185	6	2013	2013	NUM
ejpam-4746	185	7	.	.	PUNCT
ejpam-4746	186	1	[	[	X
ejpam-4746	186	2	10	10	NUM
ejpam-4746	186	3	]	]	X
ejpam-4746	186	4	r	r	NOUN
ejpam-4746	186	5	fletcher	fletcher	NOUN
ejpam-4746	186	6	and	and	CCONJ
ejpam-4746	186	7	c	c	PROPN
ejpam-4746	186	8	m	m	PROPN
ejpam-4746	186	9	reeves	reeves	PROPN
ejpam-4746	186	10	.	.	PUNCT
ejpam-4746	187	1	function	function	NOUN
ejpam-4746	187	2	minimization	minimization	NOUN
ejpam-4746	187	3	by	by	ADP
ejpam-4746	187	4	conjugate	conjugate	ADJ
ejpam-4746	187	5	gradients	gradient	NOUN
ejpam-4746	187	6	.	.	PUNCT
ejpam-4746	188	1	the	the	DET
ejpam-4746	188	2	computer	computer	NOUN
ejpam-4746	188	3	journal	journal	NOUN
ejpam-4746	188	4	,	,	PUNCT
ejpam-4746	188	5	7:149–154	7:149–154	PROPN
ejpam-4746	188	6	,	,	PUNCT
ejpam-4746	188	7	1964	1964	NUM
ejpam-4746	188	8	.	.	PUNCT
ejpam-4746	189	1	[	[	X
ejpam-4746	189	2	11	11	NUM
ejpam-4746	189	3	]	]	X
ejpam-4746	189	4	j	j	PROPN
ejpam-4746	189	5	c	c	PROPN
ejpam-4746	189	6	gilbert	gilbert	PROPN
ejpam-4746	189	7	and	and	CCONJ
ejpam-4746	189	8	j	j	PROPN
ejpam-4746	189	9	nocedal	nocedal	PROPN
ejpam-4746	189	10	.	.	PUNCT
ejpam-4746	190	1	global	global	ADJ
ejpam-4746	190	2	convergence	convergence	NOUN
ejpam-4746	190	3	properties	property	NOUN
ejpam-4746	190	4	of	of	ADP
ejpam-4746	190	5	conjugate	conjugate	ADJ
ejpam-4746	190	6	gradient	gradient	ADJ
ejpam-4746	190	7	methods	method	NOUN
ejpam-4746	190	8	for	for	ADP
ejpam-4746	190	9	optimization	optimization	NOUN
ejpam-4746	190	10	.	.	PUNCT
ejpam-4746	191	1	siam	siam	PROPN
ejpam-4746	191	2	journal	journal	PROPN
ejpam-4746	191	3	on	on	ADP
ejpam-4746	191	4	optimization	optimization	NOUN
ejpam-4746	191	5	,	,	PUNCT
ejpam-4746	191	6	2:21–42	2:21–42	NUM
ejpam-4746	191	7	,	,	PUNCT
ejpam-4746	191	8	1992	1992	NUM
ejpam-4746	191	9	.	.	PUNCT
ejpam-4746	192	1	[	[	X
ejpam-4746	192	2	12	12	NUM
ejpam-4746	192	3	]	]	X
ejpam-4746	192	4	w	w	NOUN
ejpam-4746	192	5	hager	hager	NOUN
ejpam-4746	192	6	and	and	CCONJ
ejpam-4746	192	7	h	h	PROPN
ejpam-4746	192	8	zhang	zhang	PROPN
ejpam-4746	192	9	.	.	PUNCT
ejpam-4746	193	1	a	a	DET
ejpam-4746	193	2	survey	survey	NOUN
ejpam-4746	193	3	of	of	ADP
ejpam-4746	193	4	nonlinear	nonlinear	ADJ
ejpam-4746	193	5	conjugate	conjugate	ADJ
ejpam-4746	193	6	gradient	gradient	ADJ
ejpam-4746	193	7	methods	method	NOUN
ejpam-4746	193	8	.	.	PUNCT
