id	sid	tid	token	lemma	pos
ijassa-1406	1	1	adv	adv	PROPN
ijassa-1406	1	2	syst	syst	PROPN
ijassa-1406	1	3	sci	sci	PROPN
ijassa-1406	1	4	appl	appl	PROPN
ijassa-1406	1	5	2023	2023	NUM
ijassa-1406	1	6	;	;	PUNCT
ijassa-1406	1	7	03:16–26	03:16–26	NOUN
ijassa-1406	1	8	published	publish	VERB
ijassa-1406	1	9	online	online	ADV
ijassa-1406	1	10	at	at	ADP
ijassa-1406	1	11	https://ijassa.ipu.ru	https://ijassa.ipu.ru	ADV
ijassa-1406	1	12	.	.	PUNCT
ijassa-1406	2	1	newton	newton	PROPN
ijassa-1406	2	2	method	method	PROPN
ijassa-1406	2	3	vs.	vs.	ADP
ijassa-1406	2	4	semismooth	semismooth	NOUN
ijassa-1406	2	5	newton	newton	PROPN
ijassa-1406	2	6	method	method	NOUN
ijassa-1406	2	7	for	for	ADP
ijassa-1406	2	8	singular	singular	ADJ
ijassa-1406	2	9	solutions	solution	NOUN
ijassa-1406	2	10	of	of	ADP
ijassa-1406	2	11	nonlinear	nonlinear	ADJ
ijassa-1406	2	12	complementarity	complementarity	NOUN
ijassa-1406	2	13	problems	problem	NOUN
ijassa-1406	2	14	alexey	alexey	PROPN
ijassa-1406	2	15	izmailov1	izmailov1	PROPN
ijassa-1406	2	16	*	*	PROPN
ijassa-1406	2	17	,	,	PUNCT
ijassa-1406	2	18	evgeniy	evgeniy	ADJ
ijassa-1406	2	19	uskov2	uskov2	PROPN
ijassa-1406	2	20	,	,	PUNCT
ijassa-1406	2	21	yan	yan	PROPN
ijassa-1406	2	22	zhibai1	zhibai1	PROPN
ijassa-1406	3	1	1lomonosov	1lomonosov	NUM
ijassa-1406	3	2	moscow	moscow	PROPN
ijassa-1406	3	3	state	state	PROPN
ijassa-1406	3	4	university	university	PROPN
ijassa-1406	3	5	,	,	PUNCT
ijassa-1406	3	6	moscow	moscow	PROPN
ijassa-1406	3	7	,	,	PUNCT
ijassa-1406	3	8	russia	russia	PROPN
ijassa-1406	3	9	2derzhavin	2derzhavin	NUM
ijassa-1406	3	10	tambov	tambov	PROPN
ijassa-1406	3	11	state	state	PROPN
ijassa-1406	3	12	university	university	PROPN
ijassa-1406	3	13	,	,	PUNCT
ijassa-1406	3	14	tambov	tambov	PROPN
ijassa-1406	3	15	,	,	PUNCT
ijassa-1406	3	16	russia	russia	PROPN
ijassa-1406	3	17	abstract	abstract	NOUN
ijassa-1406	3	18	:	:	PUNCT
ijassa-1406	3	19	among	among	ADP
ijassa-1406	3	20	the	the	DET
ijassa-1406	3	21	most	most	ADV
ijassa-1406	3	22	successful	successful	ADJ
ijassa-1406	3	23	techniques	technique	NOUN
ijassa-1406	3	24	for	for	ADP
ijassa-1406	3	25	solving	solve	VERB
ijassa-1406	3	26	nonlinear	nonlinear	ADJ
ijassa-1406	3	27	complementarity	complementarity	NOUN
ijassa-1406	3	28	problems	problem	NOUN
ijassa-1406	3	29	is	be	AUX
ijassa-1406	3	30	the	the	DET
ijassa-1406	3	31	one	one	NUM
ijassa-1406	3	32	consisting	consist	VERB
ijassa-1406	3	33	of	of	ADP
ijassa-1406	3	34	reformulation	reformulation	NOUN
ijassa-1406	3	35	of	of	ADP
ijassa-1406	3	36	the	the	DET
ijassa-1406	3	37	problem	problem	NOUN
ijassa-1406	3	38	in	in	ADP
ijassa-1406	3	39	question	question	NOUN
ijassa-1406	3	40	as	as	ADP
ijassa-1406	3	41	a	a	DET
ijassa-1406	3	42	system	system	NOUN
ijassa-1406	3	43	of	of	ADP
ijassa-1406	3	44	nonlinear	nonlinear	ADJ
ijassa-1406	3	45	equations	equation	NOUN
ijassa-1406	3	46	,	,	PUNCT
ijassa-1406	3	47	by	by	ADP
ijassa-1406	3	48	means	mean	NOUN
ijassa-1406	3	49	of	of	ADP
ijassa-1406	3	50	the	the	DET
ijassa-1406	3	51	so	so	ADV
ijassa-1406	3	52	-	-	PUNCT
ijassa-1406	3	53	called	call	VERB
ijassa-1406	3	54	complementarity	complementarity	NOUN
ijassa-1406	3	55	functions	function	NOUN
ijassa-1406	3	56	.	.	PUNCT
ijassa-1406	4	1	different	different	ADJ
ijassa-1406	4	2	complementarity	complementarity	NOUN
ijassa-1406	4	3	functions	function	NOUN
ijassa-1406	4	4	lead	lead	VERB
ijassa-1406	4	5	to	to	ADP
ijassa-1406	4	6	nonlinear	nonlinear	ADJ
ijassa-1406	4	7	systems	system	NOUN
ijassa-1406	4	8	with	with	ADP
ijassa-1406	4	9	different	different	ADJ
ijassa-1406	4	10	smoothness	smoothness	NOUN
ijassa-1406	4	11	and	and	CCONJ
ijassa-1406	4	12	regularity	regularity	NOUN
ijassa-1406	4	13	properties	property	NOUN
ijassa-1406	4	14	,	,	PUNCT
ijassa-1406	4	15	thus	thus	ADV
ijassa-1406	4	16	allowing	allow	VERB
ijassa-1406	4	17	for	for	ADP
ijassa-1406	4	18	application	application	NOUN
ijassa-1406	4	19	of	of	ADP
ijassa-1406	4	20	different	different	ADJ
ijassa-1406	4	21	classed	class	VERB
ijassa-1406	4	22	of	of	ADP
ijassa-1406	4	23	numerical	numerical	ADJ
ijassa-1406	4	24	methods	method	NOUN
ijassa-1406	4	25	.	.	PUNCT
ijassa-1406	5	1	in	in	ADP
ijassa-1406	5	2	this	this	DET
ijassa-1406	5	3	paper	paper	NOUN
ijassa-1406	5	4	we	we	PRON
ijassa-1406	5	5	compare	compare	VERB
ijassa-1406	5	6	the	the	DET
ijassa-1406	5	7	newton	newton	PROPN
ijassa-1406	5	8	method	method	NOUN
ijassa-1406	5	9	for	for	ADP
ijassa-1406	5	10	the	the	DET
ijassa-1406	5	11	smooth	smooth	ADJ
ijassa-1406	5	12	reformulation	reformulation	NOUN
ijassa-1406	5	13	with	with	ADP
ijassa-1406	5	14	the	the	DET
ijassa-1406	5	15	semismooth	semismooth	NOUN
ijassa-1406	5	16	newton	newton	PROPN
ijassa-1406	5	17	method	method	NOUN
ijassa-1406	5	18	for	for	ADP
ijassa-1406	5	19	the	the	DET
ijassa-1406	5	20	reformulation	reformulation	NOUN
ijassa-1406	5	21	relying	rely	VERB
ijassa-1406	5	22	on	on	ADP
ijassa-1406	5	23	the	the	DET
ijassa-1406	5	24	nonsmooth	nonsmooth	NOUN
ijassa-1406	5	25	fischer	fischer	NOUN
ijassa-1406	5	26	–	–	PUNCT
ijassa-1406	5	27	burmeister	burmeister	NOUN
ijassa-1406	5	28	complementarity	complementarity	NOUN
ijassa-1406	5	29	function	function	NOUN
ijassa-1406	5	30	,	,	PUNCT
ijassa-1406	5	31	with	with	ADP
ijassa-1406	5	32	a	a	DET
ijassa-1406	5	33	special	special	ADJ
ijassa-1406	5	34	emphasis	emphasis	NOUN
ijassa-1406	5	35	on	on	ADP
ijassa-1406	5	36	the	the	DET
ijassa-1406	5	37	cases	case	NOUN
ijassa-1406	5	38	when	when	SCONJ
ijassa-1406	5	39	the	the	DET
ijassa-1406	5	40	solution	solution	NOUN
ijassa-1406	5	41	in	in	ADP
ijassa-1406	5	42	question	question	NOUN
ijassa-1406	5	43	violates	violate	VERB
ijassa-1406	5	44	the	the	DET
ijassa-1406	5	45	strict	strict	ADJ
ijassa-1406	5	46	complementarity	complementarity	NOUN
ijassa-1406	5	47	condition	condition	NOUN
ijassa-1406	5	48	.	.	PUNCT
ijassa-1406	6	1	keywords	keyword	NOUN
ijassa-1406	6	2	:	:	PUNCT
ijassa-1406	6	3	nonlinear	nonlinear	ADJ
ijassa-1406	6	4	complementarity	complementarity	NOUN
ijassa-1406	6	5	problem	problem	NOUN
ijassa-1406	6	6	,	,	PUNCT
ijassa-1406	6	7	complementarity	complementarity	NOUN
ijassa-1406	6	8	function	function	NOUN
ijassa-1406	6	9	,	,	PUNCT
ijassa-1406	6	10	strict	strict	ADJ
ijassa-1406	6	11	complementarity	complementarity	NOUN
ijassa-1406	6	12	,	,	PUNCT
ijassa-1406	6	13	singular	singular	ADJ
ijassa-1406	6	14	solution	solution	NOUN
ijassa-1406	6	15	,	,	PUNCT
ijassa-1406	6	16	newton	newton	PROPN
ijassa-1406	6	17	method	method	PROPN
ijassa-1406	6	18	,	,	PUNCT
ijassa-1406	6	19	semismooth	semismooth	NOUN
ijassa-1406	6	20	newton	newton	PROPN
ijassa-1406	6	21	method	method	PROPN
ijassa-1406	6	22	,	,	PUNCT
ijassa-1406	6	23	extrapolation	extrapolation	NOUN
ijassa-1406	6	24	1	1	NUM
ijassa-1406	6	25	.	.	PUNCT
ijassa-1406	7	1	introduction	introduction	NOUN
ijassa-1406	7	2	we	we	PRON
ijassa-1406	7	3	consider	consider	VERB
ijassa-1406	7	4	the	the	DET
ijassa-1406	7	5	nonlinear	nonlinear	ADJ
ijassa-1406	7	6	complementarity	complementarity	NOUN
ijassa-1406	7	7	problem	problem	NOUN
ijassa-1406	7	8	(	(	PUNCT
ijassa-1406	7	9	ncp	ncp	NOUN
ijassa-1406	7	10	)	)	PUNCT
ijassa-1406	7	11	u	u	NOUN
ijassa-1406	7	12	≥	≥	NOUN
ijassa-1406	7	13	0	0	NUM
ijassa-1406	7	14	,	,	PUNCT
ijassa-1406	7	15	f	f	PROPN
ijassa-1406	7	16	(	(	PUNCT
ijassa-1406	7	17	u	u	NOUN
ijassa-1406	7	18	)	)	PUNCT
ijassa-1406	7	19	≥	≥	NOUN
ijassa-1406	7	20	0	0	NUM
ijassa-1406	7	21	,	,	PUNCT
ijassa-1406	7	22	⟨u	⟨u	NOUN
ijassa-1406	7	23	,	,	PUNCT
ijassa-1406	7	24	f	f	PROPN
ijassa-1406	7	25	(	(	PUNCT
ijassa-1406	7	26	u)⟩	u)⟩	PROPN
ijassa-1406	7	27	=	=	SYM
ijassa-1406	7	28	0	0	NUM
ijassa-1406	7	29	,	,	PUNCT
ijassa-1406	7	30	(	(	PUNCT
ijassa-1406	7	31	1.1	1.1	NUM
ijassa-1406	7	32	)	)	PUNCT
ijassa-1406	7	33	where	where	SCONJ
ijassa-1406	7	34	f	f	NOUN
ijassa-1406	7	35	:	:	PUNCT
ijassa-1406	7	36	rp	rp	NOUN
ijassa-1406	7	37	→	→	SYM
ijassa-1406	7	38	rp	rp	NOUN
ijassa-1406	7	39	is	be	AUX
ijassa-1406	7	40	a	a	DET
ijassa-1406	7	41	given	give	VERB
ijassa-1406	7	42	smooth	smooth	ADJ
ijassa-1406	7	43	mapping	mapping	NOUN
ijassa-1406	7	44	.	.	PUNCT
ijassa-1406	8	1	here	here	ADV
ijassa-1406	8	2	and	and	CCONJ
ijassa-1406	8	3	throughout	throughout	ADP
ijassa-1406	8	4	the	the	DET
ijassa-1406	8	5	paper	paper	NOUN
ijassa-1406	8	6	,	,	PUNCT
ijassa-1406	8	7	⟨	⟨	NOUN
ijassa-1406	8	8	·	·	SYM
ijassa-1406	8	9	,	,	PUNCT
ijassa-1406	8	10	·	·	PUNCT
ijassa-1406	8	11	⟩	⟩	NOUN
ijassa-1406	8	12	stands	stand	VERB
ijassa-1406	8	13	for	for	ADP
ijassa-1406	8	14	the	the	DET
ijassa-1406	8	15	euclidian	euclidian	ADJ
ijassa-1406	8	16	inner	inner	ADJ
ijassa-1406	8	17	product	product	NOUN
ijassa-1406	8	18	.	.	PUNCT
ijassa-1406	9	1	accordingly	accordingly	ADV
ijassa-1406	9	2	,	,	PUNCT
ijassa-1406	9	3	by	by	ADP
ijassa-1406	9	4	∥	∥	X
ijassa-1406	9	5	·	·	PUNCT
ijassa-1406	9	6	∥	∥	NUM
ijassa-1406	9	7	we	we	PRON
ijassa-1406	9	8	will	will	AUX
ijassa-1406	9	9	denote	denote	VERB
ijassa-1406	9	10	the	the	DET
ijassa-1406	9	11	euclidian	euclidian	ADJ
ijassa-1406	9	12	norm	norm	NOUN
ijassa-1406	9	13	.	.	PUNCT
ijassa-1406	10	1	among	among	ADP
ijassa-1406	10	2	the	the	DET
ijassa-1406	10	3	most	most	ADV
ijassa-1406	10	4	successful	successful	ADJ
ijassa-1406	10	5	approaches	approach	NOUN
ijassa-1406	10	6	to	to	ADP
ijassa-1406	10	7	numerical	numerical	ADJ
ijassa-1406	10	8	solution	solution	NOUN
ijassa-1406	10	9	of	of	ADP
ijassa-1406	10	10	ncp	ncp	PROPN
ijassa-1406	10	11	(	(	PUNCT
ijassa-1406	10	12	1.1	1.1	NUM
ijassa-1406	10	13	)	)	PUNCT
ijassa-1406	10	14	relies	rely	VERB
ijassa-1406	10	15	on	on	ADP
ijassa-1406	10	16	a	a	DET
ijassa-1406	10	17	reformulation	reformulation	NOUN
ijassa-1406	10	18	of	of	ADP
ijassa-1406	10	19	this	this	DET
ijassa-1406	10	20	problem	problem	NOUN
ijassa-1406	10	21	as	as	ADP
ijassa-1406	10	22	an	an	DET
ijassa-1406	10	23	equivalent	equivalent	ADJ
ijassa-1406	10	24	system	system	NOUN
ijassa-1406	10	25	of	of	ADP
ijassa-1406	10	26	equations	equation	NOUN
ijassa-1406	10	27	.	.	PUNCT
ijassa-1406	11	1	recall	recall	VERB
ijassa-1406	11	2	that	that	SCONJ
ijassa-1406	11	3	a	a	DET
ijassa-1406	11	4	function	function	NOUN
ijassa-1406	11	5	ψ	ψ	X
ijassa-1406	11	6	:	:	PUNCT
ijassa-1406	11	7	r×	r×	NOUN
ijassa-1406	11	8	r	r	NOUN
ijassa-1406	11	9	→	→	SYM
ijassa-1406	11	10	r	r	NOUN
ijassa-1406	11	11	is	be	AUX
ijassa-1406	11	12	referred	refer	VERB
ijassa-1406	11	13	to	to	ADP
ijassa-1406	11	14	as	as	ADP
ijassa-1406	11	15	a	a	DET
ijassa-1406	11	16	complementarity	complementarity	NOUN
ijassa-1406	11	17	function	function	NOUN
ijassa-1406	11	18	if	if	SCONJ
ijassa-1406	11	19	ψ(a	ψ(a	PROPN
ijassa-1406	11	20	,	,	PUNCT
ijassa-1406	11	21	b	b	NOUN
ijassa-1406	11	22	)	)	PUNCT
ijassa-1406	11	23	=	=	SYM
ijassa-1406	11	24	0	0	NUM
ijassa-1406	11	25	⇔	⇔	PROPN
ijassa-1406	11	26	a	a	DET
ijassa-1406	11	27	≥	≥	NOUN
ijassa-1406	11	28	0	0	NUM
ijassa-1406	11	29	,	,	PUNCT
ijassa-1406	11	30	b	b	PROPN
ijassa-1406	11	31	≥	≥	NOUN
ijassa-1406	11	32	0	0	NUM
ijassa-1406	11	33	,	,	PUNCT
ijassa-1406	11	34	ab	ab	PROPN
ijassa-1406	11	35	=	=	PUNCT
ijassa-1406	11	36	0	0	PROPN
ijassa-1406	11	37	.	.	PUNCT
ijassa-1406	12	1	with	with	ADP
ijassa-1406	12	2	any	any	DET
ijassa-1406	12	3	such	such	ADJ
ijassa-1406	12	4	function	function	NOUN
ijassa-1406	12	5	at	at	ADP
ijassa-1406	12	6	hand	hand	NOUN
ijassa-1406	12	7	,	,	PUNCT
ijassa-1406	12	8	one	one	PRON
ijassa-1406	12	9	can	can	AUX
ijassa-1406	12	10	readily	readily	ADV
ijassa-1406	12	11	observe	observe	VERB
ijassa-1406	12	12	that	that	SCONJ
ijassa-1406	12	13	(	(	PUNCT
ijassa-1406	12	14	1.1	1.1	NUM
ijassa-1406	12	15	)	)	PUNCT
ijassa-1406	12	16	is	be	AUX
ijassa-1406	12	17	equivalent	equivalent	ADJ
ijassa-1406	12	18	to	to	ADP
ijassa-1406	12	19	the	the	DET
ijassa-1406	12	20	equation	equation	NOUN
ijassa-1406	12	21	φ(u	φ(u	NOUN
ijassa-1406	12	22	)	)	PUNCT
ijassa-1406	12	23	=	=	SYM
ijassa-1406	12	24	0	0	NUM
ijassa-1406	12	25	(	(	PUNCT
ijassa-1406	12	26	1.2	1.2	NUM
ijassa-1406	12	27	)	)	PUNCT
ijassa-1406	12	28	with	with	ADP
ijassa-1406	12	29	φ	φ	PROPN
ijassa-1406	12	30	:	:	PUNCT
ijassa-1406	12	31	rp	rp	PROPN
ijassa-1406	12	32	×	×	PROPN
ijassa-1406	12	33	rp	rp	NOUN
ijassa-1406	12	34	,	,	PUNCT
ijassa-1406	12	35	φ(u	φ(u	X
ijassa-1406	12	36	)	)	PUNCT
ijassa-1406	12	37	=	=	SYM
ijassa-1406	12	38	ψ(u	ψ(u	PROPN
ijassa-1406	12	39	,	,	PUNCT
ijassa-1406	12	40	f	f	PROPN
ijassa-1406	12	41	(	(	PUNCT
ijassa-1406	12	42	u	u	NOUN
ijassa-1406	12	43	)	)	PUNCT
ijassa-1406	12	44	)	)	PUNCT
ijassa-1406	12	45	,	,	PUNCT
ijassa-1406	12	46	(	(	PUNCT
ijassa-1406	12	47	1.3	1.3	NUM
ijassa-1406	12	48	)	)	PUNCT
ijassa-1406	12	49	where	where	SCONJ
ijassa-1406	12	50	ψ	ψ	NOUN
ijassa-1406	12	51	is	be	AUX
ijassa-1406	12	52	applied	apply	VERB
ijassa-1406	12	53	componentwise	componentwise	NOUN
ijassa-1406	12	54	.	.	PUNCT
ijassa-1406	13	1	known	know	VERB
ijassa-1406	13	2	complementarity	complementarity	NOUN
ijassa-1406	13	3	functions	function	NOUN
ijassa-1406	13	4	are	be	AUX
ijassa-1406	13	5	plenty	plenty	ADJ
ijassa-1406	13	6	[	[	X
ijassa-1406	13	7	17	17	NUM
ijassa-1406	13	8	,	,	PUNCT
ijassa-1406	13	9	18	18	NUM
ijassa-1406	13	10	]	]	PUNCT
ijassa-1406	13	11	,	,	PUNCT
ijassa-1406	13	12	and	and	CCONJ
ijassa-1406	13	13	their	their	PRON
ijassa-1406	13	14	instances	instance	NOUN
ijassa-1406	13	15	may	may	AUX
ijassa-1406	13	16	possess	possess	VERB
ijassa-1406	13	17	different	different	ADJ
ijassa-1406	13	18	smoothness	smoothness	ADJ
ijassa-1406	13	19	properties	property	NOUN
ijassa-1406	13	20	.	.	PUNCT
ijassa-1406	14	1	therefore	therefore	ADV
ijassa-1406	14	2	,	,	PUNCT
ijassa-1406	14	3	the	the	DET
ijassa-1406	14	4	specific	specific	ADJ
ijassa-1406	14	5	choice	choice	NOUN
ijassa-1406	14	6	of	of	ADP
ijassa-1406	14	7	such	such	DET
ijassa-1406	14	8	a	a	DET
ijassa-1406	14	9	function	function	NOUN
ijassa-1406	14	10	naturally	naturally	ADV
ijassa-1406	14	11	∗corresponding	∗corresponde	VERB
ijassa-1406	14	12	author	author	NOUN
ijassa-1406	14	13	:	:	PUNCT
ijassa-1406	14	14	izmaf@cs.msu.ru	izmaf@cs.msu.ru	ADJ
ijassa-1406	14	15	newton	newton	PROPN
ijassa-1406	14	16	method	method	NOUN
ijassa-1406	14	17	vs.	vs.	ADP
ijassa-1406	14	18	semismooth	semismooth	NOUN
ijassa-1406	14	19	newton	newton	PROPN
ijassa-1406	14	20	method	method	PROPN
ijassa-1406	14	21	17	17	NUM
ijassa-1406	14	22	restricts	restrict	VERB
ijassa-1406	14	23	the	the	DET
ijassa-1406	14	24	class	class	NOUN
ijassa-1406	14	25	of	of	ADP
ijassa-1406	14	26	numerical	numerical	ADJ
ijassa-1406	14	27	methods	method	NOUN
ijassa-1406	14	28	applicable	applicable	ADJ
ijassa-1406	14	29	to	to	ADP
ijassa-1406	14	30	the	the	DET
ijassa-1406	14	31	corresponding	corresponding	ADJ
ijassa-1406	14	32	instance	instance	NOUN
ijassa-1406	14	33	of	of	ADP
ijassa-1406	14	34	equation	equation	NOUN
ijassa-1406	14	35	(	(	PUNCT
ijassa-1406	14	36	1.2	1.2	NUM
ijassa-1406	14	37	)	)	PUNCT
ijassa-1406	14	38	.	.	PUNCT
ijassa-1406	15	1	the	the	DET
ijassa-1406	15	2	rest	rest	NOUN
ijassa-1406	15	3	of	of	ADP
ijassa-1406	15	4	the	the	DET
ijassa-1406	15	5	paper	paper	NOUN
ijassa-1406	15	6	is	be	AUX
ijassa-1406	15	7	organized	organize	VERB
ijassa-1406	15	8	as	as	SCONJ
ijassa-1406	15	9	follows	follow	VERB
ijassa-1406	15	10	.	.	PUNCT
ijassa-1406	16	1	in	in	ADP
ijassa-1406	16	2	section	section	NOUN
ijassa-1406	16	3	2	2	NUM
ijassa-1406	16	4	,	,	PUNCT
ijassa-1406	16	5	we	we	PRON
ijassa-1406	16	6	consider	consider	VERB
ijassa-1406	16	7	a	a	DET
ijassa-1406	16	8	smooth	smooth	ADJ
ijassa-1406	16	9	complementarity	complementarity	NOUN
ijassa-1406	16	10	function	function	NOUN
ijassa-1406	16	11	,	,	PUNCT
ijassa-1406	16	12	allowing	allow	VERB
ijassa-1406	16	13	for	for	ADP
ijassa-1406	16	14	the	the	DET
ijassa-1406	16	15	basic	basic	ADJ
ijassa-1406	16	16	newton	newton	PROPN
ijassa-1406	16	17	method	method	NOUN
ijassa-1406	16	18	to	to	PART
ijassa-1406	16	19	be	be	AUX
ijassa-1406	16	20	applied	apply	VERB
ijassa-1406	16	21	to	to	ADP
ijassa-1406	16	22	the	the	DET
ijassa-1406	16	23	corresponding	correspond	VERB
ijassa-1406	16	24	equation	equation	NOUN
ijassa-1406	16	25	(	(	PUNCT