ejpam-4746	194	1	pacific	pacific	PROPN
ejpam-4746	194	2	journal	journal	PROPN
ejpam-4746	194	3	of	of	ADP
ejpam-4746	194	4	optimization	optimization	NOUN
ejpam-4746	194	5	,	,	PUNCT
ejpam-4746	194	6	2:35–58	2:35–58	NUM
ejpam-4746	194	7	,	,	PUNCT
ejpam-4746	194	8	2006	2006	NUM
ejpam-4746	194	9	.	.	PUNCT
ejpam-4746	195	1	references	reference	NOUN
ejpam-4746	195	2	1067	1067	NUM
ejpam-4746	196	1	[	[	X
ejpam-4746	196	2	13	13	NUM
ejpam-4746	196	3	]	]	SYM
ejpam-4746	196	4	m	m	VERB
ejpam-4746	196	5	r	r	NOUN
ejpam-4746	196	6	hestenes	hestene	NOUN
ejpam-4746	196	7	and	and	CCONJ
ejpam-4746	196	8	e	e	NOUN
ejpam-4746	196	9	stiefel	stiefel	NOUN
ejpam-4746	196	10	.	.	PUNCT
ejpam-4746	197	1	methods	method	NOUN
ejpam-4746	197	2	of	of	ADP
ejpam-4746	197	3	conjugate	conjugate	ADJ
ejpam-4746	197	4	gradients	gradient	NOUN
ejpam-4746	197	5	for	for	ADP
ejpam-4746	197	6	solving	solve	VERB
ejpam-4746	197	7	linear	linear	NOUN
ejpam-4746	197	8	systems	system	NOUN
ejpam-4746	197	9	.	.	PUNCT
ejpam-4746	198	1	journal	journal	PROPN
ejpam-4746	198	2	of	of	ADP
ejpam-4746	198	3	research	research	NOUN
ejpam-4746	198	4	of	of	ADP
ejpam-4746	198	5	the	the	DET
ejpam-4746	198	6	national	national	PROPN
ejpam-4746	198	7	bureau	bureau	PROPN
ejpam-4746	198	8	of	of	ADP
ejpam-4746	198	9	standards	standard	NOUN
ejpam-4746	198	10	,	,	PUNCT
ejpam-4746	198	11	49:409–436	49:409–436	PROPN
ejpam-4746	198	12	,	,	PUNCT
ejpam-4746	198	13	1952	1952	NUM
ejpam-4746	198	14	.	.	PUNCT
ejpam-4746	199	1	[	[	X
ejpam-4746	199	2	14	14	NUM
ejpam-4746	199	3	]	]	X
ejpam-4746	199	4	h	h	PROPN
ejpam-4746	199	5	m	m	PROPN
ejpam-4746	199	6	khudhur	khudhur	PROPN
ejpam-4746	199	7	and	and	CCONJ
ejpam-4746	199	8	k	k	PROPN
ejpam-4746	199	9	k	k	PROPN
ejpam-4746	199	10	abbo	abbo	PROPN
ejpam-4746	199	11	.	.	PUNCT
ejpam-4746	200	1	a	a	DET
ejpam-4746	200	2	new	new	ADJ
ejpam-4746	200	3	conjugate	conjugate	ADJ
ejpam-4746	200	4	gradient	gradient	NOUN
ejpam-4746	200	5	method	method	NOUN
ejpam-4746	200	6	for	for	ADP
ejpam-4746	200	7	learning	learn	VERB
ejpam-4746	200	8	fuzzy	fuzzy	ADJ
ejpam-4746	200	9	neural	neural	ADJ
ejpam-4746	200	10	networks	network	NOUN
ejpam-4746	200	11	.	.	PUNCT
ejpam-4746	201	1	journal	journal	NOUN
ejpam-4746	201	2	of	of	ADP
ejpam-4746	201	3	multidisciplinary	multidisciplinary	ADJ
ejpam-4746	201	4	modeling	modeling	NOUN
ejpam-4746	201	5	and	and	CCONJ