ijassa-1406	16	26	1.2	1.2	NUM
ijassa-1406	16	27	)	)	PUNCT
ijassa-1406	16	28	.	.	PUNCT
ijassa-1406	17	1	we	we	PRON
ijassa-1406	17	2	discuss	discuss	VERB
ijassa-1406	17	3	the	the	DET
ijassa-1406	17	4	local	local	ADJ
ijassa-1406	17	5	convergence	convergence	NOUN
ijassa-1406	17	6	and	and	CCONJ
ijassa-1406	17	7	rate	rate	NOUN
ijassa-1406	17	8	-	-	PUNCT
ijassa-1406	17	9	of	of	ADP
ijassa-1406	17	10	-	-	PUNCT
ijassa-1406	17	11	convergence	convergence	NOUN
ijassa-1406	17	12	properties	property	NOUN
ijassa-1406	17	13	,	,	PUNCT
ijassa-1406	17	14	as	as	ADV
ijassa-1406	17	15	well	well	ADV
ijassa-1406	17	16	the	the	DET
ijassa-1406	17	17	linesearch	linesearch	NOUN
ijassa-1406	17	18	technique	technique	NOUN
ijassa-1406	17	19	for	for	ADP
ijassa-1406	17	20	globalization	globalization	NOUN
ijassa-1406	17	21	of	of	ADP
ijassa-1406	17	22	convergence	convergence	NOUN
ijassa-1406	17	23	,	,	PUNCT
ijassa-1406	17	24	and	and	CCONJ
ijassa-1406	17	25	the	the	DET
ijassa-1406	17	26	extrapolation	extrapolation	NOUN
ijassa-1406	17	27	technique	technique	NOUN
ijassa-1406	17	28	for	for	ADP
ijassa-1406	17	29	potential	potential	ADJ
ijassa-1406	17	30	acceleration	acceleration	NOUN
ijassa-1406	17	31	of	of	ADP
ijassa-1406	17	32	convergence	convergence	NOUN
ijassa-1406	17	33	to	to	ADP
ijassa-1406	17	34	solutions	solution	NOUN
ijassa-1406	17	35	violating	violate	VERB
ijassa-1406	17	36	strict	strict	ADJ
ijassa-1406	17	37	complementarity	complementarity	NOUN
ijassa-1406	17	38	.	.	PUNCT
ijassa-1406	18	1	section	section	NOUN
ijassa-1406	18	2	3	3	NUM
ijassa-1406	18	3	deals	deal	NOUN
ijassa-1406	18	4	with	with	ADP
ijassa-1406	18	5	the	the	DET
ijassa-1406	18	6	fischer	fischer	NOUN
ijassa-1406	18	7	–	–	PUNCT
ijassa-1406	18	8	burmeister	burmeister	NOUN
ijassa-1406	18	9	complementarity	complementarity	NOUN
ijassa-1406	18	10	function	function	NOUN
ijassa-1406	18	11	,	,	PUNCT
ijassa-1406	18	12	in	in	ADP
ijassa-1406	18	13	which	which	DET
ijassa-1406	18	14	case	case	NOUN
ijassa-1406	18	15	the	the	DET
ijassa-1406	18	16	corresponding	correspond	VERB
ijassa-1406	18	17	equation	equation	NOUN
ijassa-1406	18	18	(	(	PUNCT
ijassa-1406	18	19	1.2	1.2	NUM
ijassa-1406	18	20	)	)	PUNCT
ijassa-1406	18	21	can	can	AUX
ijassa-1406	18	22	be	be	AUX
ijassa-1406	18	23	tackled	tackle	VERB
ijassa-1406	18	24	by	by	ADP
ijassa-1406	18	25	the	the	DET
ijassa-1406	18	26	semismooth	semismooth	NOUN
ijassa-1406	18	27	newton	newton	PROPN
ijassa-1406	18	28	method	method	PROPN
ijassa-1406	18	29	.	.	PUNCT
ijassa-1406	19	1	local	local	ADJ
ijassa-1406	19	2	convergence	convergence	NOUN
ijassa-1406	19	3	,	,	PUNCT
ijassa-1406	19	4	rate	rate	NOUN
ijassa-1406	19	5	-	-	PUNCT
ijassa-1406	19	6	of	of	ADP
ijassa-1406	19	7	-	-	PUNCT
ijassa-1406	19	8	convergence	convergence	NOUN
ijassa-1406	19	9	,	,	PUNCT
ijassa-1406	19	10	and	and	CCONJ
ijassa-1406	19	11	globalization	globalization	NOUN
ijassa-1406	19	12	of	of	ADP
ijassa-1406	19	13	convergence	convergence	NOUN
ijassa-1406	19	14	are	be	AUX
ijassa-1406	19	15	discussed	discuss	VERB
ijassa-1406	19	16	.	.	PUNCT
ijassa-1406	20	1	section	section	NOUN
ijassa-1406	20	2	4	4	NUM
ijassa-1406	20	3	presents	present	VERB
ijassa-1406	20	4	the	the	DET
ijassa-1406	20	5	results	result	NOUN
ijassa-1406	20	6	of	of	ADP
ijassa-1406	20	7	a	a	DET
ijassa-1406	20	8	numerical	numerical	ADJ
ijassa-1406	20	9	comparison	comparison	NOUN
ijassa-1406	20	10	of	of	ADP
ijassa-1406	20	11	the	the	DET
ijassa-1406	20	12	two	two	NUM
ijassa-1406	20	13	methods	method	NOUN
ijassa-1406	20	14	on	on	ADP
ijassa-1406	20	15	a	a	DET
ijassa-1406	20	16	collection	collection	NOUN
ijassa-1406	20	17	of	of	ADP
ijassa-1406	20	18	ncps	ncps	PROPN
ijassa-1406	20	19	with	with	ADP
ijassa-1406	20	20	solutions	solution	NOUN
ijassa-1406	20	21	violating	violate	VERB
ijassa-1406	20	22	strict	strict	ADJ
ijassa-1406	20	23	complementarity	complementarity	NOUN
ijassa-1406	20	24	.	.	PUNCT
ijassa-1406	21	1	2	2	NUM
ijassa-1406	21	2	.	.	X
ijassa-1406	21	3	smooth	smooth	ADJ
ijassa-1406	21	4	complementarity	complementarity	NOUN
ijassa-1406	21	5	function	function	NOUN
ijassa-1406	21	6	and	and	CCONJ
ijassa-1406	21	7	newton	newton	PROPN
ijassa-1406	21	8	method	method	PROPN
ijassa-1406	21	9	consider	consider	VERB
ijassa-1406	21	10	,	,	PUNCT
ijassa-1406	21	11	for	for	ADP
ijassa-1406	21	12	example	example	NOUN
ijassa-1406	21	13	,	,	PUNCT
ijassa-1406	21	14	a	a	DET
ijassa-1406	21	15	complementarity	complementarity	NOUN
ijassa-1406	21	16	function	function	NOUN
ijassa-1406	21	17	defined	define	VERB
ijassa-1406	21	18	by	by	ADP
ijassa-1406	21	19	ψ(a	ψ(a	PROPN
ijassa-1406	21	20	,	,	PUNCT
ijassa-1406	21	21	b	b	NOUN
ijassa-1406	21	22	)	)	PUNCT
ijassa-1406	22	1	=	=	SYM
ijassa-1406	22	2	2ab−	2ab−	NOUN
ijassa-1406	22	3	(	(	PUNCT
ijassa-1406	22	4	min{0	min{0	PROPN
ijassa-1406	22	5	,	,	PUNCT
ijassa-1406	22	6	a+	a+	PUNCT
ijassa-1406	22	7	b})2	b})2	NOUN
ijassa-1406	22	8	.	.	PUNCT
ijassa-1406	23	1	(	(	PUNCT
ijassa-1406	23	2	2.1	2.1	NUM
ijassa-1406	23	3	)	)	PUNCT
ijassa-1406	23	4	this	this	DET
ijassa-1406	23	5	function	function	NOUN
ijassa-1406	23	6	is	be	AUX
ijassa-1406	23	7	smooth	smooth	ADJ
ijassa-1406	23	8	,	,	PUNCT
ijassa-1406	23	9	and	and	CCONJ
ijassa-1406	23	10	assuming	assume	VERB
ijassa-1406	23	11	that	that	SCONJ
ijassa-1406	23	12	f	f	PROPN
ijassa-1406	23	13	is	be	AUX
ijassa-1406	23	14	differentiable	differentiable	ADJ
ijassa-1406	23	15	at	at	ADP
ijassa-1406	23	16	u	u	PROPN
ijassa-1406	23	17	∈	∈	PROPN
ijassa-1406	23	18	rp	rp	NOUN
ijassa-1406	23	19	,	,	PUNCT
ijassa-1406	23	20	the	the	DET
ijassa-1406	23	21	corresponding	correspond	VERB
ijassa-1406	23	22	mapping	mapping	NOUN
ijassa-1406	23	23	φ	φ	PROPN
ijassa-1406	23	24	defined	define	VERB
ijassa-1406	23	25	in	in	ADP
ijassa-1406	23	26	(	(	PUNCT
ijassa-1406	23	27	1.3	1.3	NUM
ijassa-1406	23	28	)	)	PUNCT
ijassa-1406	23	29	is	be	AUX
ijassa-1406	23	30	also	also	ADV
ijassa-1406	23	31	differentiable	differentiable	ADJ
ijassa-1406	23	32	at	at	ADP
ijassa-1406	23	33	u	u	NOUN
ijassa-1406	23	34	,	,	PUNCT
ijassa-1406	23	35	with	with	ADP
ijassa-1406	23	36	the	the	DET
ijassa-1406	23	37	rows	row	NOUN
ijassa-1406	23	38	of	of	ADP
ijassa-1406	23	39	the	the	DET
ijassa-1406	23	40	jacobian	jacobian	PROPN
ijassa-1406	23	41	φ′(u	φ′(u	PROPN
ijassa-1406	23	42	)	)	PUNCT
ijassa-1406	23	43	given	give	VERB
ijassa-1406	23	44	by	by	ADP
ijassa-1406	23	45	φ′	φ′	NUM
ijassa-1406	23	46	i(u	i(u	NOUN
ijassa-1406	23	47	)	)	PUNCT
ijassa-1406	24	1	=	=	PUNCT
ijassa-1406	25	1	2uif	2uif	NUM
ijassa-1406	25	2	′	′	NUM
ijassa-1406	26	1	i	i	PRON
ijassa-1406	26	2	(	(	PUNCT
ijassa-1406	26	3	u	u	NOUN
ijassa-1406	26	4	)	)	PUNCT
ijassa-1406	26	5	+	+	NUM
ijassa-1406	26	6	2fi(u)e	2fi(u)e	NUM
ijassa-1406	27	1	i	i	PRON
ijassa-1406	27	2	−	−	PROPN
ijassa-1406	27	3	2min{0	2min{0	NUM
ijassa-1406	27	4	,	,	PUNCT
ijassa-1406	27	5	ui	ui	NOUN
ijassa-1406	27	6	+	+	CCONJ
ijassa-1406	27	7	fi(u)}(f	fi(u)}(f	ADJ
ijassa-1406	28	1	′	′	NUM
ijassa-1406	29	1	i	i	PRON
ijassa-1406	29	2	(	(	PUNCT
ijassa-1406	29	3	u	u	NOUN
ijassa-1406	29	4	)	)	PUNCT
ijassa-1406	29	5	+	+	NUM
ijassa-1406	29	6	ei	ei	NOUN
ijassa-1406	29	7	)	)	PUNCT
ijassa-1406	29	8	,	,	PUNCT
ijassa-1406	29	9	i	i	PRON
ijassa-1406	29	10	=	=	NOUN
ijassa-1406	29	11	1	1	NUM
ijassa-1406	29	12	,	,	PUNCT
ijassa-1406	29	13	.	.	PUNCT
ijassa-1406	29	14	.	.	PUNCT
ijassa-1406	29	15	.	.	PUNCT
ijassa-1406	30	1	,	,	PUNCT
ijassa-1406	30	2	p	p	X
ijassa-1406	30	3	,	,	PUNCT
ijassa-1406	30	4	(	(	PUNCT
ijassa-1406	30	5	2.2	2.2	NUM
ijassa-1406	30	6	)	)	PUNCT
ijassa-1406	30	7	where	where	SCONJ
ijassa-1406	30	8	e1	e1	NOUN
ijassa-1406	30	9	,	,	PUNCT
ijassa-1406	30	10	.	.	PUNCT
ijassa-1406	30	11	.	.	PUNCT
ijassa-1406	31	1	.	.	PUNCT
ijassa-1406	32	1	,	,	PUNCT
ijassa-1406	32	2	ep	ep	PROPN
ijassa-1406	32	3	is	be	AUX
ijassa-1406	32	4	the	the	DET
ijassa-1406	32	5	standard	standard	ADJ
ijassa-1406	32	6	basis	basis	NOUN
ijassa-1406	32	7	in	in	ADP
ijassa-1406	32	8	rp	rp	NOUN
ijassa-1406	32	9	.	.	PUNCT
ijassa-1406	33	1	moreover	moreover	ADV
ijassa-1406	33	2	,	,	PUNCT
ijassa-1406	33	3	assuming	assume	VERB
ijassa-1406	33	4	that	that	SCONJ
ijassa-1406	33	5	f	f	PROPN
ijassa-1406	33	6	is	be	AUX
ijassa-1406	33	7	differentiable	differentiable	ADJ
ijassa-1406	33	8	on	on	ADP
ijassa-1406	33	9	a	a	DET
ijassa-1406	33	10	neighborhood	neighborhood	NOUN
ijassa-1406	33	11	of	of	ADP
ijassa-1406	33	12	some	some	DET
ijassa-1406	33	13	point	point	NOUN
ijassa-1406	33	14	in	in	ADP
ijassa-1406	33	15	rp	rp	NOUN
ijassa-1406	33	16	,	,	PUNCT
ijassa-1406	33	17	with	with	ADP
ijassa-1406	33	18	its	its	PRON
ijassa-1406	33	19	derivative	derivative	ADJ
ijassa-1406	33	20	f	f	NOUN
ijassa-1406	33	21	′	′	NOUN
ijassa-1406	33	22	being	be	AUX
ijassa-1406	33	23	lipschitz	lipschitz	NOUN
ijassa-1406	33	24	-	-	PUNCT
ijassa-1406	33	25	continuous	continuous	ADJ
ijassa-1406	33	26	on	on	ADP
ijassa-1406	33	27	this	this	DET
ijassa-1406	33	28	neighborhood	neighborhood	NOUN
ijassa-1406	33	29	,	,	PUNCT
ijassa-1406	33	30	the	the	DET
ijassa-1406	33	31	same	same	ADJ
ijassa-1406	33	32	property	property	NOUN
ijassa-1406	33	33	is	be	AUX
ijassa-1406	33	34	possessed	possess	VERB
ijassa-1406	33	35	by	by	ADP
ijassa-1406	33	36	φ′.	φ′.	ADV
ijassa-1406	33	37	under	under	ADP
ijassa-1406	33	38	these	these	DET
ijassa-1406	33	39	smoothness	smoothness	ADJ
ijassa-1406	33	40	assumptions	assumption	NOUN
ijassa-1406	33	41	,	,	PUNCT
ijassa-1406	33	42	one	one	PRON
ijassa-1406	33	43	can	can	AUX
ijassa-1406	33	44	apply	apply	VERB
ijassa-1406	33	45	the	the	DET
ijassa-1406	33	46	basic	basic	ADJ
ijassa-1406	33	47	newton	newton	PROPN
ijassa-1406	33	48	method	method	NOUN
ijassa-1406	33	49	to	to	ADP
ijassa-1406	33	50	equation	equation	NOUN
ijassa-1406	33	51	(	(	PUNCT
ijassa-1406	33	52	1.2	1.2	NUM
ijassa-1406	33	53	)	)	PUNCT
ijassa-1406	33	54	with	with	ADP
ijassa-1406	33	55	φ	φ	PROPN
ijassa-1406	33	56	defined	define	VERB
ijassa-1406	33	57	according	accord	VERB
ijassa-1406	33	58	to	to	ADP
ijassa-1406	33	59	(	(	PUNCT
ijassa-1406	33	60	1.3	1.3	NUM
ijassa-1406	33	61	)	)	PUNCT
ijassa-1406	33	62	,	,	PUNCT
ijassa-1406	33	63	(	(	PUNCT
ijassa-1406	33	64	2.1	2.1	NUM
ijassa-1406	33	65	):	):	PUNCT
ijassa-1406	33	66	for	for	ADP
ijassa-1406	33	67	a	a	DET
ijassa-1406	33	68	given	give	VERB
ijassa-1406	33	69	iterate	iterate	NOUN
ijassa-1406	33	70	uk	uk	PROPN
ijassa-1406	33	71	∈	∈	PROPN
ijassa-1406	33	72	rp	rp	NOUN
ijassa-1406	33	73	,	,	PUNCT
ijassa-1406	33	74	if	if	SCONJ
ijassa-1406	33	75	f	f	PROPN
ijassa-1406	33	76	is	be	AUX
ijassa-1406	33	77	differentiable	differentiable	ADJ
ijassa-1406	33	78	at	at	ADP
ijassa-1406	33	79	uk	uk	PROPN
ijassa-1406	33	80	,	,	PUNCT
ijassa-1406	33	81	one	one	PRON
ijassa-1406	33	82	can	can	AUX
ijassa-1406	33	83	compute	compute	VERB
ijassa-1406	33	84	the	the	DET
ijassa-1406	33	85	next	next	ADJ
ijassa-1406	33	86	iterate	iterate	NOUN
ijassa-1406	33	87	as	as	ADP
ijassa-1406	33	88	uk+1	uk+1	ADP
ijassa-1406	33	89	=	=	SYM
ijassa-1406	33	90	uk	uk	PROPN
ijassa-1406	33	91	+	+	CCONJ
ijassa-1406	33	92	vk	vk	PROPN
ijassa-1406	33	93	,	,	PUNCT
ijassa-1406	33	94	where	where	SCONJ
ijassa-1406	33	95	vk	vk	NOUN
ijassa-1406	33	96	is	be	AUX
ijassa-1406	33	97	a	a	DET
ijassa-1406	33	98	solution	solution	NOUN
ijassa-1406	33	99	of	of	ADP
ijassa-1406	33	100	the	the	DET
ijassa-1406	33	101	linear	linear	ADJ
ijassa-1406	33	102	equation	equation	NOUN
ijassa-1406	33	103	φ(uk	φ(uk	NUM
ijassa-1406	33	104	)	)	PUNCT
ijassa-1406	33	105	+	+	CCONJ
ijassa-1406	33	106	φ′(uk)v	φ′(uk)v	PROPN
ijassa-1406	33	107	=	=	SYM
ijassa-1406	33	108	0	0	NUM
ijassa-1406	33	109	;	;	PUNCT
ijassa-1406	33	110	(	(	PUNCT
ijassa-1406	33	111	2.3	2.3	NUM
ijassa-1406	33	112	)	)	PUNCT
ijassa-1406	33	113	see	see	VERB
ijassa-1406	33	114	,	,	PUNCT
ijassa-1406	33	115	e.g.	e.g.	ADV
ijassa-1406	33	116	,	,	PUNCT
ijassa-1406	33	117	[	[	X
ijassa-1406	33	118	15	15	NUM
ijassa-1406	33	119	,	,	PUNCT
ijassa-1406	33	120	section	section	NOUN
ijassa-1406	33	121	2.1.1	2.1.1	NUM
ijassa-1406	33	122	]	]	PUNCT
ijassa-1406	33	123	.	.	PUNCT
ijassa-1406	34	1	let	let	VERB
ijassa-1406	34	2	ū	ū	NOUN
ijassa-1406	34	3	be	be	AUX
ijassa-1406	34	4	a	a	DET
ijassa-1406	34	5	solution	solution	NOUN
ijassa-1406	34	6	of	of	ADP
ijassa-1406	34	7	ncp	ncp	PROPN
ijassa-1406	34	8	(	(	PUNCT
ijassa-1406	34	9	1.1	1.1	NUM
ijassa-1406	34	10	)	)	PUNCT
ijassa-1406	34	11	.	.	PUNCT
ijassa-1406	35	1	assume	assume	VERB
ijassa-1406	35	2	that	that	SCONJ
ijassa-1406	35	3	f	f	PROPN
ijassa-1406	35	4	is	be	AUX
ijassa-1406	35	5	differentiable	differentiable	ADJ
ijassa-1406	35	6	near	near	ADP
ijassa-1406	35	7	ū	ū	NOUN
ijassa-1406	35	8	,	,	PUNCT
ijassa-1406	35	9	with	with	ADP
ijassa-1406	35	10	its	its	PRON
ijassa-1406	35	11	derivative	derivative	ADJ
ijassa-1406	35	12	f	f	NOUN
ijassa-1406	35	13	′	′	NUM
ijassa-1406	35	14	being	be	AUX
ijassa-1406	35	15	continuous	continuous	ADJ
ijassa-1406	35	16	at	at	ADP
ijassa-1406	35	17	ū	ū	NOUN
ijassa-1406	35	18	,	,	PUNCT
ijassa-1406	35	19	and	and	CCONJ
ijassa-1406	35	20	that	that	SCONJ
ijassa-1406	35	21	φ′(ū	φ′(ū	PROPN
ijassa-1406	35	22	)	)	PUNCT
ijassa-1406	35	23	with	with	ADP
ijassa-1406	35	24	rows	row	NOUN
ijassa-1406	35	25	defined	define	VERB
ijassa-1406	35	26	in	in	ADP
ijassa-1406	35	27	(	(	PUNCT
ijassa-1406	35	28	2.2	2.2	NUM
ijassa-1406	35	29	)	)	PUNCT
ijassa-1406	35	30	is	be	AUX
ijassa-1406	35	31	nonsingular	nonsingular	ADJ
ijassa-1406	35	32	.	.	PUNCT
ijassa-1406	36	1	then	then	ADV
ijassa-1406	36	2	,	,	PUNCT
ijassa-1406	36	3	according	accord	VERB
ijassa-1406	36	4	to	to	ADP
ijassa-1406	36	5	[	[	X
ijassa-1406	36	6	15	15	NUM
ijassa-1406	36	7	,	,	PUNCT
ijassa-1406	36	8	theorem	theorem	VERB
ijassa-1406	36	9	2.2	2.2	NUM
ijassa-1406	36	10	]	]	PUNCT
ijassa-1406	36	11	,	,	PUNCT
ijassa-1406	36	12	for	for	ADP
ijassa-1406	36	13	any	any	DET
ijassa-1406	36	14	u0	u0	PROPN
ijassa-1406	36	15	∈	∈	PROPN
ijassa-1406	36	16	rp	rp	NOUN
ijassa-1406	36	17	close	close	VERB
ijassa-1406	36	18	enough	enough	ADV
ijassa-1406	36	19	to	to	ADP
ijassa-1406	36	20	ū	ū	VERB
ijassa-1406	36	21	,	,	PUNCT
ijassa-1406	36	22	the	the	DET
ijassa-1406	36	23	newton	newton	PROPN
ijassa-1406	36	24	method	method	NOUN
ijassa-1406	36	25	specified	specify	VERB
ijassa-1406	36	26	above	above	ADP
ijassa-1406	36	27	uniquely	uniquely	ADV
ijassa-1406	36	28	defines	define	VERB
ijassa-1406	36	29	a	a	DET
ijassa-1406	36	30	sequence	sequence	NOUN
ijassa-1406	36	31	{	{	PUNCT
ijassa-1406	36	32	uk	uk	PROPN
ijassa-1406	36	33	}	}	PUNCT
ijassa-1406	36	34	,	,	PUNCT
ijassa-1406	36	35	and	and	CCONJ
ijassa-1406	36	36	this	this	DET
ijassa-1406	36	37	sequence	sequence	NOUN
ijassa-1406	36	38	converges	converge	VERB
ijassa-1406	36	39	to	to	ADP
ijassa-1406	36	40	ū	ū	NOUN
ijassa-1406	36	41	superlinearly	superlinearly	ADV
ijassa-1406	36	42	,	,	PUNCT
ijassa-1406	36	43	or	or	CCONJ
ijassa-1406	36	44	even	even	ADV
ijassa-1406	36	45	quadratically	quadratically	ADV
ijassa-1406	36	46	if	if	SCONJ
ijassa-1406	36	47	f	f	PROPN
ijassa-1406	36	48	′	′	VERB
ijassa-1406	36	49	is	be	AUX
ijassa-1406	36	50	lipschitz	lipschitz	ADJ
ijassa-1406	36	51	-	-	PUNCT
ijassa-1406	36	52	continuous	continuous	ADJ
ijassa-1406	36	53	near	near	ADP
ijassa-1406	36	54	ū.	ū.	PUNCT
ijassa-1406	36	55	convergence	convergence	NOUN
ijassa-1406	36	56	of	of	ADP
ijassa-1406	36	57	the	the	DET
ijassa-1406	36	58	newton	newton	PROPN
ijassa-1406	36	59	method	method	NOUN
ijassa-1406	36	60	can	can	AUX
ijassa-1406	36	61	be	be	AUX
ijassa-1406	36	62	globalized	globalize	VERB
ijassa-1406	36	63	,	,	PUNCT
ijassa-1406	36	64	e.g.	e.g.	ADV
ijassa-1406	36	65	,	,	PUNCT
ijassa-1406	36	66	by	by	ADP
ijassa-1406	36	67	linesearch	linesearch	NOUN
ijassa-1406	36	68	techniques	technique	NOUN
ijassa-1406	36	69	.	.	PUNCT
ijassa-1406	37	1	the	the	DET
ijassa-1406	37	2	following	follow	VERB
ijassa-1406	37	3	is	be	AUX
ijassa-1406	37	4	essentially	essentially	ADV
ijassa-1406	37	5	[	[	X
ijassa-1406	37	6	7	7	NUM
ijassa-1406	37	7	,	,	PUNCT
ijassa-1406	37	8	algorithm	algorithm	NOUN
ijassa-1406	37	9	2.1	2.1	NUM
ijassa-1406	37	10	]	]	PUNCT
ijassa-1406	37	11	.	.	PUNCT