ejpam-4746	201	6	optimization	optimization	NOUN
ejpam-4746	201	7	,	,	PUNCT
ejpam-4746	201	8	3:57–69	3:57–69	NUM
ejpam-4746	201	9	,	,	PUNCT
ejpam-4746	201	10	2020	2020	NUM
ejpam-4746	201	11	.	.	PUNCT
ejpam-4746	202	1	[	[	X
ejpam-4746	202	2	15	15	NUM
ejpam-4746	202	3	]	]	X
ejpam-4746	202	4	h	h	NOUN
ejpam-4746	202	5	m	m	PROPN
ejpam-4746	202	6	khudhur	khudhur	PROPN
ejpam-4746	202	7	and	and	CCONJ
ejpam-4746	202	8	k	k	PROPN
ejpam-4746	202	9	k	k	PROPN
ejpam-4746	202	10	abbo	abbo	PROPN
ejpam-4746	202	11	.	.	PUNCT
ejpam-4746	203	1	a	a	DET
ejpam-4746	203	2	new	new	ADJ
ejpam-4746	203	3	type	type	NOUN
ejpam-4746	203	4	of	of	ADP
ejpam-4746	203	5	conjugate	conjugate	ADJ
ejpam-4746	203	6	gradient	gradient	NOUN
ejpam-4746	203	7	technique	technique	NOUN
ejpam-4746	203	8	for	for	ADP
ejpam-4746	203	9	solving	solve	VERB
ejpam-4746	203	10	fuzzy	fuzzy	ADJ
ejpam-4746	203	11	nonlinear	nonlinear	ADJ
ejpam-4746	203	12	algebraic	algebraic	ADJ
ejpam-4746	203	13	equations	equation	NOUN
ejpam-4746	203	14	.	.	PUNCT
ejpam-4746	204	1	in	in	ADP
ejpam-4746	204	2	journal	journal	PROPN
ejpam-4746	204	3	of	of	ADP
ejpam-4746	204	4	physics	physics	PROPN
ejpam-4746	204	5	:	:	PUNCT
ejpam-4746	204	6	conference	conference	NOUN
ejpam-4746	204	7	series	series	NOUN
ejpam-4746	204	8	,	,	PUNCT
ejpam-4746	204	9	volume	volume	NOUN
ejpam-4746	204	10	1879	1879	NUM
ejpam-4746	204	11	,	,	PUNCT
ejpam-4746	204	12	page	page	NOUN
ejpam-4746	204	13	022111	022111	NUM
ejpam-4746	204	14	,	,	PUNCT
ejpam-4746	204	15	2021	2021	NUM
ejpam-4746	204	16	.	.	PUNCT
ejpam-4746	205	1	[	[	X
ejpam-4746	205	2	16	16	NUM
ejpam-4746	205	3	]	]	X
ejpam-4746	205	4	y	y	PROPN
ejpam-4746	205	5	a	a	DET
ejpam-4746	205	6	laylani	laylani	NOUN
ejpam-4746	205	7	,	,	PUNCT
ejpam-4746	205	8	b	b	X
ejpam-4746	205	9	a	a	DET
ejpam-4746	205	10	hassan	hassan	PROPN
ejpam-4746	205	11	,	,	PUNCT
ejpam-4746	205	12	and	and	CCONJ
ejpam-4746	205	13	h	h	PROPN
ejpam-4746	205	14	m	m	PROPN
ejpam-4746	205	15	khudhur	khudhur	PROPN
ejpam-4746	205	16	.	.	PUNCT
ejpam-4746	206	1	a	a	DET
ejpam-4746	206	2	new	new	ADJ
ejpam-4746	206	3	class	class	NOUN
ejpam-4746	206	4	of	of	ADP
ejpam-4746	206	5	optimization	optimization	NOUN
ejpam-4746	206	6	methods	method	NOUN
ejpam-4746	206	7	based	base	VERB
ejpam-4746	206	8	on	on	ADP
ejpam-4746	206	9	coefficient	coefficient	NOUN
ejpam-4746	206	10	conjugate	conjugate	ADJ
ejpam-4746	206	11	gradient	gradient	NOUN
ejpam-4746	206	12	.	.	PUNCT
ejpam-4746	207	1	european	european	ADJ
ejpam-4746	207	2	journal	journal	PROPN
ejpam-4746	207	3	of	of	ADP
ejpam-4746	207	4	pure	pure	ADJ
ejpam-4746	207	5	and	and	CCONJ
ejpam-4746	207	6	applied	applied	ADJ
ejpam-4746	207	7	mathematics	mathematic	NOUN
ejpam-4746	207	8	,	,	PUNCT
ejpam-4746	207	9	15:1908–1916	15:1908–1916	NUM
ejpam-4746	207	10	,	,	PUNCT
ejpam-4746	207	11	2022	2022	NUM
ejpam-4746	207	12	.	.	PUNCT
ejpam-4746	208	1	[	[	X
ejpam-4746	208	2	17	17	NUM
ejpam-4746	208	3	]	]	X
ejpam-4746	208	4	j	j	PROPN
ejpam-4746	208	5	liu	liu	PROPN
ejpam-4746	208	6	and	and	CCONJ
ejpam-4746	208	7	s	s	PROPN
ejpam-4746	208	8	wang	wang	PROPN
ejpam-4746	208	9	.	.	PUNCT
ejpam-4746	209	1	modified	modify	VERB
ejpam-4746	209	2	nonlinear	nonlinear	ADJ
ejpam-4746	209	3	conjugate	conjugate	ADJ
ejpam-4746	209	4	gradient	gradient	NOUN
ejpam-4746	209	5	method	method	NOUN
ejpam-4746	209	6	with	with	ADP
ejpam-4746	209	7	sufficient	sufficient	ADJ
ejpam-4746	209	8	descent	descent	NOUN
ejpam-4746	209	9	condition	condition	NOUN
ejpam-4746	209	10	for	for	ADP
ejpam-4746	209	11	unconstrained	unconstrained	ADJ
ejpam-4746	209	12	optimization	optimization	NOUN
ejpam-4746	209	13	.	.	PUNCT
ejpam-4746	210	1	journal	journal	PROPN
ejpam-4746	210	2	of	of	ADP
ejpam-4746	210	3	inequalities	inequality	NOUN
ejpam-4746	210	4	and	and	CCONJ
ejpam-4746	210	5	applications	application	NOUN
ejpam-4746	210	6	,	,	PUNCT
ejpam-4746	210	7	2011:1–12	2011:1–12	NUM
ejpam-4746	210	8	,	,	PUNCT
ejpam-4746	210	9	2011	2011	NUM
ejpam-4746	210	10	.	.	PUNCT
ejpam-4746	211	1	[	[	X
ejpam-4746	211	2	18	18	NUM
ejpam-4746	211	3	]	]	X
ejpam-4746	211	4	j	j	PROPN
ejpam-4746	211	5	nocedal	nocedal	PROPN
ejpam-4746	211	6	and	and	CCONJ
ejpam-4746	211	7	s	s	PROPN
ejpam-4746	211	8	j	j	PROPN
ejpam-4746	211	9	wright	wright	PROPN
ejpam-4746	211	10	.	.	PUNCT
ejpam-4746	212	1	numerical	numerical	PROPN
ejpam-4746	212	2	optimization	optimization	PROPN
ejpam-4746	212	3	.	.	PUNCT
ejpam-4746	213	1	2006	2006	NUM
ejpam-4746	213	2	.	.	PUNCT
ejpam-4746	214	1	[	[	X
ejpam-4746	214	2	19	19	NUM
ejpam-4746	214	3	]	]	PUNCT
ejpam-4746	214	4	e	e	NOUN
ejpam-4746	214	5	polak	polak	NOUN
ejpam-4746	214	6	and	and	CCONJ
ejpam-4746	214	7	g	g	PROPN
ejpam-4746	214	8	ribiere	ribiere	NOUN
ejpam-4746	214	9	.	.	PUNCT