ijassa-1406	38	1	algorithm	algorithm	PROPN
ijassa-1406	38	2	2.1	2.1	NUM
ijassa-1406	38	3	:	:	PUNCT
ijassa-1406	38	4	define	define	VERB
ijassa-1406	38	5	the	the	DET
ijassa-1406	38	6	mapping	mapping	NOUN
ijassa-1406	38	7	φ	φ	NOUN
ijassa-1406	38	8	according	accord	VERB
ijassa-1406	38	9	to	to	ADP
ijassa-1406	38	10	(	(	PUNCT
ijassa-1406	38	11	1.3	1.3	NUM
ijassa-1406	38	12	)	)	PUNCT
ijassa-1406	38	13	,	,	PUNCT
ijassa-1406	38	14	(	(	PUNCT
ijassa-1406	38	15	2.1	2.1	NUM
ijassa-1406	38	16	)	)	PUNCT
ijassa-1406	38	17	.	.	PUNCT
ijassa-1406	39	1	choose	choose	VERB
ijassa-1406	39	2	the	the	DET
ijassa-1406	39	3	parameters	parameter	NOUN
ijassa-1406	39	4	σ	σ	PROPN
ijassa-1406	39	5	∈	∈	PROPN
ijassa-1406	39	6	(	(	PUNCT
ijassa-1406	39	7	0	0	NUM
ijassa-1406	39	8	,	,	PUNCT
ijassa-1406	39	9	1	1	NUM
ijassa-1406	39	10	)	)	PUNCT
ijassa-1406	39	11	and	and	CCONJ
ijassa-1406	39	12	θ	θ	PROPN
ijassa-1406	39	13	∈	∈	PROPN
ijassa-1406	39	14	(	(	PUNCT
ijassa-1406	39	15	0	0	NUM
ijassa-1406	39	16	,	,	PUNCT
ijassa-1406	39	17	1	1	NUM
ijassa-1406	39	18	)	)	PUNCT
ijassa-1406	39	19	.	.	PUNCT
ijassa-1406	40	1	choose	choose	VERB
ijassa-1406	40	2	u0	u0	PROPN
ijassa-1406	40	3	∈	∈	PROPN
ijassa-1406	40	4	rp	rp	NOUN
ijassa-1406	40	5	,	,	PUNCT
ijassa-1406	40	6	and	and	CCONJ
ijassa-1406	40	7	set	set	VERB
ijassa-1406	40	8	k	k	PROPN
ijassa-1406	40	9	=	=	PUNCT
ijassa-1406	40	10	0	0	NUM
ijassa-1406	40	11	.	.	NOUN
ijassa-1406	41	1	1	1	NUM
ijassa-1406	41	2	.	.	X
ijassa-1406	42	1	if	if	SCONJ
ijassa-1406	42	2	φ(uk	φ(uk	NOUN
ijassa-1406	42	3	)	)	PUNCT
ijassa-1406	42	4	=	=	SYM
ijassa-1406	42	5	0	0	NUM
ijassa-1406	42	6	,	,	PUNCT
ijassa-1406	42	7	stop	stop	VERB
ijassa-1406	42	8	with	with	ADP
ijassa-1406	42	9	success	success	NOUN
ijassa-1406	42	10	.	.	PUNCT
ijassa-1406	43	1	2	2	X
ijassa-1406	43	2	.	.	X
ijassa-1406	43	3	compute	compute	NOUN
ijassa-1406	43	4	vk	vk	PROPN
ijassa-1406	43	5	∈	∈	PROPN
ijassa-1406	43	6	rp	rp	NOUN
ijassa-1406	43	7	as	as	ADP
ijassa-1406	43	8	a	a	DET
ijassa-1406	43	9	solution	solution	NOUN
ijassa-1406	43	10	of	of	ADP
ijassa-1406	43	11	(	(	PUNCT
ijassa-1406	43	12	2.3	2.3	NUM
ijassa-1406	43	13	)	)	PUNCT
ijassa-1406	43	14	.	.	PUNCT
ijassa-1406	44	1	if	if	SCONJ
ijassa-1406	44	2	such	such	ADJ
ijassa-1406	44	3	vk	vk	NOUN
ijassa-1406	44	4	can	can	AUX
ijassa-1406	44	5	not	not	PART
ijassa-1406	44	6	be	be	AUX
ijassa-1406	44	7	found	find	VERB
ijassa-1406	44	8	,	,	PUNCT
ijassa-1406	44	9	stop	stop	VERB
ijassa-1406	44	10	with	with	ADP
ijassa-1406	44	11	a	a	DET
ijassa-1406	44	12	failure	failure	NOUN
ijassa-1406	44	13	.	.	PUNCT
ijassa-1406	45	1	3	3	X
ijassa-1406	45	2	.	.	X
ijassa-1406	45	3	set	set	VERB
ijassa-1406	45	4	τ	τ	PROPN
ijassa-1406	45	5	=	=	SYM
ijassa-1406	45	6	1	1	X
ijassa-1406	45	7	.	.	PUNCT
ijassa-1406	46	1	if	if	SCONJ
ijassa-1406	46	2	the	the	DET
ijassa-1406	46	3	inequality	inequality	NOUN
ijassa-1406	46	4	∥φ(uk	∥φ(uk	VERB
ijassa-1406	46	5	+	+	NUM
ijassa-1406	46	6	τvk)∥	τvk)∥	NOUN
ijassa-1406	46	7	≤	≤	NOUN
ijassa-1406	46	8	(	(	PUNCT
ijassa-1406	46	9	1−	1−	NUM
ijassa-1406	46	10	στ)∥φ(uk)∥	στ)∥φ(uk)∥	NOUN
ijassa-1406	46	11	(	(	PUNCT
ijassa-1406	46	12	2.4	2.4	NUM
ijassa-1406	46	13	)	)	PUNCT
ijassa-1406	46	14	is	be	AUX
ijassa-1406	46	15	satisfied	satisfied	ADJ
ijassa-1406	46	16	,	,	PUNCT
ijassa-1406	46	17	set	set	VERB
ijassa-1406	46	18	τk	τk	ADP
ijassa-1406	46	19	=	=	PROPN
ijassa-1406	46	20	τ	τ	PROPN
ijassa-1406	46	21	.	.	PUNCT
ijassa-1406	47	1	otherwise	otherwise	ADV
ijassa-1406	47	2	,	,	PUNCT
ijassa-1406	47	3	replace	replace	VERB
ijassa-1406	47	4	τ	τ	X
ijassa-1406	47	5	by	by	ADP
ijassa-1406	47	6	θτ	θτ	NOUN
ijassa-1406	47	7	,	,	PUNCT
ijassa-1406	47	8	check	check	VERB
ijassa-1406	47	9	inequality	inequality	NOUN
ijassa-1406	47	10	(	(	PUNCT
ijassa-1406	47	11	2.4	2.4	NUM
ijassa-1406	47	12	)	)	PUNCT
ijassa-1406	47	13	again	again	ADV
ijassa-1406	47	14	,	,	PUNCT
ijassa-1406	47	15	etc	etc	X
ijassa-1406	47	16	.	.	X
ijassa-1406	47	17	,	,	PUNCT
ijassa-1406	47	18	until	until	ADP
ijassa-1406	47	19	(	(	PUNCT
ijassa-1406	47	20	2.4	2.4	NUM
ijassa-1406	47	21	)	)	PUNCT
ijassa-1406	47	22	becomes	become	VERB
ijassa-1406	47	23	valid	valid	ADJ
ijassa-1406	47	24	.	.	PUNCT
ijassa-1406	48	1	copyright	copyright	NOUN
ijassa-1406	48	2	©	©	ADP
ijassa-1406	48	3	2023	2023	NUM
ijassa-1406	48	4	assa	assa	NOUN
ijassa-1406	48	5	.	.	PUNCT
ijassa-1406	49	1	adv	adv	PROPN
ijassa-1406	49	2	syst	syst	PROPN
ijassa-1406	49	3	sci	sci	PROPN
ijassa-1406	49	4	appl	appl	PROPN
ijassa-1406	49	5	(	(	PUNCT
ijassa-1406	49	6	2023	2023	NUM
ijassa-1406	49	7	)	)	PUNCT
ijassa-1406	49	8	18	18	NUM
ijassa-1406	49	9	a.	a.	NOUN
ijassa-1406	49	10	izmailov	izmailov	NOUN
ijassa-1406	49	11	,	,	PUNCT
ijassa-1406	49	12	e.	e.	PROPN
ijassa-1406	49	13	uskov	uskov	PROPN
ijassa-1406	49	14	,	,	PUNCT
ijassa-1406	49	15	y.	y.	PROPN
ijassa-1406	49	16	zhibai	zhibai	PROPN
ijassa-1406	49	17	4	4	X
ijassa-1406	49	18	.	.	PUNCT
ijassa-1406	49	19	set	set	VERB
ijassa-1406	49	20	uk+1	uk+1	NOUN
ijassa-1406	49	21	=	=	SYM
ijassa-1406	49	22	uk	uk	PROPN
ijassa-1406	49	23	+	+	CCONJ
ijassa-1406	49	24	τkv	τkv	PROPN
ijassa-1406	49	25	k.	k.	PROPN
ijassa-1406	49	26	5	5	X
ijassa-1406	49	27	.	.	PUNCT
ijassa-1406	50	1	increase	increase	VERB
ijassa-1406	50	2	k	k	X
ijassa-1406	50	3	by	by	ADP
ijassa-1406	50	4	1	1	NUM
ijassa-1406	50	5	and	and	CCONJ
ijassa-1406	50	6	go	go	VERB
ijassa-1406	50	7	to	to	PART
ijassa-1406	50	8	step	step	VERB
ijassa-1406	50	9	1	1	NUM
ijassa-1406	50	10	.	.	PUNCT
ijassa-1406	51	1	observe	observe	VERB
ijassa-1406	51	2	that	that	SCONJ
ijassa-1406	51	3	if	if	SCONJ
ijassa-1406	51	4	φ(uk	φ(uk	NOUN
ijassa-1406	51	5	)	)	PUNCT
ijassa-1406	51	6	̸=	̸=	PROPN
ijassa-1406	51	7	0	0	NUM
ijassa-1406	51	8	,	,	PUNCT
ijassa-1406	51	9	then	then	ADV
ijassa-1406	51	10	the	the	DET
ijassa-1406	51	11	function	function	NOUN
ijassa-1406	51	12	∥φ(·)∥	∥φ(·)∥	VERB
ijassa-1406	51	13	is	be	AUX
ijassa-1406	51	14	differentiable	differentiable	ADJ
ijassa-1406	51	15	at	at	ADP
ijassa-1406	51	16	uk	uk	PROPN
ijassa-1406	51	17	,	,	PUNCT
ijassa-1406	51	18	and	and	CCONJ
ijassa-1406	51	19	its	its	PRON
ijassa-1406	51	20	gradient	gradient	NOUN
ijassa-1406	51	21	is	be	AUX
ijassa-1406	51	22	(	(	PUNCT
ijassa-1406	51	23	φ′(uk))⊤φ(uk)∥φ(uk)∥.	φ′(uk))⊤φ(uk)∥φ(uk)∥.	NUM
ijassa-1406	51	24	then	then	ADV
ijassa-1406	51	25	the	the	DET
ijassa-1406	51	26	inner	inner	ADJ
ijassa-1406	51	27	product	product	NOUN
ijassa-1406	51	28	of	of	ADP
ijassa-1406	51	29	this	this	DET
ijassa-1406	51	30	gradient	gradient	NOUN
ijassa-1406	51	31	and	and	CCONJ
ijassa-1406	51	32	vk	vk	INTJ
ijassa-1406	51	33	solving	solve	VERB
ijassa-1406	51	34	(	(	PUNCT
ijassa-1406	51	35	2.3	2.3	NUM
ijassa-1406	51	36	)	)	PUNCT
ijassa-1406	51	37	evidently	evidently	ADV
ijassa-1406	51	38	equals	equal	VERB
ijassa-1406	51	39	−∥φ(uk)∥	−∥φ(uk)∥	NOUN
ijassa-1406	51	40	<	<	X
ijassa-1406	51	41	0	0	NUM
ijassa-1406	51	42	,	,	PUNCT
ijassa-1406	51	43	while	while	SCONJ
ijassa-1406	51	44	the	the	DET
ijassa-1406	51	45	stepsize	stepsize	NOUN
ijassa-1406	51	46	test	test	NOUN
ijassa-1406	51	47	(	(	PUNCT
ijassa-1406	51	48	2.4	2.4	NUM
ijassa-1406	51	49	)	)	PUNCT
ijassa-1406	51	50	is	be	AUX
ijassa-1406	51	51	nothing	nothing	PRON
ijassa-1406	51	52	else	else	ADV
ijassa-1406	51	53	but	but	CCONJ
ijassa-1406	51	54	the	the	DET
ijassa-1406	51	55	classical	classical	ADJ
ijassa-1406	51	56	armijo	armijo	PROPN
ijassa-1406	51	57	inequality	inequality	NOUN
ijassa-1406	51	58	;	;	PUNCT
ijassa-1406	51	59	see	see	VERB
ijassa-1406	51	60	,	,	PUNCT
ijassa-1406	51	61	e.g.	e.g.	ADV
ijassa-1406	51	62	,	,	PUNCT
ijassa-1406	51	63	[	[	X
ijassa-1406	51	64	15	15	NUM
ijassa-1406	51	65	,	,	PUNCT
ijassa-1406	51	66	(	(	PUNCT
ijassa-1406	51	67	2.62	2.62	NUM
ijassa-1406	51	68	)	)	PUNCT
ijassa-1406	51	69	]	]	PUNCT
ijassa-1406	51	70	,	,	PUNCT
ijassa-1406	51	71	and	and	CCONJ
ijassa-1406	51	72	step	step	NOUN
ijassa-1406	51	73	3	3	NUM
ijassa-1406	51	74	of	of	ADP
ijassa-1406	51	75	the	the	DET
ijassa-1406	51	76	algorithm	algorithm	NOUN
ijassa-1406	51	77	is	be	AUX
ijassa-1406	51	78	the	the	DET
ijassa-1406	51	79	standard	standard	ADJ
ijassa-1406	51	80	armijo	armijo	ADJ
ijassa-1406	51	81	backtracking	backtrack	VERB
ijassa-1406	51	82	procedure	procedure	NOUN
ijassa-1406	51	83	.	.	PUNCT
ijassa-1406	52	1	in	in	ADP
ijassa-1406	52	2	practical	practical	ADJ
ijassa-1406	52	3	implementations	implementation	NOUN
ijassa-1406	52	4	,	,	PUNCT
ijassa-1406	52	5	and	and	CCONJ
ijassa-1406	52	6	for	for	ADP
ijassa-1406	52	7	global	global	ADJ
ijassa-1406	52	8	convergence	convergence	NOUN
ijassa-1406	52	9	analysis	analysis	NOUN
ijassa-1406	52	10	,	,	PUNCT
ijassa-1406	52	11	instead	instead	ADV
ijassa-1406	52	12	of	of	ADP
ijassa-1406	52	13	declaring	declare	VERB
ijassa-1406	52	14	failure	failure	NOUN
ijassa-1406	52	15	when	when	SCONJ
ijassa-1406	52	16	vk	vk	PROPN
ijassa-1406	52	17	can	can	AUX
ijassa-1406	52	18	not	not	PART
ijassa-1406	52	19	be	be	AUX
ijassa-1406	52	20	found	find	VERB
ijassa-1406	52	21	in	in	ADP
ijassa-1406	52	22	step	step	NOUN
ijassa-1406	52	23	2	2	NUM
ijassa-1406	52	24	,	,	PUNCT
ijassa-1406	52	25	one	one	PRON
ijassa-1406	52	26	can	can	AUX
ijassa-1406	52	27	supply	supply	VERB
ijassa-1406	52	28	algorithm	algorithm	NOUN
ijassa-1406	52	29	2.1	2.1	NUM
ijassa-1406	52	30	with	with	ADP
ijassa-1406	52	31	some	some	DET
ijassa-1406	52	32	safeguarding	safeguard	VERB
ijassa-1406	52	33	tools	tool	NOUN
ijassa-1406	52	34	;	;	PUNCT
ijassa-1406	52	35	see	see	VERB
ijassa-1406	52	36	,	,	PUNCT
ijassa-1406	52	37	for	for	ADP
ijassa-1406	52	38	example	example	NOUN
ijassa-1406	52	39	,	,	PUNCT
ijassa-1406	52	40	[	[	X
ijassa-1406	52	41	7	7	NUM
ijassa-1406	52	42	,	,	PUNCT
ijassa-1406	52	43	algorithm	algorithm	NOUN
ijassa-1406	52	44	3.1	3.1	NUM
ijassa-1406	52	45	]	]	PUNCT
ijassa-1406	52	46	.	.	PUNCT
ijassa-1406	53	1	according	accord	VERB
ijassa-1406	53	2	to	to	ADP
ijassa-1406	53	3	[	[	X
ijassa-1406	53	4	7	7	NUM
ijassa-1406	53	5	,	,	PUNCT
ijassa-1406	53	6	theorem	theorem	VERB
ijassa-1406	53	7	3.1	3.1	NUM
ijassa-1406	53	8	]	]	PUNCT
ijassa-1406	53	9	,	,	PUNCT
ijassa-1406	53	10	any	any	DET
ijassa-1406	53	11	accumulation	accumulation	NOUN
ijassa-1406	53	12	point	point	NOUN
ijassa-1406	53	13	ū	ū	NOUN
ijassa-1406	53	14	of	of	ADP
ijassa-1406	53	15	any	any	DET
ijassa-1406	53	16	sequence	sequence	NOUN
ijassa-1406	53	17	{	{	PUNCT
ijassa-1406	53	18	uk	uk	PROPN
ijassa-1406	53	19	}	}	PUNCT
ijassa-1406	53	20	generated	generate	VERB
ijassa-1406	53	21	by	by	ADP
ijassa-1406	53	22	such	such	ADJ
ijassa-1406	53	23	enhanced	enhanced	ADJ
ijassa-1406	53	24	algorithm	algorithm	NOUN
ijassa-1406	53	25	2.1	2.1	NUM
ijassa-1406	53	26	satisfies	satisfie	NOUN
ijassa-1406	53	27	(	(	PUNCT
ijassa-1406	53	28	φ′(ū))⊤φ(ū	φ′(ū))⊤φ(ū	NUM
ijassa-1406	53	29	)	)	PUNCT
ijassa-1406	53	30	=	=	SYM
ijassa-1406	53	31	0	0	NUM
ijassa-1406	53	32	,	,	PUNCT
ijassa-1406	53	33	and	and	CCONJ
ijassa-1406	53	34	in	in	ADP
ijassa-1406	53	35	particular	particular	ADJ
ijassa-1406	53	36	,	,	PUNCT
ijassa-1406	53	37	can	can	AUX
ijassa-1406	53	38	be	be	AUX
ijassa-1406	53	39	guaranteed	guarantee	VERB
ijassa-1406	53	40	to	to	PART
ijassa-1406	53	41	be	be	AUX
ijassa-1406	53	42	a	a	DET
ijassa-1406	53	43	solution	solution	NOUN
ijassa-1406	53	44	of	of	ADP
ijassa-1406	53	45	ncp	ncp	PROPN
ijassa-1406	53	46	(	(	PUNCT
ijassa-1406	53	47	1.1	1.1	NUM
ijassa-1406	53	48	)	)	PUNCT
ijassa-1406	53	49	under	under	ADP
ijassa-1406	53	50	some	some	DET
ijassa-1406	53	51	reasonable	reasonable	ADJ
ijassa-1406	53	52	additional	additional	ADJ
ijassa-1406	53	53	assumptions	assumption	NOUN
ijassa-1406	53	54	.	.	PUNCT
ijassa-1406	54	1	however	however	ADV
ijassa-1406	54	2	,	,	PUNCT
ijassa-1406	54	3	in	in	ADP
ijassa-1406	54	4	the	the	DET
ijassa-1406	54	5	numerical	numerical	ADJ
ijassa-1406	54	6	experiments	experiment	NOUN
ijassa-1406	54	7	reported	report	VERB
ijassa-1406	54	8	in	in	ADP
ijassa-1406	54	9	section	section	NOUN
ijassa-1406	54	10	4	4	NUM
ijassa-1406	54	11	,	,	PUNCT
ijassa-1406	54	12	we	we	PRON
ijassa-1406	54	13	employ	employ	VERB
ijassa-1406	54	14	algorithm	algorithm	NOUN
ijassa-1406	54	15	2.1	2.1	NUM
ijassa-1406	54	16	as	as	SCONJ
ijassa-1406	54	17	it	it	PRON
ijassa-1406	54	18	is	be	AUX
ijassa-1406	54	19	,	,	PUNCT
ijassa-1406	54	20	without	without	ADP
ijassa-1406	54	21	any	any	DET
ijassa-1406	54	22	additional	additional	ADJ
ijassa-1406	54	23	safeguards	safeguard	NOUN
ijassa-1406	54	24	,	,	PUNCT
ijassa-1406	54	25	and	and	CCONJ
ijassa-1406	54	26	this	this	PRON
ijassa-1406	54	27	indeed	indeed	ADV
ijassa-1406	54	28	leads	lead	VERB
ijassa-1406	54	29	to	to	ADP
ijassa-1406	54	30	some	some	DET
ijassa-1406	54	31	failures	failure	NOUN
ijassa-1406	54	32	on	on	ADP
ijassa-1406	54	33	step	step	NOUN
ijassa-1406	54	34	2	2	NUM
ijassa-1406	54	35	.	.	PUNCT
ijassa-1406	55	1	moreover	moreover	ADV
ijassa-1406	55	2	,	,	PUNCT
ijassa-1406	55	3	assuming	assume	VERB
ijassa-1406	55	4	that	that	SCONJ
ijassa-1406	55	5	φ′(ū	φ′(ū	PROPN
ijassa-1406	55	6	)	)	PUNCT
ijassa-1406	55	7	is	be	AUX
ijassa-1406	55	8	nonsingular	nonsingular	ADJ
ijassa-1406	55	9	at	at	ADP
ijassa-1406	55	10	a	a	DET
ijassa-1406	55	11	solution	solution	NOUN
ijassa-1406	55	12	ū	ū	NOUN
ijassa-1406	55	13	of	of	ADP
ijassa-1406	55	14	ncp	ncp	PROPN
ijassa-1406	55	15	(	(	PUNCT
ijassa-1406	55	16	1.1	1.1	NUM
ijassa-1406	55	17	)	)	PUNCT
ijassa-1406	55	18	,	,	PUNCT
ijassa-1406	55	19	and	and	CCONJ
ijassa-1406	55	20	employing	employ	VERB
ijassa-1406	55	21	the	the	DET
ijassa-1406	55	22	argument	argument	NOUN
ijassa-1406	55	23	in	in	ADP
ijassa-1406	55	24	[	[	X
ijassa-1406	55	25	15	15	NUM
ijassa-1406	55	26	,	,	PUNCT
ijassa-1406	55	27	theorem	theorem	VERB
ijassa-1406	55	28	5.4	5.4	NUM
ijassa-1406	55	29	]	]	PUNCT
ijassa-1406	55	30	,	,	PUNCT
ijassa-1406	55	31	one	one	PRON
ijassa-1406	55	32	can	can	AUX
ijassa-1406	55	33	easily	easily	ADV
ijassa-1406	55	34	see	see	VERB
ijassa-1406	55	35	that	that	SCONJ
ijassa-1406	55	36	(	(	PUNCT
ijassa-1406	55	37	2.4	2.4	NUM
ijassa-1406	55	38	)	)	PUNCT
ijassa-1406	55	39	is	be	AUX
ijassa-1406	55	40	satisfied	satisfied	ADJ
ijassa-1406	55	41	with	with	ADP
ijassa-1406	55	42	α	α	NOUN
ijassa-1406	55	43	=	=	SYM
ijassa-1406	55	44	1	1	NUM
ijassa-1406	55	45	provided	provide	VERB
ijassa-1406	55	46	uk	uk	PROPN
ijassa-1406	55	47	is	be	AUX
ijassa-1406	55	48	close	close	ADJ
ijassa-1406	55	49	enough	enough	ADV
ijassa-1406	55	50	to	to	ADP
ijassa-1406	55	51	ū.	ū.	PUNCT
ijassa-1406	55	52	therefore	therefore	ADV
ijassa-1406	55	53	,	,	PUNCT
ijassa-1406	55	54	the	the	DET
ijassa-1406	55	55	algorithm	algorithm	NOUN
ijassa-1406	55	56	asymptotically	asymptotically	ADV
ijassa-1406	55	57	accepts	accept	VERB
ijassa-1406	55	58	the	the	DET
ijassa-1406	55	59	full	full	ADJ
ijassa-1406	55	60	step	step	NOUN
ijassa-1406	55	61	,	,	PUNCT
ijassa-1406	55	62	and	and	CCONJ
ijassa-1406	55	63	inherits	inherit	VERB
ijassa-1406	55	64	the	the	DET
ijassa-1406	55	65	local	local	ADJ
ijassa-1406	55	66	convergence	convergence	NOUN
ijassa-1406	55	67	and	and	CCONJ
ijassa-1406	55	68	rate	rate	NOUN
ijassa-1406	55	69	of	of	ADP
ijassa-1406	55	70	convergence	convergence	NOUN
ijassa-1406	55	71	properties	property	NOUN
ijassa-1406	55	72	of	of	ADP
ijassa-1406	55	73	the	the	DET
ijassa-1406	55	74	basic	basic	ADJ
ijassa-1406	55	75	newton	newton	PROPN
ijassa-1406	55	76	method	method	NOUN
ijassa-1406	55	77	.	.	PUNCT
ijassa-1406	56	1	observe	observe	VERB
ijassa-1406	56	2	,	,	PUNCT
ijassa-1406	56	3	however	however	ADV
ijassa-1406	56	4	,	,	PUNCT
ijassa-1406	56	5	that	that	SCONJ
ijassa-1406	56	6	if	if	SCONJ
ijassa-1406	56	7	ū	ū	NOUN
ijassa-1406	56	8	violates	violate	VERB
ijassa-1406	56	9	that	that	DET
ijassa-1406	56	10	strict	strict	ADJ
ijassa-1406	56	11	complementarity	complementarity	NOUN
ijassa-1406	56	12	condition	condition	NOUN
ijassa-1406	56	13	ū+	ū+	PROPN
ijassa-1406	56	14	f	f	PROPN
ijassa-1406	56	15	(	(	PUNCT
ijassa-1406	56	16	ū	ū	PROPN
ijassa-1406	56	17	)	)	PUNCT
ijassa-1406	56	18	>	>	X
ijassa-1406	56	19	0	0	NUM
ijassa-1406	56	20	,	,	PUNCT
ijassa-1406	56	21	which	which	PRON
ijassa-1406	56	22	means	mean	VERB
ijassa-1406	56	23	that	that	SCONJ
ijassa-1406	56	24	there	there	PRON
ijassa-1406	56	25	exist	exist	VERB
ijassa-1406	56	26	i	i	PRON
ijassa-1406	56	27	∈	∈	PROPN
ijassa-1406	56	28	{	{	PUNCT
ijassa-1406	56	29	1	1	NUM
ijassa-1406	56	30	,	,	PUNCT
ijassa-1406	56	31	.	.	PUNCT
ijassa-1406	56	32	.	.	PUNCT
ijassa-1406	56	33	.	.	PUNCT
ijassa-1406	57	1	,	,	PUNCT
ijassa-1406	57	2	p	p	X
ijassa-1406	57	3	}	}	PUNCT
ijassa-1406	57	4	such	such	ADJ
ijassa-1406	57	5	that	that	SCONJ
ijassa-1406	57	6	ūi	ūi	PROPN
ijassa-1406	57	7	=	=	SYM
ijassa-1406	57	8	fi(ū	fi(ū	PROPN
ijassa-1406	57	9	)	)	PUNCT
ijassa-1406	57	10	=	=	PUNCT
ijassa-1406	57	11	0	0	X
ijassa-1406	57	12	.	.	PUNCT
ijassa-1406	58	1	then	then	ADV
ijassa-1406	58	2	(	(	PUNCT
ijassa-1406	58	3	2.2	2.2	NUM
ijassa-1406	58	4	)	)	PUNCT
ijassa-1406	58	5	yields	yield	NOUN
ijassa-1406	58	6	φ′	φ′	NUM
ijassa-1406	58	7	i(ū	i(ū	PROPN
ijassa-1406	58	8	)	)	PUNCT
ijassa-1406	58	9	=	=	SYM
ijassa-1406	58	10	0	0	NUM
ijassa-1406	58	11	,	,	PUNCT
ijassa-1406	58	12	and	and	CCONJ
ijassa-1406	58	13	hence	hence	ADV
ijassa-1406	58	14	,	,	PUNCT
ijassa-1406	58	15	φ′(ū	φ′(ū	PROPN
ijassa-1406	58	16	)	)	PUNCT
ijassa-1406	58	17	is	be	AUX
ijassa-1406	58	18	necessarily	necessarily	ADV
ijassa-1406	58	19	singular	singular	ADJ
ijassa-1406	58	20	,	,	PUNCT
ijassa-1406	58	21	not	not	PART
ijassa-1406	58	22	allowing	allow	VERB
ijassa-1406	58	23	to	to	PART
ijassa-1406	58	24	apply	apply	VERB
ijassa-1406	58	25	the	the	DET
ijassa-1406	58	26	theory	theory	NOUN
ijassa-1406	58	27	outlined	outline	VERB
ijassa-1406	58	28	above	above	ADV
ijassa-1406	58	29	.	.	PUNCT
ijassa-1406	59	1	the	the	DET
ijassa-1406	59	2	strict	strict	ADJ
ijassa-1406	59	3	complementarity	complementarity	NOUN
ijassa-1406	59	4	condition	condition	NOUN
ijassa-1406	59	5	is	be	AUX
ijassa-1406	59	6	regarded	regard	VERB
ijassa-1406	59	7	as	as	ADP
ijassa-1406	59	8	rather	rather	ADV
ijassa-1406	59	9	restrictive	restrictive	ADJ
ijassa-1406	59	10	in	in	ADP
ijassa-1406	59	11	the	the	DET
ijassa-1406	59	12	literature	literature	NOUN
ijassa-1406	59	13	,	,	PUNCT
ijassa-1406	59	14	and	and	CCONJ
ijassa-1406	59	15	therefore	therefore	ADV
ijassa-1406	59	16	,	,	PUNCT
ijassa-1406	59	17	one	one	PRON
ijassa-1406	59	18	should	should	AUX
ijassa-1406	59	19	be	be	AUX
ijassa-1406	59	20	ready	ready	ADJ
ijassa-1406	59	21	to	to	PART
ijassa-1406	59	22	face	face	VERB
ijassa-1406	59	23	singularity	singularity	NOUN
ijassa-1406	59	24	of	of	ADP
ijassa-1406	59	25	a	a	DET
ijassa-1406	59	26	solution	solution	NOUN
ijassa-1406	59	27	ū	ū	NOUN
ijassa-1406	59	28	of	of	ADP
ijassa-1406	59	29	(	(	PUNCT
ijassa-1406	59	30	1.2	1.2	NUM
ijassa-1406	59	31	)	)	PUNCT
ijassa-1406	59	32	when	when	SCONJ
ijassa-1406	59	33	the	the	DET
ijassa-1406	59	34	latter	latter	ADJ
ijassa-1406	59	35	is	be	AUX
ijassa-1406	59	36	obtained	obtain	VERB
ijassa-1406	59	37	as	as	ADP
ijassa-1406	59	38	a	a	DET
ijassa-1406	59	39	reformulation	reformulation	NOUN
ijassa-1406	59	40	of	of	ADP
ijassa-1406	59	41	ncp	ncp	PROPN
ijassa-1406	59	42	(	(	PUNCT
ijassa-1406	59	43	1.1	1.1	NUM
ijassa-1406	59	44	)	)	PUNCT
ijassa-1406	59	45	,	,	PUNCT
ijassa-1406	59	46	employing	employ	VERB
ijassa-1406	59	47	the	the	DET
ijassa-1406	59	48	smooth	smooth	ADJ
ijassa-1406	59	49	complementarity	complementarity	NOUN
ijassa-1406	59	50	function	function	NOUN
ijassa-1406	59	51	(	(	PUNCT
ijassa-1406	59	52	2.1	2.1	NUM
ijassa-1406	59	53	)	)	PUNCT
ijassa-1406	59	54	(	(	PUNCT
ijassa-1406	59	55	and	and	CCONJ
ijassa-1406	59	56	actually	actually	ADV
ijassa-1406	59	57	,	,	PUNCT
ijassa-1406	59	58	any	any	DET
ijassa-1406	59	59	other	other	ADJ
ijassa-1406	59	60	smooth	smooth	ADJ
ijassa-1406	59	61	complementarity	complementarity	NOUN
ijassa-1406	59	62	function	function	NOUN
ijassa-1406	59	63	)	)	PUNCT
ijassa-1406	59	64	.	.	PUNCT
ijassa-1406	60	1	there	there	PRON
ijassa-1406	60	2	exists	exist	VERB
ijassa-1406	60	3	quite	quite	DET
ijassa-1406	60	4	a	a	DET
ijassa-1406	60	5	rich	rich	ADJ
ijassa-1406	60	6	literature	literature	NOUN
ijassa-1406	60	7	on	on	ADP
ijassa-1406	60	8	the	the	DET
ijassa-1406	60	9	behavior	behavior	NOUN
ijassa-1406	60	10	of	of	ADP
ijassa-1406	60	11	newton	newton	PROPN
ijassa-1406	60	12	-	-	PUNCT
ijassa-1406	60	13	type	type	NOUN
ijassa-1406	60	14	methods	method	NOUN
ijassa-1406	60	15	near	near	ADP
ijassa-1406	60	16	singular	singular	ADJ
ijassa-1406	60	17	solutions	solution	NOUN
ijassa-1406	60	18	of	of	ADP
ijassa-1406	60	19	nonlinear	nonlinear	ADJ
ijassa-1406	60	20	equations	equation	NOUN
ijassa-1406	60	21	;	;	PUNCT
ijassa-1406	60	22	we	we	PRON
ijassa-1406	60	23	mention	mention	VERB
ijassa-1406	60	24	only	only	ADV
ijassa-1406	60	25	some	some	DET
ijassa-1406	60	26	references	reference	NOUN
ijassa-1406	60	27	most	most	ADV
ijassa-1406	60	28	tightly	tightly	ADV
ijassa-1406	60	29	related	relate	VERB
ijassa-1406	60	30	to	to	ADP
ijassa-1406	60	31	the	the	DET
ijassa-1406	60	32	contents	content	NOUN
ijassa-1406	60	33	of	of	ADP
ijassa-1406	60	34	this	this	DET
ijassa-1406	60	35	work	work	NOUN
ijassa-1406	60	36	:	:	PUNCT
ijassa-1406	61	1	[	[	X
ijassa-1406	61	2	7–11	7–11	NOUN
ijassa-1406	61	3	,	,	PUNCT
ijassa-1406	61	4	13	13	NUM
ijassa-1406	61	5	]	]	PUNCT
ijassa-1406	61	6	.	.	PUNCT
ijassa-1406	62	1	apart	apart	ADV
ijassa-1406	62	2	from	from	ADP
ijassa-1406	62	3	characterizing	characterize	VERB
ijassa-1406	62	4	local	local	ADJ
ijassa-1406	62	5	linear	linear	ADJ
ijassa-1406	62	6	convergence	convergence	NOUN
ijassa-1406	62	7	from	from	ADP
ijassa-1406	62	8	asymptotically	asymptotically	ADV
ijassa-1406	62	9	dense	dense	ADJ
ijassa-1406	62	10	domains	domain	NOUN
ijassa-1406	62	11	starlike	starlike	NOUN
ijassa-1406	62	12	with	with	ADP
ijassa-1406	62	13	respect	respect	NOUN
ijassa-1406	62	14	to	to	ADP
ijassa-1406	62	15	such	such	ADJ
ijassa-1406	62	16	solution	solution	NOUN
ijassa-1406	62	17	,	,	PUNCT
ijassa-1406	62	18	some	some	DET
ijassa-1406	62	19	acceleration	acceleration	NOUN
ijassa-1406	62	20	techniques	technique	NOUN
ijassa-1406	62	21	were	be	AUX
ijassa-1406	62	22	developed	develop	VERB
ijassa-1406	62	23	,	,	PUNCT
ijassa-1406	62	24	such	such	ADJ
ijassa-1406	62	25	as	as	ADP
ijassa-1406	62	26	the	the	DET
ijassa-1406	62	27	so	so	ADV
ijassa-1406	62	28	-	-	PUNCT
ijassa-1406	62	29	called	call	VERB
ijassa-1406	62	30	extrapolation	extrapolation	NOUN
ijassa-1406	63	1	[	[	X
ijassa-1406	63	2	9	9	NUM
ijassa-1406	63	3	,	,	PUNCT
ijassa-1406	63	4	11	11	NUM
ijassa-1406	63	5	]	]	PUNCT
ijassa-1406	63	6	.	.	PUNCT
ijassa-1406	64	1	in	in	ADP
ijassa-1406	64	2	its	its	PRON
ijassa-1406	64	3	simplest	simple	ADJ
ijassa-1406	64	4	form	form	NOUN
ijassa-1406	64	5	,	,	PUNCT
ijassa-1406	64	6	this	this	DET
ijassa-1406	64	7	procedure	procedure	NOUN
ijassa-1406	64	8	amounts	amount	VERB
ijassa-1406	64	9	to	to	ADP
ijassa-1406	64	10	generating	generate	VERB
ijassa-1406	64	11	,	,	PUNCT
ijassa-1406	64	12	in	in	ADP
ijassa-1406	64	13	parallel	parallel	NOUN
ijassa-1406	64	14	with	with	ADP
ijassa-1406	64	15	the	the	DET
ijassa-1406	64	16	main	main	ADJ
ijassa-1406	64	17	sequence	sequence	NOUN
ijassa-1406	64	18	{	{	PUNCT
ijassa-1406	64	19	uk	uk	PROPN
ijassa-1406	64	20	}	}	PUNCT
ijassa-1406	64	21	of	of	ADP
ijassa-1406	64	22	the	the	DET
ijassa-1406	64	23	newton	newton	PROPN
ijassa-1406	64	24	method	method	NOUN
ijassa-1406	64	25	,	,	PUNCT
ijassa-1406	64	26	an	an	DET
ijassa-1406	64	27	auxiliary	auxiliary	ADJ
ijassa-1406	64	28	sequence	sequence	NOUN
ijassa-1406	64	29	{	{	PUNCT
ijassa-1406	64	30	ûk	ûk	NOUN
ijassa-1406	64	31	}	}	PUNCT
ijassa-1406	64	32	obtained	obtain	VERB
ijassa-1406	64	33	by	by	ADP
ijassa-1406	64	34	doubling	double	VERB
ijassa-1406	64	35	the	the	DET
ijassa-1406	64	36	newton	newton	PROPN
ijassa-1406	64	37	step	step	NOUN
ijassa-1406	64	38	:	:	PUNCT
ijassa-1406	64	39	for	for	SCONJ
ijassa-1406	64	40	each	each	DET
ijassa-1406	64	41	k	k	NOUN
ijassa-1406	64	42	set	set	VERB
ijassa-1406	64	43	ûk+1	ûk+1	ADP
ijassa-1406	64	44	=	=	PUNCT
ijassa-1406	64	45	uk	uk	PROPN
ijassa-1406	64	46	+	+	CCONJ
ijassa-1406	64	47	2vk	2vk	ADJ
ijassa-1406	64	48	.	.	PUNCT
ijassa-1406	65	1	(	(	PUNCT
ijassa-1406	65	2	2.5	2.5	NUM
ijassa-1406	65	3	)	)	PUNCT
ijassa-1406	65	4	this	this	DET
ijassa-1406	65	5	specific	specific	ADJ
ijassa-1406	65	6	procedure	procedure	NOUN
ijassa-1406	65	7	is	be	AUX
ijassa-1406	65	8	suggested	suggest	VERB
ijassa-1406	65	9	by	by	ADP
ijassa-1406	65	10	the	the	DET
ijassa-1406	65	11	convergence	convergence	NOUN
ijassa-1406	65	12	pattern	pattern	NOUN
ijassa-1406	65	13	of	of	ADP
ijassa-1406	65	14	the	the	DET
ijassa-1406	65	15	newton	newton	PROPN
ijassa-1406	65	16	method	method	NOUN
ijassa-1406	65	17	to	to	ADP
ijassa-1406	65	18	singular	singular	ADJ
ijassa-1406	65	19	solutions	solution	NOUN
ijassa-1406	65	20	of	of	ADP
ijassa-1406	65	21	certain	certain	ADJ
ijassa-1406	65	22	wide	wide	ADJ
ijassa-1406	65	23	classes	class	NOUN
ijassa-1406	65	24	.	.	PUNCT
ijassa-1406	66	1	according	accord	VERB
ijassa-1406	66	2	to	to	ADP
ijassa-1406	66	3	[	[	X
ijassa-1406	66	4	11	11	NUM
ijassa-1406	66	5	,	,	PUNCT
ijassa-1406	66	6	theorem	theorem	VERB
ijassa-1406	66	7	4.1	4.1	NUM
ijassa-1406	66	8	]	]	PUNCT
ijassa-1406	66	9	,	,	PUNCT
ijassa-1406	66	10	under	under	ADP
ijassa-1406	66	11	the	the	DET
ijassa-1406	66	12	appropriate	appropriate	ADJ
ijassa-1406	66	13	assumptions	assumption	NOUN
ijassa-1406	66	14	,	,	PUNCT
ijassa-1406	66	15	the	the	DET
ijassa-1406	66	16	sequence	sequence	NOUN
ijassa-1406	66	17	{	{	PUNCT
ijassa-1406	66	18	ûk	ûk	PRON
ijassa-1406	66	19	}	}	PUNCT
ijassa-1406	66	20	generated	generate	VERB
ijassa-1406	66	21	this	this	DET
ijassa-1406	66	22	way	way	NOUN
ijassa-1406	66	23	converges	converge	VERB
ijassa-1406	66	24	to	to	ADP
ijassa-1406	66	25	ū	ū	NOUN
ijassa-1406	66	26	linearly	linearly	ADV
ijassa-1406	66	27	with	with	ADP
ijassa-1406	66	28	the	the	DET
ijassa-1406	66	29	asymptotic	asymptotic	ADJ
ijassa-1406	66	30	ratio	ratio	NOUN
ijassa-1406	66	31	of	of	ADP
ijassa-1406	66	32	1/4	1/4	NUM
ijassa-1406	66	33	(	(	PUNCT
ijassa-1406	66	34	instead	instead	ADV
ijassa-1406	66	35	of	of	ADP
ijassa-1406	66	36	1/2	1/2	NUM
ijassa-1406	66	37	for	for	ADP
ijassa-1406	66	38	the	the	DET
ijassa-1406	66	39	sequence	sequence	NOUN
ijassa-1406	66	40	{	{	PUNCT
ijassa-1406	66	41	uk	uk	PROPN
ijassa-1406	66	42	}	}	PUNCT
ijassa-1406	66	43	generated	generate	VERB
ijassa-1406	66	44	by	by	ADP
ijassa-1406	66	45	the	the	DET
ijassa-1406	66	46	newton	newton	PROPN
ijassa-1406	66	47	method	method	PROPN
ijassa-1406	66	48	)	)	PUNCT
ijassa-1406	66	49	,	,	PUNCT
ijassa-1406	66	50	from	from	ADP
ijassa-1406	66	51	all	all	DET
ijassa-1406	66	52	points	point	NOUN
ijassa-1406	66	53	in	in	ADP
ijassa-1406	66	54	the	the	DET
ijassa-1406	66	55	domain	domain	NOUN
ijassa-1406	66	56	of	of	ADP
ijassa-1406	66	57	convergence	convergence	NOUN
ijassa-1406	66	58	of	of	ADP
ijassa-1406	66	59	newtonian	newtonian	ADJ
ijassa-1406	66	60	sequences	sequence	NOUN
ijassa-1406	66	61	.	.	PUNCT
ijassa-1406	67	1	the	the	DET
ijassa-1406	67	2	main	main	ADJ
ijassa-1406	67	3	iterative	iterative	NOUN
ijassa-1406	67	4	sequences	sequence	NOUN
ijassa-1406	67	5	{	{	PUNCT
ijassa-1406	67	6	uk	uk	PROPN
ijassa-1406	67	7	}	}	PUNCT
ijassa-1406	67	8	are	be	AUX
ijassa-1406	67	9	not	not	PART
ijassa-1406	67	10	affected	affect	VERB
ijassa-1406	67	11	by	by	ADP
ijassa-1406	67	12	this	this	DET
ijassa-1406	67	13	acceleration	acceleration	NOUN
ijassa-1406	67	14	technique	technique	NOUN
ijassa-1406	67	15	in	in	ADP
ijassa-1406	67	16	any	any	DET
ijassa-1406	67	17	way	way	NOUN
ijassa-1406	67	18	,	,	PUNCT
ijassa-1406	67	19	and	and	CCONJ
ijassa-1406	67	20	generating	generate	VERB
ijassa-1406	67	21	the	the	DET
ijassa-1406	67	22	auxiliary	auxiliary	ADJ
ijassa-1406	67	23	sequence	sequence	NOUN
ijassa-1406	67	24	{	{	PUNCT
ijassa-1406	67	25	ûk	ûk	PROPN
ijassa-1406	67	26	}	}	PUNCT
ijassa-1406	67	27	is	be	AUX
ijassa-1406	67	28	very	very	ADV
ijassa-1406	67	29	cheap	cheap	ADJ
ijassa-1406	67	30	.	.	PUNCT
ijassa-1406	68	1	therefore	therefore	ADV
ijassa-1406	68	2	,	,	PUNCT
ijassa-1406	68	3	this	this	DET
ijassa-1406	68	4	acceleration	acceleration	NOUN
ijassa-1406	68	5	technique	technique	NOUN
ijassa-1406	68	6	is	be	AUX
ijassa-1406	68	7	is	be	AUX
ijassa-1406	68	8	fully	fully	ADV
ijassa-1406	68	9	practical	practical	ADJ
ijassa-1406	68	10	,	,	PUNCT
ijassa-1406	68	11	and	and	CCONJ
ijassa-1406	68	12	can	can	AUX
ijassa-1406	68	13	be	be	AUX
ijassa-1406	68	14	easily	easily	ADV
ijassa-1406	68	15	incorporated	incorporate	VERB
ijassa-1406	68	16	into	into	ADP
ijassa-1406	68	17	the	the	DET
ijassa-1406	68	18	globalized	globalized	ADJ
ijassa-1406	68	19	algorithm	algorithm	NOUN
ijassa-1406	68	20	2.1	2.1	NUM
ijassa-1406	69	1	[	[	X
ijassa-1406	69	2	7	7	NUM
ijassa-1406	69	3	]	]	PUNCT
ijassa-1406	69	4	.	.	PUNCT
ijassa-1406	70	1	that	that	PRON
ijassa-1406	70	2	said	say	VERB
ijassa-1406	70	3	,	,	PUNCT
ijassa-1406	70	4	in	in	ADP
ijassa-1406	70	5	all	all	DET
ijassa-1406	70	6	the	the	DET
ijassa-1406	70	7	references	reference	NOUN
ijassa-1406	70	8	cited	cite	VERB
ijassa-1406	70	9	above	above	ADV
ijassa-1406	70	10	in	in	ADP
ijassa-1406	70	11	connection	connection	NOUN
ijassa-1406	70	12	with	with	ADP
ijassa-1406	70	13	newton	newton	NOUN
ijassa-1406	70	14	-	-	PUNCT
ijassa-1406	70	15	type	type	NOUN
ijassa-1406	70	16	methods	method	NOUN
ijassa-1406	70	17	near	near	ADP
ijassa-1406	70	18	singular	singular	ADJ
ijassa-1406	70	19	solutions	solution	NOUN
ijassa-1406	70	20	it	it	PRON
ijassa-1406	70	21	is	be	AUX
ijassa-1406	70	22	assumed	assume	VERB
ijassa-1406	70	23	that	that	SCONJ
ijassa-1406	70	24	φ	φ	PROPN
ijassa-1406	70	25	is	be	AUX
ijassa-1406	70	26	al	al	PROPN
ijassa-1406	70	27	least	least	ADV
ijassa-1406	70	28	twice	twice	ADV
ijassa-1406	70	29	differentiable	differentiable	ADJ
ijassa-1406	70	30	,	,	PUNCT
ijassa-1406	70	31	which	which	PRON
ijassa-1406	70	32	is	be	AUX
ijassa-1406	70	33	not	not	PART
ijassa-1406	70	34	the	the	DET
ijassa-1406	70	35	case	case	NOUN
ijassa-1406	70	36	for	for	ADP
ijassa-1406	70	37	the	the	DET
ijassa-1406	70	38	mapping	mapping	NOUN
ijassa-1406	70	39	defined	define	VERB
ijassa-1406	70	40	by	by	ADP
ijassa-1406	70	41	(	(	PUNCT
ijassa-1406	70	42	1.3	1.3	NUM
ijassa-1406	70	43	)	)	PUNCT
ijassa-1406	70	44	,	,	PUNCT
ijassa-1406	70	45	(	(	PUNCT
ijassa-1406	70	46	2.1	2.1	NUM
ijassa-1406	70	47	)	)	PUNCT
ijassa-1406	70	48	.	.	PUNCT
ijassa-1406	71	1	to	to	ADP
ijassa-1406	71	2	the	the	DET
ijassa-1406	71	3	best	good	ADJ
ijassa-1406	71	4	of	of	ADP
ijassa-1406	71	5	our	our	PRON
ijassa-1406	71	6	knowledge	knowledge	NOUN
ijassa-1406	71	7	,	,	PUNCT
ijassa-1406	71	8	the	the	DET
ijassa-1406	71	9	current	current	ADJ
ijassa-1406	71	10	paper	paper	NOUN
ijassa-1406	71	11	is	be	AUX
ijassa-1406	71	12	the	the	DET
ijassa-1406	71	13	first	first	ADJ
ijassa-1406	71	14	one	one	NUM
ijassa-1406	71	15	where	where	SCONJ
ijassa-1406	71	16	the	the	DET
ijassa-1406	71	17	properties	property	NOUN
ijassa-1406	71	18	in	in	ADP
ijassa-1406	71	19	question	question	NOUN
ijassa-1406	71	20	will	will	AUX
ijassa-1406	71	21	be	be	AUX
ijassa-1406	71	22	assessed	assess	VERB
ijassa-1406	71	23	for	for	ADP
ijassa-1406	71	24	equations	equation	NOUN
ijassa-1406	71	25	with	with	ADP
ijassa-1406	71	26	locally	locally	ADV
ijassa-1406	71	27	lipchitzian	lipchitzian	ADJ
ijassa-1406	71	28	first	first	ADJ
ijassa-1406	71	29	derivatives	derivative	NOUN
ijassa-1406	71	30	but	but	CCONJ
ijassa-1406	71	31	perhaps	perhaps	ADV
ijassa-1406	71	32	without	without	ADP
ijassa-1406	71	33	second	second	ADJ
ijassa-1406	71	34	derivatives	derivative	NOUN
ijassa-1406	71	35	.	.	PUNCT
ijassa-1406	72	1	copyright	copyright	NOUN
ijassa-1406	72	2	©	©	PROPN
ijassa-1406	72	3	2023	2023	NUM
ijassa-1406	72	4	assa	assa	NOUN
ijassa-1406	72	5	.	.	PUNCT
ijassa-1406	73	1	adv	adv	PROPN
ijassa-1406	73	2	syst	syst	PROPN
ijassa-1406	73	3	sci	sci	PROPN
ijassa-1406	73	4	appl	appl	PROPN
ijassa-1406	73	5	(	(	PUNCT
ijassa-1406	73	6	2023	2023	NUM
ijassa-1406	73	7	)	)	PUNCT
ijassa-1406	73	8	newton	newton	PROPN
ijassa-1406	73	9	method	method	NOUN