ejpam-4746	215	1	note	note	VERB
ejpam-4746	215	2	sur	sur	PROPN
ejpam-4746	215	3	la	la	X
ejpam-4746	215	4	convergence	convergence	NOUN
ejpam-4746	215	5	de	de	X
ejpam-4746	215	6	méthodes	méthodes	X
ejpam-4746	215	7	de	de	PROPN
ejpam-4746	215	8	directions	direction	NOUN
ejpam-4746	215	9	conjuguées	conjuguées	PROPN
ejpam-4746	215	10	.	.	PUNCT
ejpam-4746	216	1	revue	revue	PROPN
ejpam-4746	216	2	française	française	PROPN
ejpam-4746	216	3	d’informatique	d’informatique	NOUN
ejpam-4746	216	4	et	et	X
ejpam-4746	216	5	de	de	X
ejpam-4746	216	6	recherche	recherche	X
ejpam-4746	216	7	opérationnelle	opérationnelle	PROPN
ejpam-4746	216	8	.	.	PUNCT
ejpam-4746	217	1	série	série	PROPN
ejpam-4746	217	2	rouge	rouge	PROPN
ejpam-4746	217	3	,	,	PUNCT
ejpam-4746	217	4	3:35–43	3:35–43	NUM
ejpam-4746	217	5	,	,	PUNCT
ejpam-4746	217	6	1969	1969	NUM
ejpam-4746	217	7	.	.	PUNCT
ejpam-4746	218	1	[	[	X
ejpam-4746	218	2	20	20	NUM
ejpam-4746	218	3	]	]	PUNCT
ejpam-4746	218	4	m	m	VERB
ejpam-4746	218	5	powell	powell	NOUN
ejpam-4746	218	6	.	.	PUNCT
ejpam-4746	219	1	a	a	DET
ejpam-4746	219	2	survey	survey	NOUN
ejpam-4746	219	3	of	of	ADP
ejpam-4746	219	4	numerical	numerical	ADJ
ejpam-4746	219	5	methods	method	NOUN
ejpam-4746	219	6	for	for	ADP
ejpam-4746	219	7	unconstrained	unconstrained	ADJ
ejpam-4746	219	8	optimization	optimization	NOUN
ejpam-4746	219	9	.	.	PUNCT
ejpam-4746	220	1	siam	siam	PROPN
ejpam-4746	220	2	review	review	PROPN
ejpam-4746	220	3	,	,	PUNCT
ejpam-4746	220	4	12:79–97	12:79–97	NUM
ejpam-4746	220	5	,	,	PUNCT
ejpam-4746	220	6	1970	1970	NUM
ejpam-4746	220	7	.	.	PUNCT
ejpam-4746	221	1	[	[	X
ejpam-4746	221	2	21	21	NUM
ejpam-4746	221	3	]	]	X
ejpam-4746	221	4	a	a	DET
ejpam-4746	221	5	sahiner	sahiner	NOUN
ejpam-4746	221	6	,	,	PUNCT
ejpam-4746	221	7	i	i	PRON
ejpam-4746	221	8	a	a	DET
ejpam-4746	221	9	m	m	VERB
ejpam-4746	221	10	abdulhamid	abdulhamid	NOUN
ejpam-4746	221	11	,	,	PUNCT
ejpam-4746	221	12	and	and	CCONJ
ejpam-4746	221	13	s	s	VERB
ejpam-4746	221	14	a	a	DET
ejpam-4746	221	15	ibrahem	ibrahem	NOUN
ejpam-4746	221	16	.	.	PUNCT
ejpam-4746	222	1	a	a	DET
ejpam-4746	222	2	new	new	ADJ
ejpam-4746	222	3	filled	fill	VERB
ejpam-4746	222	4	function	function	NOUN
ejpam-4746	222	5	method	method	NOUN
ejpam-4746	222	6	with	with	ADP
ejpam-4746	222	7	two	two	NUM
ejpam-4746	222	8	parameters	parameter	NOUN
ejpam-4746	222	9	in	in	ADP