ijassa-1406	73	10	vs.	vs.	ADP
ijassa-1406	73	11	semismooth	semismooth	NOUN
ijassa-1406	73	12	newton	newton	PROPN
ijassa-1406	73	13	method	method	VERB
ijassa-1406	73	14	19	19	NUM
ijassa-1406	73	15	3	3	NUM
ijassa-1406	73	16	.	.	PUNCT
ijassa-1406	74	1	fischer	fischer	PROPN
ijassa-1406	74	2	–	–	PUNCT
ijassa-1406	74	3	burmeister	burmeister	NOUN
ijassa-1406	74	4	complementarity	complementarity	NOUN
ijassa-1406	74	5	function	function	NOUN
ijassa-1406	74	6	and	and	CCONJ
ijassa-1406	74	7	semismooth	semismooth	NOUN
ijassa-1406	74	8	newton	newton	PROPN
ijassa-1406	74	9	method	method	NOUN
ijassa-1406	74	10	if	if	SCONJ
ijassa-1406	74	11	one	one	PRON
ijassa-1406	74	12	does	do	AUX
ijassa-1406	74	13	not	not	PART
ijassa-1406	74	14	want	want	VERB
ijassa-1406	74	15	to	to	PART
ijassa-1406	74	16	deal	deal	VERB
ijassa-1406	74	17	with	with	ADP
ijassa-1406	74	18	potential	potential	ADJ
ijassa-1406	74	19	singularity	singularity	NOUN
ijassa-1406	74	20	of	of	ADP
ijassa-1406	74	21	solutions	solution	NOUN
ijassa-1406	74	22	(	(	PUNCT
ijassa-1406	74	23	as	as	ADP
ijassa-1406	74	24	in	in	ADP
ijassa-1406	74	25	section	section	NOUN
ijassa-1406	74	26	2	2	NUM
ijassa-1406	74	27	)	)	PUNCT
ijassa-1406	74	28	,	,	PUNCT
ijassa-1406	74	29	a	a	DET
ijassa-1406	74	30	natural	natural	ADJ
ijassa-1406	74	31	thing	thing	NOUN
ijassa-1406	74	32	to	to	PART
ijassa-1406	74	33	do	do	VERB
ijassa-1406	74	34	is	be	AUX
ijassa-1406	74	35	to	to	PART
ijassa-1406	74	36	employ	employ	VERB
ijassa-1406	74	37	different	different	ADJ
ijassa-1406	74	38	(	(	PUNCT
ijassa-1406	74	39	nonsmooth	nonsmooth	NOUN
ijassa-1406	74	40	)	)	PUNCT
ijassa-1406	74	41	complementarity	complementarity	NOUN
ijassa-1406	74	42	functions	function	NOUN
ijassa-1406	74	43	.	.	PUNCT
ijassa-1406	75	1	one	one	NUM
ijassa-1406	75	2	of	of	ADP
ijassa-1406	75	3	the	the	DET
ijassa-1406	75	4	most	most	ADV
ijassa-1406	75	5	successful	successful	ADJ
ijassa-1406	75	6	and	and	CCONJ
ijassa-1406	75	7	widely	widely	ADV
ijassa-1406	75	8	used	use	VERB
ijassa-1406	75	9	is	be	AUX
ijassa-1406	75	10	the	the	DET
ijassa-1406	75	11	so	so	ADV
ijassa-1406	75	12	-	-	PUNCT
ijassa-1406	75	13	called	call	VERB
ijassa-1406	75	14	fischer	fischer	NOUN
ijassa-1406	75	15	–	–	PUNCT
ijassa-1406	75	16	burmeister	burmeister	NOUN
ijassa-1406	75	17	complementarity	complementarity	NOUN
ijassa-1406	75	18	function	function	NOUN
ijassa-1406	75	19	defined	define	VERB
ijassa-1406	75	20	by	by	ADP
ijassa-1406	75	21	ψ(a	ψ(a	PROPN
ijassa-1406	75	22	,	,	PUNCT
ijassa-1406	75	23	b	b	NOUN
ijassa-1406	75	24	)	)	PUNCT
ijassa-1406	75	25	=	=	SYM
ijassa-1406	75	26	a+	a+	PUNCT
ijassa-1406	75	27	b−	b−	PROPN
ijassa-1406	75	28	√	√	PROPN
ijassa-1406	75	29	a2	a2	PROPN
ijassa-1406	75	30	+	+	CCONJ
ijassa-1406	75	31	b2	b2	NOUN
ijassa-1406	75	32	.	.	PUNCT
ijassa-1406	76	1	(	(	PUNCT
ijassa-1406	76	2	3.1	3.1	NUM
ijassa-1406	76	3	)	)	PUNCT
ijassa-1406	76	4	this	this	DET
ijassa-1406	76	5	function	function	NOUN
ijassa-1406	76	6	is	be	AUX
ijassa-1406	76	7	not	not	PART
ijassa-1406	76	8	differentiable	differentiable	ADJ
ijassa-1406	76	9	at	at	ADP
ijassa-1406	76	10	(	(	PUNCT
ijassa-1406	76	11	0	0	NUM
ijassa-1406	76	12	,	,	PUNCT
ijassa-1406	76	13	0	0	NUM
ijassa-1406	76	14	)	)	PUNCT
ijassa-1406	76	15	,	,	PUNCT
ijassa-1406	76	16	and	and	CCONJ
ijassa-1406	76	17	the	the	DET
ijassa-1406	76	18	corresponding	correspond	VERB
ijassa-1406	76	19	mapping	mapping	NOUN
ijassa-1406	76	20	φ	φ	PROPN
ijassa-1406	76	21	defined	define	VERB
ijassa-1406	76	22	in	in	ADP
ijassa-1406	76	23	(	(	PUNCT
ijassa-1406	76	24	1.3	1.3	NUM
ijassa-1406	76	25	)	)	PUNCT
ijassa-1406	76	26	need	need	AUX
ijassa-1406	76	27	not	not	PART
ijassa-1406	76	28	be	be	AUX
ijassa-1406	76	29	differentiable	differentiable	ADJ
ijassa-1406	76	30	at	at	ADP
ijassa-1406	76	31	u	u	PROPN
ijassa-1406	76	32	∈	∈	PROPN
ijassa-1406	76	33	rp	rp	NOUN
ijassa-1406	76	34	with	with	ADP
ijassa-1406	76	35	ui	ui	PROPN
ijassa-1406	76	36	=	=	PUNCT
ijassa-1406	76	37	fi(u	fi(u	NOUN
ijassa-1406	76	38	)	)	PUNCT
ijassa-1406	76	39	=	=	SYM
ijassa-1406	76	40	0	0	NUM
ijassa-1406	76	41	for	for	ADP
ijassa-1406	76	42	at	at	ADV
ijassa-1406	76	43	least	least	ADV
ijassa-1406	76	44	one	one	NUM
ijassa-1406	76	45	i	i	PRON
ijassa-1406	76	46	∈	∈	PROPN
ijassa-1406	76	47	{	{	PUNCT
ijassa-1406	76	48	1	1	NUM
ijassa-1406	76	49	,	,	PUNCT
ijassa-1406	76	50	.	.	PUNCT
ijassa-1406	76	51	.	.	PUNCT
ijassa-1406	77	1	.	.	PUNCT
ijassa-1406	78	1	,	,	PUNCT
ijassa-1406	78	2	p	p	X
ijassa-1406	78	3	}	}	PUNCT
ijassa-1406	78	4	,	,	PUNCT
ijassa-1406	78	5	no	no	ADV
ijassa-1406	78	6	matter	matter	ADV
ijassa-1406	78	7	how	how	SCONJ
ijassa-1406	78	8	smooth	smooth	ADJ
ijassa-1406	78	9	is	be	AUX
ijassa-1406	78	10	f	f	PROPN
ijassa-1406	78	11	.	.	PUNCT
ijassa-1406	79	1	in	in	ADP
ijassa-1406	79	2	particular	particular	ADJ
ijassa-1406	79	3	,	,	PUNCT
ijassa-1406	79	4	φ	φ	PROPN
ijassa-1406	79	5	need	need	AUX
ijassa-1406	79	6	not	not	PART
ijassa-1406	79	7	be	be	AUX
ijassa-1406	79	8	differentiable	differentiable	ADJ
ijassa-1406	79	9	at	at	ADP
ijassa-1406	79	10	a	a	DET
ijassa-1406	79	11	solution	solution	NOUN
ijassa-1406	79	12	violating	violate	VERB
ijassa-1406	79	13	strict	strict	ADJ
ijassa-1406	79	14	complementarity	complementarity	NOUN
ijassa-1406	79	15	.	.	PUNCT
ijassa-1406	80	1	at	at	ADP
ijassa-1406	80	2	the	the	DET
ijassa-1406	80	3	same	same	ADJ
ijassa-1406	80	4	time	time	NOUN
ijassa-1406	80	5	,	,	PUNCT
ijassa-1406	80	6	if	if	SCONJ
ijassa-1406	80	7	f	f	PROPN
ijassa-1406	80	8	is	be	AUX
ijassa-1406	80	9	differentiable	differentiable	ADJ
ijassa-1406	80	10	near	near	ADP
ijassa-1406	80	11	u	u	PROPN
ijassa-1406	80	12	∈	∈	PROPN
ijassa-1406	80	13	rp	rp	NOUN
ijassa-1406	80	14	,	,	PUNCT
ijassa-1406	80	15	with	with	ADP
ijassa-1406	80	16	f	f	PROPN
ijassa-1406	80	17	′	′	NUM
ijassa-1406	80	18	being	be	AUX
ijassa-1406	80	19	continuous	continuous	ADJ
ijassa-1406	80	20	at	at	ADP
ijassa-1406	80	21	u	u	NOUN
ijassa-1406	80	22	,	,	PUNCT
ijassa-1406	80	23	then	then	ADV
ijassa-1406	80	24	φ	φ	PROPN
ijassa-1406	80	25	is	be	AUX
ijassa-1406	80	26	lipschitz	lipschitz	NOUN
ijassa-1406	80	27	continuous	continuous	ADJ
ijassa-1406	80	28	at	at	ADP
ijassa-1406	80	29	u	u	NOUN
ijassa-1406	80	30	,	,	PUNCT
ijassa-1406	80	31	and	and	CCONJ
ijassa-1406	80	32	even	even	ADV
ijassa-1406	80	33	semismooth	semismooth	VERB
ijassa-1406	80	34	at	at	ADP
ijassa-1406	80	35	u	u	NOUN
ijassa-1406	80	36	;	;	PUNCT
ijassa-1406	80	37	see	see	VERB
ijassa-1406	80	38	[	[	X
ijassa-1406	80	39	15	15	NUM
ijassa-1406	80	40	,	,	PUNCT
ijassa-1406	80	41	proposition	proposition	NOUN
ijassa-1406	80	42	3.8	3.8	NUM
ijassa-1406	80	43	]	]	PUNCT
ijassa-1406	80	44	therefore	therefore	ADV
ijassa-1406	80	45	,	,	PUNCT
ijassa-1406	80	46	even	even	ADV
ijassa-1406	80	47	though	though	SCONJ
ijassa-1406	80	48	the	the	DET
ijassa-1406	80	49	newton	newton	PROPN
ijassa-1406	80	50	method	method	NOUN
ijassa-1406	80	51	is	be	AUX
ijassa-1406	80	52	in	in	ADP
ijassa-1406	80	53	general	general	ADJ
ijassa-1406	80	54	not	not	PART
ijassa-1406	80	55	applicable	applicable	ADJ
ijassa-1406	80	56	to	to	ADP
ijassa-1406	80	57	equation	equation	NOUN
ijassa-1406	80	58	(	(	PUNCT
ijassa-1406	80	59	1.2	1.2	NUM
ijassa-1406	80	60	)	)	PUNCT
ijassa-1406	80	61	with	with	ADP
ijassa-1406	80	62	φ	φ	PROPN
ijassa-1406	80	63	defined	define	VERB
ijassa-1406	80	64	according	accord	VERB
ijassa-1406	80	65	to	to	ADP
ijassa-1406	80	66	(	(	PUNCT
ijassa-1406	80	67	1.3	1.3	NUM
ijassa-1406	80	68	)	)	PUNCT
ijassa-1406	80	69	,	,	PUNCT
ijassa-1406	80	70	(	(	PUNCT
ijassa-1406	80	71	3.1	3.1	NUM
ijassa-1406	80	72	)	)	PUNCT
ijassa-1406	80	73	,	,	PUNCT
ijassa-1406	80	74	one	one	PRON
ijassa-1406	80	75	can	can	AUX
ijassa-1406	80	76	make	make	VERB
ijassa-1406	80	77	use	use	NOUN
ijassa-1406	80	78	of	of	ADP
ijassa-1406	80	79	the	the	DET
ijassa-1406	80	80	so	so	ADV
ijassa-1406	80	81	-	-	PUNCT
ijassa-1406	80	82	called	call	VERB
ijassa-1406	80	83	semismooth	semismooth	NOUN
ijassa-1406	80	84	newton	newton	PROPN
ijassa-1406	80	85	method	method	NOUN
ijassa-1406	81	1	[	[	X
ijassa-1406	81	2	15	15	NUM
ijassa-1406	81	3	,	,	PUNCT
ijassa-1406	81	4	section	section	NOUN
ijassa-1406	81	5	2.4.1	2.4.1	NUM
ijassa-1406	81	6	]	]	PUNCT
ijassa-1406	81	7	,	,	PUNCT
ijassa-1406	81	8	which	which	PRON
ijassa-1406	81	9	is	be	AUX
ijassa-1406	81	10	the	the	DET
ijassa-1406	81	11	iterative	iterative	ADJ
ijassa-1406	81	12	procedure	procedure	NOUN
ijassa-1406	81	13	specified	specify	VERB
ijassa-1406	81	14	above	above	ADV
ijassa-1406	81	15	for	for	ADP
ijassa-1406	81	16	newton	newton	PROPN
ijassa-1406	81	17	method	method	NOUN
ijassa-1406	81	18	,	,	PUNCT
ijassa-1406	81	19	but	but	CCONJ
ijassa-1406	81	20	with	with	ADP
ijassa-1406	81	21	the	the	DET
ijassa-1406	81	22	iteration	iteration	NOUN
ijassa-1406	81	23	equation	equation	NOUN
ijassa-1406	81	24	(	(	PUNCT
ijassa-1406	81	25	2.3	2.3	NUM
ijassa-1406	81	26	)	)	PUNCT
ijassa-1406	81	27	replaced	replace	VERB
ijassa-1406	81	28	by	by	ADP
ijassa-1406	81	29	φ(uk	φ(uk	NOUN
ijassa-1406	81	30	)	)	PUNCT
ijassa-1406	81	31	+	+	CCONJ
ijassa-1406	81	32	jkv	jkv	X
ijassa-1406	81	33	=	=	SYM
ijassa-1406	81	34	0	0	NUM
ijassa-1406	81	35	,	,	PUNCT
ijassa-1406	81	36	(	(	PUNCT
ijassa-1406	81	37	3.2	3.2	NUM
ijassa-1406	81	38	)	)	PUNCT
ijassa-1406	81	39	where	where	SCONJ
ijassa-1406	81	40	jk	jk	PROPN
ijassa-1406	81	41	is	be	AUX
ijassa-1406	81	42	some	some	DET
ijassa-1406	81	43	element	element	NOUN
ijassa-1406	81	44	of	of	ADP
ijassa-1406	81	45	∂bφ(uk	∂bφ(uk	ADJ
ijassa-1406	81	46	)	)	PUNCT
ijassa-1406	81	47	,	,	PUNCT
ijassa-1406	81	48	here	here	ADV
ijassa-1406	81	49	,	,	PUNCT
ijassa-1406	81	50	for	for	ADP
ijassa-1406	81	51	any	any	DET
ijassa-1406	81	52	u	u	PROPN
ijassa-1406	81	53	∈	∈	PROPN
ijassa-1406	81	54	rp	rp	NOUN
ijassa-1406	81	55	,	,	PUNCT
ijassa-1406	81	56	∂bφ(u	∂bφ(u	PROPN
ijassa-1406	81	57	)	)	PUNCT
ijassa-1406	82	1	=	=	PRON
ijassa-1406	82	2	{	{	PUNCT
ijassa-1406	82	3	j	j	NOUN
ijassa-1406	82	4	∈	∈	PROPN
ijassa-1406	83	1	rp×p	rp×p	PROPN
ijassa-1406	84	1	|	|	ADV
ijassa-1406	84	2	∃	∃	PROPN
ijassa-1406	84	3	{	{	PUNCT
ijassa-1406	84	4	uj	uj	PROPN
ijassa-1406	84	5	}	}	PUNCT
ijassa-1406	84	6	⊂	⊂	PROPN
ijassa-1406	84	7	sφ	sφ	PROPN
ijassa-1406	84	8	:	:	PUNCT
ijassa-1406	84	9	{	{	PUNCT
ijassa-1406	84	10	uj	uj	PROPN
ijassa-1406	84	11	}	}	PUNCT
ijassa-1406	84	12	→	→	SYM
ijassa-1406	84	13	u	u	NOUN
ijassa-1406	84	14	,	,	PUNCT
ijassa-1406	84	15	{	{	PUNCT
ijassa-1406	84	16	φ(uj	φ(uj	NOUN
ijassa-1406	84	17	)	)	PUNCT
ijassa-1406	84	18	}	}	PUNCT
ijassa-1406	84	19	→	→	SYM
ijassa-1406	84	20	j	j	X
ijassa-1406	84	21	}	}	PUNCT
ijassa-1406	84	22	,	,	PUNCT
ijassa-1406	84	23	is	be	AUX
ijassa-1406	84	24	the	the	DET
ijassa-1406	84	25	so	so	ADV
ijassa-1406	84	26	-	-	PUNCT
ijassa-1406	84	27	called	call	VERB
ijassa-1406	84	28	b	b	NOUN
ijassa-1406	84	29	-	-	PUNCT
ijassa-1406	84	30	differential	differential	NOUN
ijassa-1406	84	31	of	of	ADP
ijassa-1406	84	32	φ	φ	PROPN
ijassa-1406	84	33	at	at	ADP
ijassa-1406	84	34	u	u	NOUN
ijassa-1406	84	35	,	,	PUNCT
ijassa-1406	84	36	with	with	ADP
ijassa-1406	84	37	sφ	sφ	PROPN
ijassa-1406	84	38	standing	stand	VERB
ijassa-1406	84	39	for	for	ADP
ijassa-1406	84	40	the	the	DET
ijassa-1406	84	41	set	set	NOUN
ijassa-1406	84	42	of	of	ADP
ijassa-1406	84	43	all	all	DET
ijassa-1406	84	44	points	point	NOUN
ijassa-1406	84	45	where	where	SCONJ
ijassa-1406	84	46	φ	φ	PROPN
ijassa-1406	84	47	is	be	AUX
ijassa-1406	84	48	differentiable	differentiable	ADJ
ijassa-1406	84	49	;	;	PUNCT
ijassa-1406	84	50	see	see	VERB
ijassa-1406	84	51	,	,	PUNCT
ijassa-1406	84	52	e.g.	e.g.	ADV
ijassa-1406	84	53	,	,	PUNCT
ijassa-1406	84	54	[	[	X
ijassa-1406	84	55	15	15	NUM
ijassa-1406	84	56	,	,	PUNCT
ijassa-1406	84	57	section	section	NOUN
ijassa-1406	84	58	1.4.1	1.4.1	NUM
ijassa-1406	84	59	]	]	PUNCT
ijassa-1406	84	60	.	.	PUNCT
ijassa-1406	85	1	if	if	SCONJ
ijassa-1406	85	2	ū	ū	NOUN
ijassa-1406	85	3	is	be	AUX
ijassa-1406	85	4	a	a	DET
ijassa-1406	85	5	solution	solution	NOUN
ijassa-1406	85	6	of	of	ADP
ijassa-1406	85	7	ncp	ncp	PROPN
ijassa-1406	85	8	(	(	PUNCT
ijassa-1406	85	9	1.1	1.1	NUM
ijassa-1406	85	10	)	)	PUNCT
ijassa-1406	85	11	,	,	PUNCT
ijassa-1406	85	12	and	and	CCONJ
ijassa-1406	85	13	all	all	DET
ijassa-1406	85	14	matrices	matrix	NOUN
ijassa-1406	85	15	in	in	ADP
ijassa-1406	85	16	∂bφ(ū	∂bφ(ū	PROPN
ijassa-1406	85	17	)	)	PUNCT
ijassa-1406	85	18	are	be	AUX
ijassa-1406	85	19	nonsingular	nonsingular	ADJ
ijassa-1406	85	20	,	,	PUNCT
ijassa-1406	85	21	then	then	ADV
ijassa-1406	85	22	,	,	PUNCT
ijassa-1406	85	23	according	accord	VERB
ijassa-1406	85	24	to	to	ADP
ijassa-1406	85	25	[	[	X
ijassa-1406	85	26	15	15	NUM
ijassa-1406	85	27	,	,	PUNCT
ijassa-1406	85	28	theorem	theorem	VERB
ijassa-1406	85	29	2.42	2.42	NUM
ijassa-1406	85	30	]	]	PUNCT
ijassa-1406	85	31	,	,	PUNCT
ijassa-1406	85	32	for	for	ADP
ijassa-1406	85	33	any	any	DET
ijassa-1406	85	34	u0	u0	PROPN
ijassa-1406	85	35	∈	∈	PROPN
ijassa-1406	85	36	rp	rp	NOUN
ijassa-1406	85	37	close	close	VERB
ijassa-1406	85	38	enough	enough	ADV
ijassa-1406	85	39	to	to	ADP
ijassa-1406	85	40	ū	ū	VERB
ijassa-1406	85	41	,	,	PUNCT
ijassa-1406	85	42	the	the	DET
ijassa-1406	85	43	semismooth	semismooth	NOUN
ijassa-1406	85	44	newton	newton	PROPN
ijassa-1406	85	45	method	method	NOUN
ijassa-1406	85	46	uniquely	uniquely	ADV
ijassa-1406	85	47	defines	define	VERB
ijassa-1406	85	48	a	a	DET
ijassa-1406	85	49	sequence	sequence	NOUN
ijassa-1406	85	50	{	{	PUNCT
ijassa-1406	85	51	uk	uk	PROPN
ijassa-1406	85	52	}	}	PUNCT
ijassa-1406	85	53	,	,	PUNCT
ijassa-1406	85	54	and	and	CCONJ
ijassa-1406	85	55	this	this	DET
ijassa-1406	85	56	sequence	sequence	NOUN
ijassa-1406	85	57	converges	converge	VERB
ijassa-1406	85	58	to	to	ADP
ijassa-1406	85	59	ū	ū	NOUN
ijassa-1406	85	60	superlinearly	superlinearly	ADV
ijassa-1406	85	61	,	,	PUNCT
ijassa-1406	85	62	or	or	CCONJ
ijassa-1406	85	63	even	even	ADV
ijassa-1406	85	64	quadratically	quadratically	ADV
ijassa-1406	85	65	under	under	ADP
ijassa-1406	85	66	further	further	ADJ
ijassa-1406	85	67	smoothness	smoothness	ADJ
ijassa-1406	85	68	assumptions	assumption	NOUN
ijassa-1406	85	69	on	on	ADP
ijassa-1406	85	70	f	f	PROPN
ijassa-1406	85	71	.	.	PUNCT
ijassa-1406	86	1	the	the	DET
ijassa-1406	86	2	upper	upper	ADJ
ijassa-1406	86	3	estimate	estimate	NOUN
ijassa-1406	86	4	of	of	ADP
ijassa-1406	86	5	∂bφ(u	∂bφ(u	NOUN
ijassa-1406	86	6	)	)	PUNCT
ijassa-1406	86	7	for	for	ADP
ijassa-1406	86	8	φ	φ	NUM
ijassa-1406	86	9	defined	define	VERB
ijassa-1406	86	10	according	accord	VERB
ijassa-1406	86	11	to	to	ADP
ijassa-1406	86	12	(	(	PUNCT
ijassa-1406	86	13	1.3	1.3	NUM
ijassa-1406	86	14	)	)	PUNCT
ijassa-1406	86	15	,	,	PUNCT
ijassa-1406	86	16	(	(	PUNCT
ijassa-1406	86	17	3.1	3.1	NUM
ijassa-1406	86	18	)	)	PUNCT
ijassa-1406	86	19	is	be	AUX
ijassa-1406	86	20	given	give	VERB
ijassa-1406	86	21	in	in	ADP
ijassa-1406	86	22	[	[	X
ijassa-1406	86	23	15	15	NUM
ijassa-1406	86	24	,	,	PUNCT
ijassa-1406	86	25	proposition	proposition	NOUN
ijassa-1406	86	26	3.11	3.11	NUM
ijassa-1406	86	27	]	]	PUNCT
ijassa-1406	86	28	:	:	PUNCT
ijassa-1406	86	29	the	the	DET
ijassa-1406	86	30	rows	row	NOUN
ijassa-1406	86	31	of	of	ADP
ijassa-1406	86	32	any	any	DET
ijassa-1406	86	33	matrix	matrix	NOUN
ijassa-1406	86	34	j	j	PROPN
ijassa-1406	86	35	∈	∈	PROPN
ijassa-1406	86	36	∂bφ(u	∂bφ(u	PROPN
ijassa-1406	86	37	)	)	PUNCT
ijassa-1406	86	38	satisfy	satisfy	VERB
ijassa-1406	86	39	the	the	DET
ijassa-1406	86	40	equalities	equality	NOUN
ijassa-1406	87	1	ji	ji	X
ijassa-1406	88	1	=	=	PUNCT
ijassa-1406	88	2			PRON
ijassa-1406	88	3	αif	αif	NOUN
ijassa-1406	88	4	′	′	NUM
ijassa-1406	89	1	i	i	PRON
ijassa-1406	89	2	(	(	PUNCT
ijassa-1406	89	3	u	u	NOUN
ijassa-1406	89	4	)	)	PUNCT
ijassa-1406	89	5	+	+	CCONJ
ijassa-1406	89	6	βie	βie	VERB
ijassa-1406	89	7	i	i	PRON
ijassa-1406	89	8	if	if	SCONJ
ijassa-1406	89	9	ui	ui	NOUN
ijassa-1406	89	10	=	=	NOUN
ijassa-1406	89	11	fi(u	fi(u	NOUN
ijassa-1406	89	12	)	)	PUNCT
ijassa-1406	89	13	=	=	SYM
ijassa-1406	89	14	0	0	NUM
ijassa-1406	89	15	,	,	PUNCT
ijassa-1406	89	16	f	f	NOUN
ijassa-1406	89	17	′	′	NUM
ijassa-1406	90	1	i	i	PRON
ijassa-1406	90	2	(	(	PUNCT
ijassa-1406	90	3	u	u	NOUN
ijassa-1406	90	4	)	)	PUNCT
ijassa-1406	90	5	+	+	CCONJ
ijassa-1406	90	6	ei	ei	X
ijassa-1406	90	7	−	−	NOUN
ijassa-1406	90	8	fi(u)f	fi(u)f	NUM
ijassa-1406	90	9	′	′	NUM
ijassa-1406	91	1	i	i	PRON
ijassa-1406	91	2	(	(	PUNCT
ijassa-1406	91	3	u	u	NOUN
ijassa-1406	91	4	)	)	PUNCT
ijassa-1406	91	5	+	+	CCONJ
ijassa-1406	91	6	uie	uie	PROPN
ijassa-1406	91	7	i√	i√	VERB
ijassa-1406	91	8	u2i	u2i	X
ijassa-1406	91	9	+	+	PUNCT
ijassa-1406	91	10	(	(	PUNCT
ijassa-1406	91	11	fi(u))2	fi(u))2	PROPN
ijassa-1406	91	12	if	if	SCONJ
ijassa-1406	91	13	ui	ui	PROPN
ijassa-1406	91	14	̸=	̸=	PROPN
ijassa-1406	91	15	0	0	NUM
ijassa-1406	91	16	or	or	CCONJ
ijassa-1406	91	17	fi(u	fi(u	NOUN
ijassa-1406	91	18	)	)	PUNCT
ijassa-1406	91	19	̸=	̸=	PROPN
ijassa-1406	91	20	0	0	NUM
ijassa-1406	91	21	,	,	PUNCT
ijassa-1406	91	22	i	i	PRON
ijassa-1406	91	23	=	=	NOUN
ijassa-1406	91	24	1	1	NUM
ijassa-1406	91	25	,	,	PUNCT
ijassa-1406	91	26	.	.	PUNCT
ijassa-1406	91	27	.	.	PUNCT
ijassa-1406	91	28	.	.	PUNCT
ijassa-1406	92	1	,	,	PUNCT
ijassa-1406	93	1	p	p	X
ijassa-1406	93	2	,	,	PUNCT
ijassa-1406	93	3	(	(	PUNCT
ijassa-1406	93	4	3.3	3.3	NUM
ijassa-1406	93	5	)	)	PUNCT
ijassa-1406	93	6	with	with	ADP
ijassa-1406	93	7	some	some	DET
ijassa-1406	93	8	(	(	PUNCT
ijassa-1406	93	9	αi	αi	NOUN
ijassa-1406	93	10	,	,	PUNCT
ijassa-1406	93	11	βi	βi	PRON
ijassa-1406	93	12	)	)	PUNCT
ijassa-1406	93	13	∈	∈	PROPN
ijassa-1406	93	14	s	s	PART
ijassa-1406	93	15	for	for	ADP
ijassa-1406	93	16	i	i	PROPN
ijassa-1406	93	17	=	=	NOUN
ijassa-1406	93	18	1	1	NUM
ijassa-1406	93	19	,	,	PUNCT
ijassa-1406	93	20	.	.	PUNCT
ijassa-1406	93	21	.	.	PUNCT
ijassa-1406	93	22	.	.	PUNCT
ijassa-1406	94	1	,	,	PUNCT
ijassa-1406	94	2	p	p	X
ijassa-1406	94	3	such	such	ADJ
ijassa-1406	94	4	that	that	DET
ijassa-1406	94	5	ui	ui	NOUN
ijassa-1406	94	6	=	=	NOUN
ijassa-1406	94	7	fi(u	fi(u	NOUN
ijassa-1406	94	8	)	)	PUNCT
ijassa-1406	94	9	=	=	SYM
ijassa-1406	94	10	0	0	NUM
ijassa-1406	94	11	,	,	PUNCT
ijassa-1406	94	12	where	where	SCONJ
ijassa-1406	94	13	s	s	VERB
ijassa-1406	94	14	=	=	X
ijassa-1406	94	15	{	{	PUNCT
ijassa-1406	94	16	(	(	PUNCT
ijassa-1406	94	17	a	a	PRON
ijassa-1406	94	18	,	,	PUNCT
ijassa-1406	94	19	b	b	NOUN
ijassa-1406	94	20	)	)	PUNCT
ijassa-1406	94	21	∈	∈	NOUN
ijassa-1406	94	22	r2	r2	NOUN
ijassa-1406	94	23	|	|	ADV
ijassa-1406	94	24	(	(	PUNCT
ijassa-1406	94	25	a−	a−	PROPN
ijassa-1406	94	26	1)2	1)2	NUM
ijassa-1406	94	27	+	+	CCONJ
ijassa-1406	94	28	(	(	PUNCT
ijassa-1406	94	29	b−	b−	PROPN
ijassa-1406	94	30	1)2	1)2	NUM
ijassa-1406	94	31	=	=	SYM
ijassa-1406	94	32	1	1	NUM
ijassa-1406	94	33	}	}	PUNCT
ijassa-1406	94	34	.	.	PUNCT
ijassa-1406	95	1	this	this	DET
ijassa-1406	95	2	upper	upper	ADJ
ijassa-1406	95	3	estimate	estimate	NOUN
ijassa-1406	95	4	serves	serve	VERB
ijassa-1406	95	5	as	as	ADP
ijassa-1406	95	6	the	the	DET
ijassa-1406	95	7	basis	basis	NOUN
ijassa-1406	95	8	for	for	ADP
ijassa-1406	95	9	practical	practical	ADJ
ijassa-1406	95	10	procedures	procedure	NOUN
ijassa-1406	95	11	allowing	allow	VERB
ijassa-1406	95	12	to	to	PART
ijassa-1406	95	13	compute	compute	VERB
ijassa-1406	95	14	an	an	DET
ijassa-1406	95	15	element	element	NOUN
ijassa-1406	95	16	jk	jk	PROPN
ijassa-1406	95	17	∈	∈	PROPN
ijassa-1406	95	18	∂bφ(u	∂bφ(u	PROPN
ijassa-1406	95	19	k	k	PROPN
ijassa-1406	95	20	)	)	PUNCT
ijassa-1406	95	21	,	,	PUNCT
ijassa-1406	95	22	to	to	PART
ijassa-1406	95	23	be	be	AUX
ijassa-1406	95	24	used	use	VERB
ijassa-1406	95	25	in	in	ADP
ijassa-1406	95	26	(	(	PUNCT
ijassa-1406	95	27	3.2	3.2	NUM
ijassa-1406	95	28	)	)	PUNCT
ijassa-1406	95	29	;	;	PUNCT
ijassa-1406	95	30	see	see	VERB
ijassa-1406	95	31	,	,	PUNCT
ijassa-1406	95	32	e.g.	e.g.	ADV
ijassa-1406	95	33	,	,	PUNCT
ijassa-1406	95	34	[	[	X
ijassa-1406	95	35	15	15	NUM
ijassa-1406	95	36	,	,	PUNCT
ijassa-1406	95	37	p.	p.	NOUN
ijassa-1406	95	38	161	161	NUM
ijassa-1406	95	39	]	]	PUNCT
ijassa-1406	95	40	.	.	PUNCT
ijassa-1406	96	1	however	however	ADV
ijassa-1406	96	2	,	,	PUNCT
ijassa-1406	96	3	in	in	ADP
ijassa-1406	96	4	section	section	NOUN
ijassa-1406	96	5	4	4	NUM
ijassa-1406	96	6	,	,	PUNCT
ijassa-1406	96	7	we	we	PRON
ijassa-1406	96	8	employ	employ	VERB
ijassa-1406	96	9	the	the	DET
ijassa-1406	96	10	upper	upper	ADJ
ijassa-1406	96	11	estimate	estimate	NOUN
ijassa-1406	96	12	above	above	ADP
ijassa-1406	96	13	directly	directly	ADV
ijassa-1406	96	14	,	,	PUNCT
ijassa-1406	96	15	i.e.	i.e.	X
ijassa-1406	96	16	,	,	PUNCT
ijassa-1406	96	17	we	we	PRON
ijassa-1406	96	18	pick	pick	VERB
ijassa-1406	96	19	up	up	ADP
ijassa-1406	96	20	jk	jk	PROPN
ijassa-1406	96	21	in	in	ADP
ijassa-1406	96	22	(	(	PUNCT
ijassa-1406	96	23	3.2	3.2	NUM
ijassa-1406	96	24	)	)	PUNCT
ijassa-1406	96	25	as	as	ADP
ijassa-1406	96	26	some	some	DET
ijassa-1406	96	27	matrix	matrix	NOUN
ijassa-1406	96	28	with	with	ADP
ijassa-1406	96	29	rows	row	NOUN
ijassa-1406	96	30	satisfying	satisfy	VERB
ijassa-1406	96	31	(	(	PUNCT
ijassa-1406	96	32	3.3	3.3	NUM
ijassa-1406	96	33	)	)	PUNCT
ijassa-1406	96	34	for	for	ADP
ijassa-1406	96	35	u	u	NOUN
ijassa-1406	96	36	=	=	PROPN
ijassa-1406	96	37	uk	uk	PROPN
ijassa-1406	96	38	.	.	PUNCT
ijassa-1406	97	1	this	this	DET
ijassa-1406	97	2	choice	choice	NOUN
ijassa-1406	97	3	is	be	AUX
ijassa-1406	97	4	not	not	PART
ijassa-1406	97	5	fully	fully	ADV
ijassa-1406	97	6	clean	clean	ADJ
ijassa-1406	97	7	theoretically	theoretically	ADV
ijassa-1406	97	8	,	,	PUNCT
ijassa-1406	97	9	but	but	CCONJ
ijassa-1406	97	10	it	it	PRON
ijassa-1406	97	11	is	be	AUX
ijassa-1406	97	12	somehow	somehow	ADV
ijassa-1406	97	13	practically	practically	ADV
ijassa-1406	97	14	justified	justified	ADJ
ijassa-1406	97	15	,	,	PUNCT
ijassa-1406	97	16	in	in	ADP
ijassa-1406	97	17	particular	particular	ADJ
ijassa-1406	97	18	,	,	PUNCT
ijassa-1406	97	19	by	by	ADP
ijassa-1406	97	20	the	the	DET
ijassa-1406	97	21	natural	natural	ADJ
ijassa-1406	97	22	expectation	expectation	NOUN
ijassa-1406	97	23	that	that	SCONJ
ijassa-1406	97	24	the	the	DET
ijassa-1406	97	25	case	case	NOUN
ijassa-1406	97	26	when	when	SCONJ
ijassa-1406	97	27	uki	uki	PROPN
ijassa-1406	97	28	=	=	SYM
ijassa-1406	97	29	fi(u	fi(u	NOUN
ijassa-1406	97	30	k	k	NOUN
ijassa-1406	97	31	)	)	PUNCT
ijassa-1406	97	32	=	=	SYM
ijassa-1406	97	33	0	0	NUM
ijassa-1406	97	34	for	for	ADP
ijassa-1406	97	35	some	some	DET
ijassa-1406	97	36	i	i	PRON
ijassa-1406	97	37	∈	∈	PROPN
ijassa-1406	97	38	{	{	PUNCT
ijassa-1406	97	39	1	1	NUM
ijassa-1406	97	40	,	,	PUNCT
ijassa-1406	97	41	.	.	PUNCT
ijassa-1406	97	42	.	.	PUNCT
ijassa-1406	97	43	.	.	PUNCT
ijassa-1406	98	1	,	,	PUNCT
ijassa-1406	98	2	p	p	X
ijassa-1406	98	3	}	}	PUNCT
ijassa-1406	98	4	will	will	AUX
ijassa-1406	98	5	not	not	PART
ijassa-1406	98	6	be	be	AUX
ijassa-1406	98	7	encountered	encounter	VERB
ijassa-1406	98	8	along	along	ADP
ijassa-1406	98	9	the	the	DET
ijassa-1406	98	10	iteration	iteration	NOUN
ijassa-1406	98	11	sequences	sequence	NOUN
ijassa-1406	98	12	{	{	PUNCT
ijassa-1406	98	13	uk	uk	PROPN
ijassa-1406	98	14	}	}	PUNCT
ijassa-1406	98	15	,	,	PUNCT
ijassa-1406	98	16	and	and	CCONJ
ijassa-1406	98	17	hence	hence	ADV
ijassa-1406	98	18	,	,	PUNCT
ijassa-1406	98	19	φ	φ	PROPN
ijassa-1406	98	20	will	will	AUX
ijassa-1406	98	21	differentiable	differentiable	VERB
ijassa-1406	98	22	at	at	ADP
ijassa-1406	98	23	uk	uk	PROPN
ijassa-1406	98	24	,	,	PUNCT
ijassa-1406	98	25	and	and	CCONJ
ijassa-1406	98	26	the	the	DET
ijassa-1406	98	27	upper	upper	ADJ
ijassa-1406	98	28	estimate	estimate	NOUN
ijassa-1406	98	29	of	of	ADP
ijassa-1406	98	30	∂bφ(uk	∂bφ(uk	ADJ
ijassa-1406	98	31	)	)	PUNCT
ijassa-1406	98	32	given	give	VERB
ijassa-1406	98	33	be	be	NOUN
ijassa-1406	98	34	(	(	PUNCT
ijassa-1406	98	35	3.3	3.3	NUM
ijassa-1406	98	36	)	)	PUNCT
ijassa-1406	98	37	will	will	AUX
ijassa-1406	98	38	reduce	reduce	VERB
ijassa-1406	98	39	to	to	ADP
ijassa-1406	98	40	{	{	PUNCT
ijassa-1406	98	41	φ′(uk	φ′(uk	PROPN
ijassa-1406	98	42	)	)	PUNCT
ijassa-1406	98	43	}	}	PUNCT
ijassa-1406	98	44	,	,	PUNCT
ijassa-1406	98	45	for	for	SCONJ
ijassa-1406	98	46	all	all	DET
ijassa-1406	98	47	k.	k.	PROPN
ijassa-1406	98	48	as	as	ADP
ijassa-1406	98	49	for	for	ADP
ijassa-1406	98	50	globalization	globalization	NOUN
ijassa-1406	98	51	of	of	ADP
ijassa-1406	98	52	convergence	convergence	NOUN
ijassa-1406	98	53	,	,	PUNCT
ijassa-1406	98	54	we	we	PRON
ijassa-1406	98	55	next	next	VERB
ijassa-1406	98	56	present	present	VERB
ijassa-1406	98	57	a	a	DET
ijassa-1406	98	58	counterpart	counterpart	NOUN
ijassa-1406	98	59	of	of	ADP
ijassa-1406	98	60	algorithm	algorithm	NOUN
ijassa-1406	98	61	2.1	2.1	NUM
ijassa-1406	98	62	for	for	ADP
ijassa-1406	98	63	the	the	DET
ijassa-1406	98	64	semismooth	semismooth	NOUN
ijassa-1406	98	65	newton	newton	PROPN
ijassa-1406	98	66	method	method	PROPN
ijassa-1406	98	67	.	.	PUNCT
ijassa-1406	99	1	copyright	copyright	NOUN
ijassa-1406	99	2	©	©	PROPN
ijassa-1406	99	3	2023	2023	NUM
ijassa-1406	99	4	assa	assa	NOUN
ijassa-1406	99	5	.	.	PUNCT
ijassa-1406	100	1	adv	adv	PROPN
ijassa-1406	100	2	syst	syst	PROPN
ijassa-1406	100	3	sci	sci	PROPN
ijassa-1406	100	4	appl	appl	PROPN
ijassa-1406	100	5	(	(	PUNCT
ijassa-1406	100	6	2023	2023	NUM
ijassa-1406	100	7	)	)	PUNCT
ijassa-1406	100	8	20	20	NUM
ijassa-1406	100	9	a.	a.	NOUN
ijassa-1406	100	10	izmailov	izmailov	NOUN
ijassa-1406	100	11	,	,	PUNCT
ijassa-1406	100	12	e.	e.	PROPN
ijassa-1406	100	13	uskov	uskov	PROPN
ijassa-1406	100	14	,	,	PUNCT
ijassa-1406	100	15	y.	y.	PROPN
ijassa-1406	100	16	zhibai	zhibai	PROPN
ijassa-1406	100	17	algorithm	algorithm	PROPN
ijassa-1406	100	18	3.1	3.1	NUM
ijassa-1406	100	19	:	:	PUNCT
ijassa-1406	100	20	define	define	VERB
ijassa-1406	100	21	the	the	DET
ijassa-1406	100	22	mapping	mapping	NOUN
ijassa-1406	100	23	φ	φ	NOUN
ijassa-1406	100	24	according	accord	VERB
ijassa-1406	100	25	to	to	ADP
ijassa-1406	100	26	(	(	PUNCT
ijassa-1406	100	27	1.3	1.3	NUM
ijassa-1406	100	28	)	)	PUNCT
ijassa-1406	100	29	,	,	PUNCT
ijassa-1406	100	30	(	(	PUNCT
ijassa-1406	100	31	3.1	3.1	NUM
ijassa-1406	100	32	)	)	PUNCT
ijassa-1406	100	33	.	.	PUNCT
ijassa-1406	101	1	choose	choose	VERB
ijassa-1406	101	2	the	the	DET
ijassa-1406	101	3	parameters	parameter	NOUN
ijassa-1406	101	4	σ	σ	PROPN
ijassa-1406	101	5	∈	∈	PROPN
ijassa-1406	101	6	(	(	PUNCT
ijassa-1406	101	7	0	0	NUM
ijassa-1406	101	8	,	,	PUNCT
ijassa-1406	101	9	1	1	NUM
ijassa-1406	101	10	)	)	PUNCT
ijassa-1406	101	11	and	and	CCONJ
ijassa-1406	101	12	θ	θ	PROPN
ijassa-1406	101	13	∈	∈	PROPN
ijassa-1406	101	14	(	(	PUNCT
ijassa-1406	101	15	0	0	NUM
ijassa-1406	101	16	,	,	PUNCT
ijassa-1406	101	17	1	1	NUM
ijassa-1406	101	18	)	)	PUNCT
ijassa-1406	101	19	.	.	PUNCT
ijassa-1406	102	1	choose	choose	VERB
ijassa-1406	102	2	u0	u0	PROPN
ijassa-1406	102	3	∈	∈	PROPN
ijassa-1406	102	4	rp	rp	NOUN
ijassa-1406	102	5	,	,	PUNCT
ijassa-1406	102	6	and	and	CCONJ
ijassa-1406	102	7	set	set	VERB
ijassa-1406	102	8	k	k	PROPN
ijassa-1406	102	9	=	=	PUNCT
ijassa-1406	102	10	0	0	NUM
ijassa-1406	102	11	.	.	NOUN
ijassa-1406	103	1	1	1	NUM
ijassa-1406	103	2	.	.	X
ijassa-1406	104	1	if	if	SCONJ
ijassa-1406	104	2	φ(uk	φ(uk	NOUN
ijassa-1406	104	3	)	)	PUNCT
ijassa-1406	104	4	=	=	SYM
ijassa-1406	104	5	0	0	NUM
ijassa-1406	104	6	,	,	PUNCT
ijassa-1406	104	7	stop	stop	VERB
ijassa-1406	104	8	with	with	ADP
ijassa-1406	104	9	success	success	NOUN
ijassa-1406	104	10	.	.	PUNCT
ijassa-1406	105	1	2	2	X
ijassa-1406	105	2	.	.	X
ijassa-1406	105	3	compute	compute	VERB
ijassa-1406	105	4	some	some	DET
ijassa-1406	105	5	jk	jk	PROPN
ijassa-1406	105	6	∈	∈	PROPN
ijassa-1406	105	7	∂bφ(u	∂bφ(u	PROPN
ijassa-1406	105	8	k	k	PROPN
ijassa-1406	105	9	)	)	PUNCT
ijassa-1406	105	10	.	.	PUNCT
ijassa-1406	106	1	compute	compute	NOUN
ijassa-1406	106	2	vk	vk	PROPN
ijassa-1406	106	3	∈	∈	PROPN
ijassa-1406	106	4	rp	rp	NOUN
ijassa-1406	106	5	as	as	ADP
ijassa-1406	106	6	a	a	DET
ijassa-1406	106	7	solution	solution	NOUN
ijassa-1406	106	8	of	of	ADP
ijassa-1406	106	9	(	(	PUNCT
ijassa-1406	106	10	3.2	3.2	NUM
ijassa-1406	106	11	)	)	PUNCT
ijassa-1406	106	12	.	.	PUNCT
ijassa-1406	107	1	if	if	SCONJ
ijassa-1406	107	2	such	such	ADJ
ijassa-1406	107	3	vk	vk	NOUN
ijassa-1406	107	4	can	can	AUX
ijassa-1406	107	5	not	not	PART
ijassa-1406	107	6	be	be	AUX
ijassa-1406	107	7	found	find	VERB
ijassa-1406	107	8	,	,	PUNCT
ijassa-1406	107	9	stop	stop	VERB
ijassa-1406	107	10	with	with	ADP
ijassa-1406	107	11	a	a	DET
ijassa-1406	107	12	failure	failure	NOUN
ijassa-1406	107	13	.	.	PUNCT
ijassa-1406	108	1	3	3	X
ijassa-1406	108	2	.	.	X
ijassa-1406	108	3	set	set	VERB
ijassa-1406	108	4	τ	τ	PROPN
ijassa-1406	108	5	=	=	SYM
ijassa-1406	108	6	1	1	X
ijassa-1406	108	7	.	.	PUNCT
ijassa-1406	109	1	if	if	SCONJ
ijassa-1406	109	2	the	the	DET
ijassa-1406	109	3	inequality	inequality	NOUN
ijassa-1406	109	4	(	(	PUNCT
ijassa-1406	109	5	2.4	2.4	NUM
ijassa-1406	109	6	)	)	PUNCT
ijassa-1406	109	7	is	be	AUX
ijassa-1406	109	8	satisfied	satisfied	ADJ
ijassa-1406	109	9	,	,	PUNCT
ijassa-1406	109	10	set	set	VERB
ijassa-1406	109	11	τk	τk	ADP
ijassa-1406	109	12	=	=	PROPN
ijassa-1406	109	13	τ	τ	PROPN
ijassa-1406	109	14	.	.	PUNCT
ijassa-1406	110	1	otherwise	otherwise	ADV
ijassa-1406	110	2	,	,	PUNCT
ijassa-1406	110	3	replace	replace	VERB
ijassa-1406	110	4	τ	τ	X
ijassa-1406	110	5	by	by	ADP
ijassa-1406	110	6	θτ	θτ	NOUN
ijassa-1406	110	7	,	,	PUNCT
ijassa-1406	110	8	check	check	VERB
ijassa-1406	110	9	inequality	inequality	NOUN
ijassa-1406	110	10	(	(	PUNCT
ijassa-1406	110	11	2.4	2.4	NUM
ijassa-1406	110	12	)	)	PUNCT
ijassa-1406	110	13	again	again	ADV
ijassa-1406	110	14	,	,	PUNCT
ijassa-1406	110	15	etc	etc	X
ijassa-1406	110	16	.	.	X
ijassa-1406	110	17	,	,	PUNCT
ijassa-1406	110	18	until	until	ADP
ijassa-1406	110	19	(	(	PUNCT
ijassa-1406	110	20	2.4	2.4	NUM
ijassa-1406	110	21	)	)	PUNCT
ijassa-1406	110	22	becomes	become	VERB
ijassa-1406	110	23	valid	valid	ADJ
ijassa-1406	110	24	.	.	PUNCT
ijassa-1406	111	1	4	4	X
ijassa-1406	111	2	.	.	X
ijassa-1406	111	3	set	set	VERB
ijassa-1406	111	4	uk+1	uk+1	NOUN
ijassa-1406	111	5	=	=	SYM
ijassa-1406	111	6	uk	uk	PROPN
ijassa-1406	111	7	+	+	CCONJ
ijassa-1406	111	8	τkv	τkv	PROPN
ijassa-1406	111	9	k.	k.	PROPN
ijassa-1406	111	10	5	5	X
ijassa-1406	111	11	.	.	PUNCT
ijassa-1406	112	1	increase	increase	VERB
ijassa-1406	112	2	k	k	X
ijassa-1406	112	3	by	by	ADP
ijassa-1406	112	4	1	1	NUM
ijassa-1406	112	5	and	and	CCONJ
ijassa-1406	112	6	go	go	VERB
ijassa-1406	112	7	to	to	PART
ijassa-1406	112	8	step	step	VERB
ijassa-1406	112	9	1	1	NUM
ijassa-1406	112	10	.	.	PUNCT
ijassa-1406	113	1	the	the	DET
ijassa-1406	113	2	use	use	NOUN
ijassa-1406	113	3	of	of	ADP
ijassa-1406	113	4	the	the	DET
ijassa-1406	113	5	stepsize	stepsize	NOUN
ijassa-1406	113	6	test	test	NOUN
ijassa-1406	113	7	(	(	PUNCT
ijassa-1406	113	8	2.4	2.4	NUM
ijassa-1406	113	9	)	)	PUNCT
ijassa-1406	113	10	in	in	ADP
ijassa-1406	113	11	this	this	DET
ijassa-1406	113	12	context	context	NOUN
ijassa-1406	113	13	can	can	AUX
ijassa-1406	113	14	be	be	AUX
ijassa-1406	113	15	explained	explain	VERB
ijassa-1406	113	16	as	as	SCONJ
ijassa-1406	113	17	follows	follow	VERB
ijassa-1406	113	18	.	.	PUNCT
ijassa-1406	114	1	the	the	DET
ijassa-1406	114	2	function	function	NOUN
ijassa-1406	114	3	∥φ(·)∥	∥φ(·)∥	VERB
ijassa-1406	114	4	with	with	ADP
ijassa-1406	114	5	φ	φ	PROPN
ijassa-1406	114	6	defined	define	VERB
ijassa-1406	114	7	according	accord	VERB
ijassa-1406	114	8	to	to	ADP
ijassa-1406	114	9	(	(	PUNCT
ijassa-1406	114	10	1.3	1.3	NUM
ijassa-1406	114	11	)	)	PUNCT
ijassa-1406	114	12	,	,	PUNCT
ijassa-1406	114	13	(	(	PUNCT
ijassa-1406	114	14	3.1	3.1	NUM
ijassa-1406	114	15	)	)	PUNCT
ijassa-1406	114	16	need	need	AUX
ijassa-1406	114	17	not	not	PART
ijassa-1406	114	18	be	be	AUX
ijassa-1406	114	19	differential	differential	ADJ
ijassa-1406	114	20	at	at	ADP
ijassa-1406	114	21	uk	uk	PROPN
ijassa-1406	114	22	,	,	PUNCT
ijassa-1406	114	23	even	even	ADV
ijassa-1406	114	24	if	if	SCONJ
ijassa-1406	114	25	φ(uk	φ(uk	NOUN
ijassa-1406	114	26	)	)	PUNCT
ijassa-1406	114	27	̸=	̸=	PROPN
ijassa-1406	114	28	0	0	NUM
ijassa-1406	114	29	.	.	PUNCT
ijassa-1406	115	1	that	that	PRON
ijassa-1406	115	2	said	say	VERB
ijassa-1406	115	3	,	,	PUNCT