ejpam-4746	222	10	a	a	DET
ejpam-4746	222	11	directional	directional	ADJ
ejpam-4746	222	12	search	search	NOUN
ejpam-4746	222	13	.	.	PUNCT
ejpam-4746	223	1	journal	journal	NOUN
ejpam-4746	223	2	of	of	ADP
ejpam-4746	223	3	multidisciplinary	multidisciplinary	ADJ
ejpam-4746	223	4	modeling	modeling	NOUN
ejpam-4746	223	5	and	and	CCONJ
ejpam-4746	223	6	optimization	optimization	NOUN
ejpam-4746	223	7	,	,	PUNCT
ejpam-4746	223	8	2:34–42	2:34–42	NUM
ejpam-4746	223	9	,	,	PUNCT
ejpam-4746	223	10	2019	2019	NUM
ejpam-4746	223	11	.	.	PUNCT
ejpam-4746	224	1	[	[	X
ejpam-4746	224	2	22	22	NUM
ejpam-4746	224	3	]	]	PUNCT
ejpam-4746	224	4	a	a	DET
ejpam-4746	224	5	sahiner	sahiner	NOUN
ejpam-4746	224	6	and	and	CCONJ
ejpam-4746	224	7	s	s	VERB
ejpam-4746	224	8	a	a	DET
ejpam-4746	224	9	ibrahem	ibrahem	NOUN
ejpam-4746	224	10	.	.	PUNCT
ejpam-4746	225	1	a	a	DET
ejpam-4746	225	2	new	new	ADJ
ejpam-4746	225	3	global	global	ADJ
ejpam-4746	225	4	optimization	optimization	NOUN
ejpam-4746	225	5	technique	technique	NOUN
ejpam-4746	225	6	by	by	ADP
ejpam-4746	225	7	auxiliary	auxiliary	ADJ
ejpam-4746	225	8	function	function	NOUN
ejpam-4746	225	9	method	method	NOUN
ejpam-4746	225	10	in	in	ADP
ejpam-4746	225	11	a	a	DET
ejpam-4746	225	12	directional	directional	ADJ
ejpam-4746	225	13	search	search	NOUN
ejpam-4746	225	14	.	.	PUNCT
ejpam-4746	226	1	optimization	optimization	NOUN
ejpam-4746	226	2	letters	letter	NOUN
ejpam-4746	226	3	,	,	PUNCT
ejpam-4746	226	4	13:309–323	13:309–323	PROPN
ejpam-4746	226	5	,	,	PUNCT
ejpam-4746	226	6	2019	2019	NUM
ejpam-4746	226	7	.	.	PUNCT
ejpam-4746	227	1	[	[	X
ejpam-4746	227	2	23	23	NUM
ejpam-4746	227	3	]	]	X
ejpam-4746	227	4	p	p	X
ejpam-4746	227	5	wolfe	wolfe	PROPN
ejpam-4746	227	6	.	.	PUNCT
ejpam-4746	227	7	convergence	convergence	NOUN
ejpam-4746	227	8	conditions	condition	NOUN
ejpam-4746	227	9	for	for	ADP
ejpam-4746	227	10	ascent	ascent	ADJ
ejpam-4746	227	11	methods	method	NOUN
ejpam-4746	227	12	.	.	PUNCT
ejpam-4746	228	1	ii	ii	PROPN
ejpam-4746	228	2	:	:	PUNCT
ejpam-4746	228	3	some	some	DET
ejpam-4746	228	4	corrections	correction	NOUN
ejpam-4746	228	5	.	.	PUNCT
ejpam-4746	229	1	siam	siam	PROPN
ejpam-4746	229	2	review	review	PROPN
ejpam-4746	229	3	,	,	PUNCT
ejpam-4746	229	4	13:185–188	13:185–188	NUM
ejpam-4746	229	5	,	,	PUNCT
ejpam-4746	229	6	1971	1971	NUM
ejpam-4746	229	7	.	.	PUNCT