ijassa-1406	115	4	according	accord	VERB
ijassa-1406	115	5	to	to	ADP
ijassa-1406	115	6	[	[	X
ijassa-1406	115	7	15	15	NUM
ijassa-1406	115	8	,	,	PUNCT
ijassa-1406	115	9	proposition	proposition	NOUN
ijassa-1406	115	10	5.5	5.5	NUM
ijassa-1406	115	11	]	]	PUNCT
ijassa-1406	115	12	,	,	PUNCT
ijassa-1406	115	13	the	the	DET
ijassa-1406	115	14	function	function	NOUN
ijassa-1406	115	15	φ	φ	NOUN
ijassa-1406	115	16	:	:	PUNCT
ijassa-1406	116	1	rp	rp	NOUN
ijassa-1406	116	2	→	→	SYM
ijassa-1406	116	3	r	r	NOUN
ijassa-1406	116	4	,	,	PUNCT
ijassa-1406	116	5	φ(u	φ(u	PROPN
ijassa-1406	116	6	)	)	PUNCT
ijassa-1406	116	7	=	=	SYM
ijassa-1406	116	8	∥φ(u)∥2	∥φ(u)∥2	NOUN
ijassa-1406	116	9	,	,	PUNCT
ijassa-1406	116	10	is	be	AUX
ijassa-1406	116	11	differentiable	differentiable	ADJ
ijassa-1406	116	12	at	at	ADP
ijassa-1406	116	13	every	every	DET
ijassa-1406	116	14	point	point	NOUN
ijassa-1406	116	15	u	u	NOUN
ijassa-1406	116	16	∈	∈	PROPN
ijassa-1406	116	17	rp	rp	NOUN
ijassa-1406	116	18	where	where	SCONJ
ijassa-1406	116	19	f	f	PROPN
ijassa-1406	116	20	is	be	AUX
ijassa-1406	116	21	differentiable	differentiable	ADJ
ijassa-1406	116	22	,	,	PUNCT
ijassa-1406	116	23	and	and	CCONJ
ijassa-1406	116	24	its	its	PRON
ijassa-1406	116	25	gradient	gradient	NOUN
ijassa-1406	116	26	satisfies	satisfie	NOUN
ijassa-1406	116	27	φ′(u	φ′(u	PROPN
ijassa-1406	116	28	)	)	PUNCT
ijassa-1406	116	29	=	=	SYM
ijassa-1406	116	30	2j⊤φ(u	2j⊤φ(u	NUM
ijassa-1406	116	31	)	)	PUNCT
ijassa-1406	116	32	∀	∀	PUNCT
ijassa-1406	116	33	j	j	PROPN
ijassa-1406	116	34	∈	∈	PROPN
ijassa-1406	116	35	∂φ(u	∂φ(u	PROPN
ijassa-1406	116	36	)	)	PUNCT
ijassa-1406	116	37	,	,	PUNCT
ijassa-1406	116	38	(	(	PUNCT
ijassa-1406	116	39	3.4	3.4	NUM
ijassa-1406	116	40	)	)	PUNCT
ijassa-1406	116	41	where	where	SCONJ
ijassa-1406	116	42	∂φ(u	∂φ(u	PROPN
ijassa-1406	116	43	)	)	PUNCT
ijassa-1406	116	44	is	be	AUX
ijassa-1406	116	45	clarke	clarke	PROPN
ijassa-1406	116	46	’s	’s	PART
ijassa-1406	116	47	generalized	generalize	VERB
ijassa-1406	116	48	jacobian	jacobian	NOUN
ijassa-1406	116	49	of	of	ADP
ijassa-1406	116	50	φ	φ	PROPN
ijassa-1406	116	51	at	at	ADP
ijassa-1406	116	52	ū	ū	NOUN
ijassa-1406	116	53	,	,	PUNCT
ijassa-1406	116	54	defined	define	VERB
ijassa-1406	116	55	as	as	ADP
ijassa-1406	116	56	the	the	DET
ijassa-1406	116	57	convex	convex	PROPN
ijassa-1406	116	58	hull	hull	NOUN
ijassa-1406	116	59	of	of	ADP
ijassa-1406	116	60	∂bφ(u	∂bφ(u	NOUN
ijassa-1406	116	61	)	)	PUNCT
ijassa-1406	116	62	;	;	PUNCT
ijassa-1406	116	63	see	see	VERB
ijassa-1406	116	64	,	,	PUNCT
ijassa-1406	116	65	e.g.	e.g.	ADV
ijassa-1406	116	66	,	,	PUNCT
ijassa-1406	116	67	[	[	X
ijassa-1406	116	68	15	15	NUM
ijassa-1406	116	69	,	,	PUNCT
ijassa-1406	116	70	section	section	NOUN
ijassa-1406	116	71	1.4.1	1.4.1	NUM
ijassa-1406	116	72	]	]	PUNCT
ijassa-1406	116	73	.	.	PUNCT
ijassa-1406	117	1	therefore	therefore	ADV
ijassa-1406	117	2	,	,	PUNCT
ijassa-1406	117	3	for	for	ADP
ijassa-1406	117	4	vk	vk	NOUN
ijassa-1406	117	5	solving	solve	VERB
ijassa-1406	117	6	(	(	PUNCT
ijassa-1406	117	7	3.2	3.2	NUM
ijassa-1406	117	8	)	)	PUNCT
ijassa-1406	117	9	it	it	PRON
ijassa-1406	117	10	holds	hold	VERB
ijassa-1406	117	11	that	that	DET
ijassa-1406	117	12	⟨φ′(uk	⟨φ′(uk	PROPN
ijassa-1406	117	13	)	)	PUNCT
ijassa-1406	117	14	,	,	PUNCT
ijassa-1406	117	15	vk⟩	vk⟩	PUNCT
ijassa-1406	117	16	=	=	SYM
ijassa-1406	117	17	2⟨φ(uk	2⟨φ(uk	NUM
ijassa-1406	117	18	)	)	PUNCT
ijassa-1406	117	19	,	,	PUNCT
ijassa-1406	117	20	jkvk⟩	jkvk⟩	PROPN
ijassa-1406	118	1	=	=	PUNCT
ijassa-1406	119	1	−2∥φ(uk)∥2	−2∥φ(uk)∥2	PROPN
ijassa-1406	119	2	=	=	SYM
ijassa-1406	119	3	−2φ(uk	−2φ(uk	PROPN
ijassa-1406	119	4	)	)	PUNCT
ijassa-1406	119	5	.	.	PUNCT
ijassa-1406	120	1	(	(	PUNCT
ijassa-1406	120	2	3.5	3.5	NUM
ijassa-1406	120	3	)	)	PUNCT
ijassa-1406	120	4	hence	hence	ADV
ijassa-1406	120	5	,	,	PUNCT
ijassa-1406	120	6	∥φ(uk	∥φ(uk	VERB
ijassa-1406	120	7	+	+	CCONJ
ijassa-1406	120	8	τvk)∥2	τvk)∥2	NOUN
ijassa-1406	120	9	=	=	SYM
ijassa-1406	120	10	φ(uk	φ(uk	PROPN
ijassa-1406	120	11	+	+	CCONJ
ijassa-1406	120	12	tvk	tvk	ADJ
ijassa-1406	120	13	)	)	PUNCT
ijassa-1406	120	14	=	=	SYM
ijassa-1406	120	15	φ(uk	φ(uk	VERB
ijassa-1406	120	16	)	)	PUNCT
ijassa-1406	120	17	+	+	CCONJ
ijassa-1406	120	18	τ⟨φ′(uk	τ⟨φ′(uk	PROPN
ijassa-1406	120	19	)	)	PUNCT
ijassa-1406	120	20	,	,	PUNCT
ijassa-1406	120	21	vk⟩+	vk⟩+	PROPN
ijassa-1406	120	22	o(τ	o(τ	PROPN
ijassa-1406	120	23	)	)	PUNCT
ijassa-1406	121	1	=	=	SYM
ijassa-1406	121	2	∥φ(uk)∥2	∥φ(uk)∥2	PROPN
ijassa-1406	122	1	−	−	PROPN
ijassa-1406	122	2	2τ∥φ(uk)∥2	2τ∥φ(uk)∥2	NUM
ijassa-1406	123	1	+	+	CCONJ
ijassa-1406	123	2	o(τ	o(τ	PROPN
ijassa-1406	123	3	)	)	PUNCT
ijassa-1406	123	4	=	=	PUNCT
ijassa-1406	123	5	(	(	PUNCT
ijassa-1406	123	6	1−	1−	NUM
ijassa-1406	123	7	2τ	2τ	NUM
ijassa-1406	123	8	+	+	CCONJ
ijassa-1406	123	9	o(τ))∥φ(uk)∥2	o(τ))∥φ(uk)∥2	NOUN
ijassa-1406	123	10	as	as	ADP
ijassa-1406	123	11	t→	t→	X
ijassa-1406	123	12	0	0	NUM
ijassa-1406	123	13	,	,	PUNCT
ijassa-1406	123	14	implying	imply	VERB
ijassa-1406	123	15	that	that	SCONJ
ijassa-1406	123	16	(	(	PUNCT
ijassa-1406	123	17	2.4	2.4	NUM
ijassa-1406	123	18	)	)	PUNCT
ijassa-1406	123	19	is	be	AUX
ijassa-1406	123	20	satisfied	satisfied	ADJ
ijassa-1406	123	21	for	for	ADP
ijassa-1406	123	22	all	all	PRON
ijassa-1406	123	23	τ	τ	PROPN
ijassa-1406	123	24	>	>	X
ijassa-1406	123	25	0	0	PUNCT
ijassa-1406	123	26	small	small	ADJ
ijassa-1406	123	27	enough	enough	ADV
ijassa-1406	123	28	,	,	PUNCT
ijassa-1406	123	29	for	for	ADP
ijassa-1406	123	30	any	any	DET
ijassa-1406	123	31	fixed	fix	VERB
ijassa-1406	123	32	σ	σ	PROPN
ijassa-1406	123	33	∈	∈	PROPN
ijassa-1406	123	34	(	(	PUNCT
ijassa-1406	123	35	0	0	NUM
ijassa-1406	123	36	,	,	PUNCT
ijassa-1406	123	37	1	1	NUM
ijassa-1406	123	38	)	)	PUNCT
ijassa-1406	123	39	.	.	PUNCT
ijassa-1406	124	1	observe	observe	VERB
ijassa-1406	124	2	further	far	ADV
ijassa-1406	124	3	that	that	SCONJ
ijassa-1406	124	4	employing	employ	VERB
ijassa-1406	124	5	(	(	PUNCT
ijassa-1406	124	6	3.5	3.5	NUM
ijassa-1406	124	7	)	)	PUNCT
ijassa-1406	124	8	,	,	PUNCT
ijassa-1406	124	9	condition	condition	NOUN
ijassa-1406	124	10	(	(	PUNCT
ijassa-1406	124	11	2.4	2.4	NUM
ijassa-1406	124	12	)	)	PUNCT
ijassa-1406	124	13	can	can	AUX
ijassa-1406	124	14	be	be	AUX
ijassa-1406	124	15	equivalently	equivalently	ADV
ijassa-1406	124	16	written	write	VERB
ijassa-1406	124	17	in	in	ADP
ijassa-1406	124	18	the	the	DET
ijassa-1406	124	19	form	form	NOUN
ijassa-1406	124	20	φ(uk	φ(uk	X
ijassa-1406	124	21	+	+	CCONJ
ijassa-1406	124	22	τvk	τvk	NOUN
ijassa-1406	124	23	)	)	PUNCT
ijassa-1406	124	24	≤	≤	NOUN
ijassa-1406	124	25	(	(	PUNCT
ijassa-1406	124	26	1−	1−	NUM
ijassa-1406	124	27	2στ	2στ	NOUN
ijassa-1406	125	1	+	+	CCONJ
ijassa-1406	125	2	σ2τ	σ2τ	X
ijassa-1406	125	3	2)φ(uk	2)φ(uk	NUM
ijassa-1406	125	4	)	)	PUNCT
ijassa-1406	125	5	=	=	SYM
ijassa-1406	125	6	φ(uk	φ(uk	PROPN
ijassa-1406	125	7	)	)	PUNCT
ijassa-1406	125	8	+	+	CCONJ
ijassa-1406	125	9	στ(1−	στ(1−	PROPN
ijassa-1406	125	10	στ/2)⟨φ′(uk	στ/2)⟨φ′(uk	NUM
ijassa-1406	125	11	)	)	PUNCT
ijassa-1406	125	12	,	,	PUNCT
ijassa-1406	125	13	vk⟩.	vk⟩.	PROPN
ijassa-1406	125	14	(	(	PUNCT
ijassa-1406	125	15	3.6	3.6	NUM
ijassa-1406	125	16	)	)	PUNCT
ijassa-1406	125	17	since	since	SCONJ
ijassa-1406	125	18	we	we	PRON
ijassa-1406	125	19	are	be	AUX
ijassa-1406	125	20	not	not	PART
ijassa-1406	125	21	aware	aware	ADJ
ijassa-1406	125	22	of	of	ADP
ijassa-1406	125	23	any	any	DET
ijassa-1406	125	24	existing	exist	VERB
ijassa-1406	125	25	global	global	ADJ
ijassa-1406	125	26	convergence	convergence	NOUN
ijassa-1406	125	27	theories	theory	NOUN
ijassa-1406	125	28	for	for	ADP
ijassa-1406	125	29	the	the	DET
ijassa-1406	125	30	linesearch	linesearch	NOUN
ijassa-1406	125	31	semismooth	semismooth	PROPN
ijassa-1406	125	32	newton	newton	PROPN
ijassa-1406	125	33	method	method	PROPN
ijassa-1406	125	34	with	with	ADP
ijassa-1406	125	35	the	the	DET
ijassa-1406	125	36	specific	specific	ADJ
ijassa-1406	125	37	stepsize	stepsize	NOUN
ijassa-1406	125	38	test	test	NOUN
ijassa-1406	125	39	(	(	PUNCT
ijassa-1406	125	40	2.4	2.4	NUM
ijassa-1406	125	41	)	)	PUNCT
ijassa-1406	125	42	,	,	PUNCT
ijassa-1406	125	43	we	we	PRON
ijassa-1406	125	44	next	next	VERB
ijassa-1406	125	45	address	address	VERB
ijassa-1406	125	46	this	this	DET
ijassa-1406	125	47	issue	issue	NOUN
ijassa-1406	125	48	for	for	ADP
ijassa-1406	125	49	the	the	DET
ijassa-1406	125	50	following	follow	VERB
ijassa-1406	125	51	safeguarded	safeguard	VERB
ijassa-1406	125	52	version	version	NOUN
ijassa-1406	125	53	of	of	ADP
ijassa-1406	125	54	algorithm	algorithm	NOUN
ijassa-1406	125	55	3.1	3.1	NUM
ijassa-1406	125	56	.	.	PUNCT
ijassa-1406	126	1	algorithm	algorithm	PROPN
ijassa-1406	126	2	3.2	3.2	NUM
ijassa-1406	126	3	:	:	PUNCT
ijassa-1406	126	4	define	define	VERB
ijassa-1406	126	5	the	the	DET
ijassa-1406	126	6	mapping	mapping	NOUN
ijassa-1406	126	7	φ	φ	NOUN
ijassa-1406	126	8	according	accord	VERB
ijassa-1406	126	9	to	to	ADP
ijassa-1406	126	10	(	(	PUNCT
ijassa-1406	126	11	1.3	1.3	NUM
ijassa-1406	126	12	)	)	PUNCT
ijassa-1406	126	13	,	,	PUNCT
ijassa-1406	126	14	(	(	PUNCT
ijassa-1406	126	15	3.1	3.1	NUM
ijassa-1406	126	16	)	)	PUNCT
ijassa-1406	126	17	.	.	PUNCT
ijassa-1406	127	1	choose	choose	VERB
ijassa-1406	127	2	the	the	DET
ijassa-1406	127	3	parameters	parameter	NOUN
ijassa-1406	127	4	c	c	X
ijassa-1406	127	5	>	>	X
ijassa-1406	127	6	0	0	PROPN
ijassa-1406	127	7	,	,	PUNCT
ijassa-1406	127	8	q	q	X
ijassa-1406	127	9	>	>	X
ijassa-1406	127	10	0	0	NUM
ijassa-1406	127	11	,	,	PUNCT
ijassa-1406	127	12	σ	σ	PROPN
ijassa-1406	127	13	∈	∈	PROPN
ijassa-1406	127	14	(	(	PUNCT
ijassa-1406	127	15	0	0	NUM
ijassa-1406	127	16	,	,	PUNCT
ijassa-1406	127	17	1	1	NUM
ijassa-1406	127	18	)	)	PUNCT
ijassa-1406	127	19	and	and	CCONJ
ijassa-1406	127	20	θ	θ	PROPN
ijassa-1406	127	21	∈	∈	PROPN
ijassa-1406	127	22	(	(	PUNCT
ijassa-1406	127	23	0	0	NUM
ijassa-1406	127	24	,	,	PUNCT
ijassa-1406	127	25	1	1	NUM
ijassa-1406	127	26	)	)	PUNCT
ijassa-1406	127	27	.	.	PUNCT
ijassa-1406	128	1	choose	choose	VERB
ijassa-1406	128	2	u0	u0	PROPN
ijassa-1406	128	3	∈	∈	PROPN
ijassa-1406	128	4	rp	rp	NOUN
ijassa-1406	128	5	,	,	PUNCT
ijassa-1406	128	6	and	and	CCONJ
ijassa-1406	128	7	set	set	VERB
ijassa-1406	128	8	k	k	PROPN
ijassa-1406	128	9	=	=	PUNCT
ijassa-1406	128	10	0	0	NUM
ijassa-1406	128	11	.	.	NOUN
ijassa-1406	129	1	1	1	NUM
ijassa-1406	129	2	.	.	X
ijassa-1406	130	1	if	if	SCONJ
ijassa-1406	130	2	φ(uk	φ(uk	NOUN
ijassa-1406	130	3	)	)	PUNCT
ijassa-1406	130	4	=	=	SYM
ijassa-1406	130	5	0	0	NUM
ijassa-1406	130	6	,	,	PUNCT
ijassa-1406	130	7	stop	stop	VERB
ijassa-1406	130	8	with	with	ADP
ijassa-1406	130	9	success	success	NOUN
ijassa-1406	130	10	.	.	PUNCT
ijassa-1406	131	1	2	2	X
ijassa-1406	131	2	.	.	X
ijassa-1406	131	3	compute	compute	VERB
ijassa-1406	131	4	some	some	DET
ijassa-1406	131	5	jk	jk	PROPN
ijassa-1406	131	6	∈	∈	PROPN
ijassa-1406	131	7	∂bφ(u	∂bφ(u	PROPN
ijassa-1406	131	8	k	k	PROPN
ijassa-1406	131	9	)	)	PUNCT
ijassa-1406	131	10	.	.	PUNCT
ijassa-1406	132	1	compute	compute	NOUN
ijassa-1406	132	2	vk	vk	PROPN
ijassa-1406	132	3	∈	∈	PROPN
ijassa-1406	132	4	rp	rp	NOUN
ijassa-1406	132	5	as	as	ADP
ijassa-1406	132	6	a	a	DET
ijassa-1406	132	7	solution	solution	NOUN
ijassa-1406	132	8	of	of	ADP
ijassa-1406	132	9	(	(	PUNCT
ijassa-1406	132	10	3.2	3.2	NUM
ijassa-1406	132	11	)	)	PUNCT
ijassa-1406	132	12	.	.	PUNCT
ijassa-1406	133	1	if	if	SCONJ
ijassa-1406	133	2	such	such	ADJ
ijassa-1406	133	3	vk	vk	NOUN
ijassa-1406	133	4	can	can	AUX
ijassa-1406	133	5	not	not	PART
ijassa-1406	133	6	be	be	AUX
ijassa-1406	133	7	found	find	VERB
ijassa-1406	133	8	,	,	PUNCT
ijassa-1406	133	9	or	or	CCONJ
ijassa-1406	133	10	violates	violate	VERB
ijassa-1406	133	11	∥vk∥	∥vk∥	NOUN
ijassa-1406	133	12	≤	≤	PUNCT
ijassa-1406	133	13	max{c	max{c	PROPN
ijassa-1406	133	14	,	,	PUNCT
ijassa-1406	133	15	1/∥φ(uk)∥q	1/∥φ(uk)∥q	PROPN
ijassa-1406	133	16	}	}	PUNCT
ijassa-1406	133	17	,	,	PUNCT
ijassa-1406	133	18	(	(	PUNCT
ijassa-1406	133	19	3.7	3.7	NUM
ijassa-1406	133	20	)	)	PUNCT
ijassa-1406	133	21	go	go	VERB
ijassa-1406	133	22	to	to	PART
ijassa-1406	133	23	step	step	VERB
ijassa-1406	133	24	4	4	NUM
ijassa-1406	133	25	.	.	NOUN
ijassa-1406	134	1	3	3	X
ijassa-1406	134	2	.	.	X
ijassa-1406	134	3	set	set	VERB
ijassa-1406	134	4	τ	τ	PROPN
ijassa-1406	134	5	=	=	SYM
ijassa-1406	134	6	1	1	X
ijassa-1406	134	7	.	.	PUNCT
ijassa-1406	135	1	if	if	SCONJ
ijassa-1406	135	2	the	the	DET
ijassa-1406	135	3	inequality	inequality	NOUN
ijassa-1406	135	4	(	(	PUNCT
ijassa-1406	135	5	2.4	2.4	NUM
ijassa-1406	135	6	)	)	PUNCT
ijassa-1406	135	7	is	be	AUX
ijassa-1406	135	8	satisfied	satisfied	ADJ
ijassa-1406	135	9	,	,	PUNCT
ijassa-1406	135	10	set	set	VERB
ijassa-1406	135	11	τk	τk	ADP
ijassa-1406	135	12	=	=	PROPN
ijassa-1406	135	13	τ	τ	PROPN
ijassa-1406	135	14	.	.	PUNCT
ijassa-1406	136	1	otherwise	otherwise	ADV
ijassa-1406	136	2	,	,	PUNCT
ijassa-1406	136	3	replace	replace	VERB
ijassa-1406	136	4	τ	τ	X
ijassa-1406	136	5	by	by	ADP
ijassa-1406	136	6	θτ	θτ	NOUN
ijassa-1406	136	7	,	,	PUNCT
ijassa-1406	136	8	check	check	VERB
ijassa-1406	136	9	inequality	inequality	NOUN
ijassa-1406	136	10	(	(	PUNCT
ijassa-1406	136	11	2.4	2.4	NUM
ijassa-1406	136	12	)	)	PUNCT
ijassa-1406	136	13	again	again	ADV
ijassa-1406	136	14	,	,	PUNCT
ijassa-1406	136	15	etc	etc	X
ijassa-1406	136	16	.	.	X
ijassa-1406	136	17	,	,	PUNCT
ijassa-1406	136	18	until	until	ADP
ijassa-1406	136	19	(	(	PUNCT
ijassa-1406	136	20	2.4	2.4	NUM
ijassa-1406	136	21	)	)	PUNCT
ijassa-1406	136	22	becomes	become	VERB
ijassa-1406	136	23	valid	valid	ADJ
ijassa-1406	136	24	.	.	PUNCT
ijassa-1406	137	1	go	go	VERB
ijassa-1406	137	2	to	to	PART
ijassa-1406	137	3	step	step	VERB
ijassa-1406	137	4	6	6	NUM
ijassa-1406	137	5	4	4	NUM
ijassa-1406	137	6	.	.	PUNCT
ijassa-1406	138	1	set	set	VERB
ijassa-1406	138	2	vk	vk	NOUN
ijassa-1406	138	3	=	=	PUNCT
ijassa-1406	138	4	−2j⊤	−2j⊤	PROPN
ijassa-1406	138	5	k	k	PROPN
ijassa-1406	138	6	φ(u	φ(u	PROPN
ijassa-1406	138	7	k	k	PROPN
ijassa-1406	138	8	)	)	PUNCT
ijassa-1406	138	9	.	.	PUNCT
ijassa-1406	139	1	if	if	SCONJ
ijassa-1406	139	2	vk	vk	VERB
ijassa-1406	139	3	=	=	SYM
ijassa-1406	139	4	0	0	NUM
ijassa-1406	139	5	,	,	PUNCT
ijassa-1406	139	6	stop	stop	VERB
ijassa-1406	139	7	.	.	PUNCT
ijassa-1406	140	1	copyright	copyright	NOUN
ijassa-1406	140	2	©	©	ADP
ijassa-1406	140	3	2023	2023	NUM
ijassa-1406	140	4	assa	assa	NOUN
ijassa-1406	140	5	.	.	PUNCT
ijassa-1406	141	1	adv	adv	PROPN
ijassa-1406	141	2	syst	syst	PROPN
ijassa-1406	141	3	sci	sci	PROPN
ijassa-1406	141	4	appl	appl	PROPN
ijassa-1406	141	5	(	(	PUNCT
ijassa-1406	141	6	2023	2023	NUM
ijassa-1406	141	7	)	)	PUNCT
ijassa-1406	141	8	newton	newton	PROPN
ijassa-1406	141	9	method	method	NOUN
ijassa-1406	141	10	vs.	vs.	ADP
ijassa-1406	141	11	semismooth	semismooth	PROPN
ijassa-1406	141	12	newton	newton	PROPN
ijassa-1406	141	13	method	method	NOUN
ijassa-1406	141	14	21	21	NUM
ijassa-1406	141	15	5	5	NUM
ijassa-1406	141	16	.	.	PUNCT
ijassa-1406	142	1	set	set	VERB
ijassa-1406	142	2	τ	τ	PROPN
ijassa-1406	142	3	=	=	SYM
ijassa-1406	142	4	1	1	X
ijassa-1406	142	5	.	.	PUNCT
ijassa-1406	143	1	if	if	SCONJ
ijassa-1406	143	2	the	the	DET
ijassa-1406	143	3	inequality	inequality	NOUN
ijassa-1406	143	4	φ(uk	φ(uk	X
ijassa-1406	143	5	+	+	CCONJ
ijassa-1406	143	6	τvk	τvk	NOUN
ijassa-1406	143	7	)	)	PUNCT
ijassa-1406	143	8	≤	≤	NOUN
ijassa-1406	143	9	φ(uk)−	φ(uk)−	ADJ
ijassa-1406	143	10	στ∥vk∥2	στ∥vk∥2	PROPN
ijassa-1406	143	11	(	(	PUNCT
ijassa-1406	143	12	3.8	3.8	NUM
ijassa-1406	143	13	)	)	PUNCT
ijassa-1406	143	14	is	be	AUX
ijassa-1406	143	15	satisfied	satisfied	ADJ
ijassa-1406	143	16	,	,	PUNCT
ijassa-1406	143	17	set	set	VERB
ijassa-1406	143	18	τk	τk	ADP
ijassa-1406	143	19	=	=	PROPN
ijassa-1406	143	20	τ	τ	PROPN
ijassa-1406	143	21	.	.	PUNCT
ijassa-1406	144	1	otherwise	otherwise	ADV
ijassa-1406	144	2	,	,	PUNCT
ijassa-1406	144	3	replace	replace	VERB
ijassa-1406	144	4	τ	τ	X
ijassa-1406	144	5	by	by	ADP
ijassa-1406	144	6	θτ	θτ	NOUN
ijassa-1406	144	7	,	,	PUNCT
ijassa-1406	144	8	check	check	NOUN
ijassa-1406	144	9	(	(	PUNCT
ijassa-1406	144	10	3.8	3.8	NUM
ijassa-1406	144	11	)	)	PUNCT
ijassa-1406	144	12	,	,	PUNCT
ijassa-1406	144	13	etc	etc	X
ijassa-1406	144	14	.	.	X
ijassa-1406	144	15	,	,	PUNCT
ijassa-1406	144	16	until	until	ADP
ijassa-1406	144	17	(	(	PUNCT
ijassa-1406	144	18	3.8	3.8	NUM
ijassa-1406	144	19	)	)	PUNCT
ijassa-1406	144	20	becomes	become	VERB
ijassa-1406	144	21	valid	valid	ADJ
ijassa-1406	144	22	.	.	PUNCT
ijassa-1406	145	1	6	6	X
ijassa-1406	145	2	.	.	X
ijassa-1406	145	3	set	set	VERB
ijassa-1406	145	4	uk+1	uk+1	NOUN
ijassa-1406	145	5	=	=	SYM
ijassa-1406	145	6	uk	uk	PROPN
ijassa-1406	145	7	+	+	CCONJ
ijassa-1406	145	8	τkv	τkv	VERB
ijassa-1406	145	9	k.	k.	PROPN
ijassa-1406	145	10	7	7	X
ijassa-1406	145	11	.	.	PUNCT
ijassa-1406	146	1	increase	increase	VERB
ijassa-1406	146	2	k	k	X
ijassa-1406	146	3	by	by	ADP
ijassa-1406	146	4	1	1	NUM
ijassa-1406	146	5	and	and	CCONJ
ijassa-1406	146	6	go	go	VERB
ijassa-1406	146	7	to	to	PART
ijassa-1406	146	8	step	step	VERB
ijassa-1406	146	9	1	1	NUM
ijassa-1406	146	10	.	.	PUNCT
ijassa-1406	147	1	theorem	theorem	VERB
ijassa-1406	147	2	3.1	3.1	NUM
ijassa-1406	147	3	:	:	PUNCT
ijassa-1406	147	4	let	let	VERB
ijassa-1406	147	5	f	f	NOUN
ijassa-1406	147	6	:	:	PUNCT
ijassa-1406	147	7	rp	rp	NOUN
ijassa-1406	147	8	→	→	SYM
ijassa-1406	147	9	rp	rp	NOUN
ijassa-1406	147	10	be	be	AUX
ijassa-1406	147	11	continuously	continuously	ADV
ijassa-1406	147	12	differentiable	differentiable	ADJ
ijassa-1406	147	13	.	.	PUNCT
ijassa-1406	148	1	then	then	ADV
ijassa-1406	148	2	,	,	PUNCT
ijassa-1406	148	3	for	for	ADP
ijassa-1406	148	4	any	any	DET
ijassa-1406	148	5	starting	starting	NOUN
ijassa-1406	148	6	point	point	NOUN
ijassa-1406	148	7	u0	u0	PROPN
ijassa-1406	148	8	∈	∈	PROPN
ijassa-1406	148	9	rp	rp	NOUN
ijassa-1406	148	10	,	,	PUNCT
ijassa-1406	148	11	algorithm	algorithm	NOUN
ijassa-1406	148	12	3.2	3.2	NUM
ijassa-1406	148	13	either	either	CCONJ
ijassa-1406	148	14	terminates	terminate	VERB
ijassa-1406	148	15	with	with	ADP
ijassa-1406	148	16	some	some	DET
ijassa-1406	148	17	iterate	iterate	NOUN
ijassa-1406	148	18	uk	uk	NOUN
ijassa-1406	148	19	satisfying	satisfy	VERB
ijassa-1406	148	20	j⊤φ(uk	j⊤φ(uk	PROPN
ijassa-1406	148	21	)	)	PUNCT
ijassa-1406	149	1	=	=	SYM
ijassa-1406	149	2	0	0	NUM
ijassa-1406	149	3	∀	∀	NOUN
ijassa-1406	149	4	j	j	PROPN
ijassa-1406	149	5	∈	∈	PROPN
ijassa-1406	149	6	∂φ(uk	∂φ(uk	PROPN
ijassa-1406	149	7	)	)	PUNCT
ijassa-1406	149	8	,	,	PUNCT
ijassa-1406	149	9	(	(	PUNCT
ijassa-1406	149	10	3.9	3.9	NUM
ijassa-1406	149	11	)	)	PUNCT
ijassa-1406	150	1	or	or	CCONJ
ijassa-1406	150	2	generates	generate	VERB
ijassa-1406	150	3	an	an	DET
ijassa-1406	150	4	infinite	infinite	ADJ
ijassa-1406	150	5	sequence	sequence	NOUN
ijassa-1406	150	6	{	{	PUNCT
ijassa-1406	150	7	uk	uk	PROPN
ijassa-1406	150	8	}	}	PUNCT
ijassa-1406	150	9	such	such	ADJ
ijassa-1406	150	10	that	that	SCONJ
ijassa-1406	150	11	every	every	DET
ijassa-1406	150	12	accumulation	accumulation	NOUN
ijassa-1406	150	13	point	point	NOUN
ijassa-1406	150	14	ū	ū	NOUN
ijassa-1406	150	15	of	of	ADP
ijassa-1406	150	16	this	this	DET
ijassa-1406	150	17	sequence	sequence	NOUN
ijassa-1406	150	18	satisfies	satisfy	VERB
ijassa-1406	150	19	j⊤φ(ū	j⊤φ(ū	PROPN
ijassa-1406	150	20	)	)	PUNCT
ijassa-1406	151	1	=	=	SYM
ijassa-1406	151	2	0	0	NUM
ijassa-1406	151	3	∀	∀	PUNCT
ijassa-1406	151	4	j	j	PROPN
ijassa-1406	151	5	∈	∈	PROPN
ijassa-1406	151	6	∂φ(ū	∂φ(ū	PROPN
ijassa-1406	151	7	)	)	PUNCT
ijassa-1406	151	8	,	,	PUNCT
ijassa-1406	151	9	(	(	PUNCT
ijassa-1406	151	10	3.10	3.10	NUM
ijassa-1406	151	11	)	)	PUNCT
ijassa-1406	151	12	where	where	SCONJ
ijassa-1406	151	13	φ	φ	PROPN
ijassa-1406	151	14	according	accord	VERB
ijassa-1406	151	15	to	to	ADP
ijassa-1406	151	16	(	(	PUNCT
ijassa-1406	151	17	1.3	1.3	NUM
ijassa-1406	151	18	)	)	PUNCT
ijassa-1406	151	19	,	,	PUNCT
ijassa-1406	151	20	(	(	PUNCT
ijassa-1406	151	21	3.1	3.1	NUM
ijassa-1406	151	22	)	)	PUNCT
ijassa-1406	151	23	.	.	PUNCT
ijassa-1406	152	1	moreover	moreover	ADV
ijassa-1406	152	2	,	,	PUNCT
ijassa-1406	152	3	if	if	SCONJ
ijassa-1406	152	4	for	for	ADP
ijassa-1406	152	5	some	some	DET
ijassa-1406	152	6	ū	ū	NOUN
ijassa-1406	152	7	there	there	ADV
ijassa-1406	152	8	exists	exist	VERB
ijassa-1406	152	9	an	an	DET
ijassa-1406	152	10	infinite	infinite	ADJ
ijassa-1406	152	11	subsequence	subsequence	NOUN
ijassa-1406	152	12	{	{	PUNCT
ijassa-1406	152	13	ukj	ukj	NOUN
ijassa-1406	152	14	}	}	PUNCT
ijassa-1406	152	15	convergent	convergent	NOUN
ijassa-1406	152	16	to	to	ADP
ijassa-1406	152	17	ū	ū	NOUN
ijassa-1406	152	18	such	such	ADJ
ijassa-1406	152	19	that	that	SCONJ
ijassa-1406	152	20	the	the	DET
ijassa-1406	152	21	semismooth	semismooth	NOUN
ijassa-1406	152	22	newton	newton	PROPN
ijassa-1406	152	23	direction	direction	NOUN
ijassa-1406	152	24	is	be	AUX
ijassa-1406	152	25	used	use	VERB
ijassa-1406	152	26	by	by	ADP
ijassa-1406	152	27	algorithm	algorithm	NOUN
ijassa-1406	152	28	3.2	3.2	NUM
ijassa-1406	152	29	for	for	ADP
ijassa-1406	152	30	all	all	DET
ijassa-1406	152	31	indices	index	NOUN
ijassa-1406	152	32	k	k	PROPN
ijassa-1406	152	33	=	=	X
ijassa-1406	152	34	kj	kj	PROPN
ijassa-1406	152	35	(	(	PUNCT
ijassa-1406	152	36	i.e.	i.e.	X
ijassa-1406	152	37	,	,	PUNCT
ijassa-1406	152	38	for	for	ADP
ijassa-1406	152	39	all	all	DET
ijassa-1406	152	40	j	j	PROPN
ijassa-1406	152	41	,	,	PUNCT
ijassa-1406	152	42	for	for	ADP
ijassa-1406	152	43	k	k	PROPN
ijassa-1406	152	44	=	=	PUNCT
ijassa-1406	152	45	kj	kj	PROPN
ijassa-1406	152	46	equation	equation	NOUN
ijassa-1406	152	47	(	(	PUNCT
ijassa-1406	152	48	3.2	3.2	NUM
ijassa-1406	152	49	)	)	PUNCT
ijassa-1406	152	50	is	be	AUX
ijassa-1406	152	51	solvable	solvable	ADJ
ijassa-1406	152	52	,	,	PUNCT
ijassa-1406	152	53	and	and	CCONJ
ijassa-1406	152	54	the	the	DET
ijassa-1406	152	55	computed	compute	VERB
ijassa-1406	152	56	solution	solution	NOUN
ijassa-1406	152	57	satisfies	satisfie	NOUN
ijassa-1406	152	58	(	(	PUNCT
ijassa-1406	152	59	3.7	3.7	NUM
ijassa-1406	152	60	)	)	PUNCT
ijassa-1406	152	61	)	)	PUNCT
ijassa-1406	152	62	,	,	PUNCT
ijassa-1406	152	63	then	then	ADV
ijassa-1406	152	64	{	{	PUNCT
ijassa-1406	152	65	φ(uk	φ(uk	PROPN
ijassa-1406	152	66	)	)	PUNCT
ijassa-1406	152	67	}	}	PUNCT
ijassa-1406	152	68	→	→	SYM
ijassa-1406	152	69	0	0	NUM
ijassa-1406	152	70	(	(	PUNCT
ijassa-1406	152	71	3.11	3.11	NUM
ijassa-1406	152	72	)	)	PUNCT
ijassa-1406	152	73	as	as	ADP
ijassa-1406	152	74	k	k	PROPN
ijassa-1406	152	75	→	→	SYM
ijassa-1406	152	76	∞	∞	PROPN
ijassa-1406	152	77	,	,	PUNCT
ijassa-1406	152	78	and	and	CCONJ
ijassa-1406	152	79	in	in	ADP
ijassa-1406	152	80	particular	particular	ADJ
ijassa-1406	152	81	,	,	PUNCT
ijassa-1406	152	82	all	all	DET
ijassa-1406	152	83	accumulation	accumulation	NOUN
ijassa-1406	152	84	points	point	NOUN
ijassa-1406	152	85	of	of	ADP
ijassa-1406	152	86	{	{	PUNCT
ijassa-1406	152	87	uk	uk	PROPN
ijassa-1406	152	88	}	}	PUNCT
ijassa-1406	152	89	are	be	AUX
ijassa-1406	152	90	solutions	solution	NOUN
ijassa-1406	152	91	of	of	ADP
ijassa-1406	152	92	the	the	DET
ijassa-1406	152	93	ncp	ncp	PROPN
ijassa-1406	152	94	(	(	PUNCT
ijassa-1406	152	95	1.1	1.1	NUM
ijassa-1406	152	96	)	)	PUNCT
ijassa-1406	152	97	.	.	PUNCT
ijassa-1406	153	1	proof	proof	NOUN
ijassa-1406	153	2	if	if	SCONJ
ijassa-1406	153	3	for	for	ADP
ijassa-1406	153	4	a	a	DET
ijassa-1406	153	5	current	current	ADJ
ijassa-1406	153	6	iterate	iterate	NOUN
ijassa-1406	153	7	uk	uk	PROPN
ijassa-1406	153	8	it	it	PRON
ijassa-1406	153	9	holds	hold	VERB
ijassa-1406	153	10	that	that	SCONJ
ijassa-1406	153	11	φ(uk	φ(uk	PROPN
ijassa-1406	153	12	)	)	PUNCT
ijassa-1406	153	13	=	=	SYM
ijassa-1406	153	14	0	0	NUM
ijassa-1406	153	15	,	,	PUNCT
ijassa-1406	153	16	the	the	DET
ijassa-1406	153	17	algorithm	algorithm	NOUN
ijassa-1406	153	18	terminates	terminate	VERB
ijassa-1406	153	19	,	,	PUNCT
ijassa-1406	153	20	and	and	CCONJ
ijassa-1406	153	21	(	(	PUNCT
ijassa-1406	153	22	3.9	3.9	NUM
ijassa-1406	153	23	)	)	PUNCT
ijassa-1406	153	24	is	be	AUX
ijassa-1406	153	25	evidently	evidently	ADV
ijassa-1406	153	26	satisfied	satisfied	ADJ
ijassa-1406	153	27	in	in	ADP
ijassa-1406	153	28	this	this	DET
ijassa-1406	153	29	case	case	NOUN
ijassa-1406	153	30	.	.	PUNCT
ijassa-1406	154	1	otherwise	otherwise	ADV
ijassa-1406	154	2	,	,	PUNCT
ijassa-1406	154	3	if	if	SCONJ
ijassa-1406	154	4	the	the	DET
ijassa-1406	154	5	algorithm	algorithm	NOUN
ijassa-1406	154	6	accepts	accept	VERB
ijassa-1406	154	7	the	the	DET
ijassa-1406	154	8	semismooth	semismooth	NOUN
ijassa-1406	154	9	newton	newton	PROPN
ijassa-1406	154	10	direction	direction	PROPN
ijassa-1406	154	11	vk	vk	PROPN
ijassa-1406	154	12	,	,	PUNCT
ijassa-1406	154	13	then	then	ADV
ijassa-1406	154	14	the	the	DET
ijassa-1406	154	15	discussion	discussion	NOUN
ijassa-1406	154	16	before	before	ADP
ijassa-1406	154	17	algorithm	algorithm	PROPN
ijassa-1406	154	18	3.1	3.1	NUM
ijassa-1406	154	19	implies	imply	VERB
ijassa-1406	154	20	that	that	SCONJ
ijassa-1406	154	21	(	(	PUNCT
ijassa-1406	154	22	2.4	2.4	NUM
ijassa-1406	154	23	)	)	PUNCT
ijassa-1406	154	24	is	be	AUX
ijassa-1406	154	25	always	always	ADV
ijassa-1406	154	26	satisfied	satisfied	ADJ
ijassa-1406	154	27	after	after	ADP
ijassa-1406	154	28	a	a	DET
ijassa-1406	154	29	finite	finite	ADJ
ijassa-1406	154	30	number	number	NOUN
ijassa-1406	154	31	of	of	ADP
ijassa-1406	154	32	backtrackings	backtracking	NOUN
ijassa-1406	154	33	,	,	PUNCT
ijassa-1406	154	34	i.e.	i.e.	X
ijassa-1406	154	35	,	,	PUNCT
ijassa-1406	154	36	the	the	DET
ijassa-1406	154	37	linesearch	linesearch	NOUN
ijassa-1406	154	38	procedure	procedure	NOUN
ijassa-1406	154	39	at	at	ADP
ijassa-1406	154	40	step	step	NOUN
ijassa-1406	154	41	3	3	NUM
ijassa-1406	154	42	of	of	ADP
ijassa-1406	154	43	algorithm	algorithm	NOUN
ijassa-1406	154	44	3.2	3.2	NUM
ijassa-1406	154	45	terminates	terminate	VERB
ijassa-1406	154	46	with	with	ADP
ijassa-1406	154	47	some	some	PRON
ijassa-1406	154	48	τk	τk	NOUN
ijassa-1406	154	49	>	>	X
ijassa-1406	154	50	0	0	X
ijassa-1406	154	51	.	.	PUNCT
ijassa-1406	155	1	if	if	SCONJ
ijassa-1406	155	2	the	the	DET
ijassa-1406	155	3	newton	newton	PROPN
ijassa-1406	155	4	direction	direction	NOUN
ijassa-1406	155	5	is	be	AUX
ijassa-1406	155	6	not	not	PART
ijassa-1406	155	7	used	use	VERB
ijassa-1406	155	8	,	,	PUNCT
ijassa-1406	155	9	then	then	ADV
ijassa-1406	155	10	,	,	PUNCT
ijassa-1406	155	11	according	accord	VERB
ijassa-1406	155	12	to	to	ADP
ijassa-1406	155	13	(	(	PUNCT
ijassa-1406	155	14	3.4	3.4	NUM
ijassa-1406	155	15	)	)	PUNCT
ijassa-1406	155	16	,	,	PUNCT
ijassa-1406	155	17	at	at	ADP
ijassa-1406	155	18	step	step	NOUN
ijassa-1406	155	19	4	4	NUM
ijassa-1406	155	20	the	the	DET
ijassa-1406	155	21	algorithm	algorithm	NOUN
ijassa-1406	155	22	picks	pick	VERB
ijassa-1406	155	23	up	up	ADP
ijassa-1406	155	24	vk	vk	ADP
ijassa-1406	155	25	=	=	SYM
ijassa-1406	155	26	−φ′(uk	−φ′(uk	ADJ
ijassa-1406	155	27	)	)	PUNCT
ijassa-1406	155	28	.	.	PUNCT
ijassa-1406	156	1	in	in	ADP
ijassa-1406	156	2	this	this	DET
ijassa-1406	156	3	case	case	NOUN
ijassa-1406	156	4	,	,	PUNCT
ijassa-1406	156	5	the	the	DET
ijassa-1406	156	6	linesearch	linesearch	NOUN
ijassa-1406	156	7	procedure	procedure	NOUN
ijassa-1406	156	8	at	at	ADP
ijassa-1406	156	9	step	step	NOUN
ijassa-1406	156	10	5	5	NUM
ijassa-1406	156	11	of	of	ADP
ijassa-1406	156	12	the	the	DET
ijassa-1406	156	13	algorithm	algorithm	NOUN
ijassa-1406	156	14	with	with	ADP
ijassa-1406	156	15	the	the	DET
ijassa-1406	156	16	stepsize	stepsize	NOUN
ijassa-1406	156	17	test	test	NOUN
ijassa-1406	156	18	(	(	PUNCT
ijassa-1406	156	19	3.8	3.8	NUM
ijassa-1406	156	20	)	)	PUNCT
ijassa-1406	156	21	terminates	terminate	VERB
ijassa-1406	156	22	finitely	finitely	ADV
ijassa-1406	156	23	with	with	ADP
ijassa-1406	156	24	some	some	PRON
ijassa-1406	156	25	τk	τk	NOUN
ijassa-1406	156	26	>	>	X
ijassa-1406	156	27	0	0	PUNCT
ijassa-1406	157	1	(	(	PUNCT
ijassa-1406	157	2	as	as	SCONJ
ijassa-1406	157	3	it	it	PRON
ijassa-1406	157	4	is	be	AUX
ijassa-1406	157	5	the	the	DET
ijassa-1406	157	6	standard	standard	ADJ
ijassa-1406	157	7	armijo	armijo	PROPN
ijassa-1406	157	8	linesearch	linesearch	NOUN
ijassa-1406	157	9	procedure	procedure	NOUN
ijassa-1406	157	10	for	for	ADP
ijassa-1406	157	11	a	a	DET
ijassa-1406	157	12	function	function	NOUN
ijassa-1406	157	13	which	which	PRON
ijassa-1406	157	14	is	be	AUX
ijassa-1406	157	15	smooth	smooth	ADJ
ijassa-1406	157	16	at	at	ADP
ijassa-1406	157	17	uk	uk	PROPN
ijassa-1406	157	18	,	,	PUNCT
ijassa-1406	157	19	and	and	CCONJ
ijassa-1406	157	20	in	in	ADP
ijassa-1406	157	21	the	the	DET
ijassa-1406	157	22	direction	direction	NOUN
ijassa-1406	157	23	the	the	DET
ijassa-1406	157	24	direction	direction	NOUN
ijassa-1406	157	25	of	of	ADP
ijassa-1406	157	26	the	the	DET
ijassa-1406	157	27	negative	negative	ADJ
ijassa-1406	157	28	gradient	gradient	NOUN
ijassa-1406	157	29	of	of	ADP
ijassa-1406	157	30	this	this	DET
ijassa-1406	157	31	function	function	NOUN
ijassa-1406	157	32	at	at	ADP
ijassa-1406	157	33	uk	uk	PROPN
ijassa-1406	157	34	)	)	PUNCT
ijassa-1406	157	35	if	if	SCONJ
ijassa-1406	157	36	φ′(uk	φ′(uk	PROPN
ijassa-1406	157	37	)	)	PUNCT
ijassa-1406	157	38	̸=	̸=	PROPN
ijassa-1406	157	39	0	0	NUM
ijassa-1406	157	40	,	,	PUNCT
ijassa-1406	157	41	while	while	SCONJ
ijassa-1406	157	42	otherwise	otherwise	ADV
ijassa-1406	157	43	,	,	PUNCT
ijassa-1406	157	44	the	the	DET
ijassa-1406	157	45	algorithm	algorithm	NOUN
ijassa-1406	157	46	terminates	terminate	VERB
ijassa-1406	157	47	with	with	ADP
ijassa-1406	157	48	(	(	PUNCT
ijassa-1406	157	49	3.9	3.9	NUM
ijassa-1406	157	50	)	)	PUNCT
ijassa-1406	158	1	being	be	AUX
ijassa-1406	158	2	satisfied	satisfied	ADJ
ijassa-1406	158	3	again	again	ADV
ijassa-1406	158	4	,	,	PUNCT
ijassa-1406	158	5	the	the	DET
ijassa-1406	158	6	latter	latter	ADJ
ijassa-1406	158	7	following	follow	VERB
ijassa-1406	158	8	from	from	ADP
ijassa-1406	158	9	(	(	PUNCT
ijassa-1406	158	10	3.4	3.4	NUM
ijassa-1406	158	11	)	)	PUNCT
ijassa-1406	158	12	.	.	PUNCT
ijassa-1406	159	1	therefore	therefore	ADV
ijassa-1406	159	2	,	,	PUNCT
ijassa-1406	159	3	algorithm	algorithm	NOUN
ijassa-1406	159	4	3.2	3.2	NUM
ijassa-1406	159	5	either	either	CCONJ
ijassa-1406	159	6	terminates	terminate	VERB
ijassa-1406	159	7	with	with	ADP
ijassa-1406	159	8	some	some	DET
ijassa-1406	159	9	iterate	iterate	NOUN
ijassa-1406	159	10	uk	uk	NOUN
ijassa-1406	159	11	satisfying	satisfy	VERB
ijassa-1406	159	12	(	(	PUNCT
ijassa-1406	159	13	3.9	3.9	NUM
ijassa-1406	159	14	)	)	PUNCT
ijassa-1406	159	15	,	,	PUNCT
ijassa-1406	159	16	or	or	CCONJ
ijassa-1406	159	17	generates	generate	VERB
ijassa-1406	159	18	an	an	DET
ijassa-1406	159	19	infinite	infinite	ADJ
ijassa-1406	159	20	sequence	sequence	NOUN
ijassa-1406	159	21	{	{	PUNCT
ijassa-1406	159	22	uk	uk	PROPN
ijassa-1406	159	23	}	}	PUNCT
ijassa-1406	159	24	,	,	PUNCT
ijassa-1406	159	25	and	and	CCONJ
ijassa-1406	159	26	it	it	PRON
ijassa-1406	159	27	remains	remain	VERB
ijassa-1406	159	28	to	to	PART
ijassa-1406	159	29	analyze	analyze	VERB
ijassa-1406	159	30	the	the	DET
ijassa-1406	159	31	latter	latter	ADJ
ijassa-1406	159	32	case	case	NOUN
ijassa-1406	159	33	.	.	PUNCT
ijassa-1406	160	1	observe	observe	VERB
ijassa-1406	160	2	that	that	SCONJ
ijassa-1406	160	3	the	the	DET
ijassa-1406	160	4	sequence	sequence	NOUN
ijassa-1406	160	5	{	{	PUNCT
ijassa-1406	160	6	∥φ(uk)∥	∥φ(uk)∥	PROPN
ijassa-1406	160	7	}	}	PUNCT
ijassa-1406	160	8	is	be	AUX
ijassa-1406	160	9	always	always	ADV
ijassa-1406	160	10	monotonically	monotonically	ADV
ijassa-1406	160	11	non	non	ADJ
ijassa-1406	160	12	-	-	ADJ
ijassa-1406	160	13	increasing	increasing	ADJ
ijassa-1406	160	14	,	,	PUNCT
ijassa-1406	160	15	no	no	ADV
ijassa-1406	160	16	matter	matter	ADV
ijassa-1406	160	17	which	which	DET
ijassa-1406	160	18	search	search	NOUN
ijassa-1406	160	19	directions	direction	NOUN
ijassa-1406	160	20	are	be	AUX
ijassa-1406	160	21	used	use	VERB
ijassa-1406	160	22	.	.	PUNCT
ijassa-1406	161	1	but	but	CCONJ
ijassa-1406	161	2	this	this	DET
ijassa-1406	161	3	sequence	sequence	NOUN
ijassa-1406	161	4	is	be	AUX
ijassa-1406	161	5	bounded	bound	VERB
ijassa-1406	161	6	below	below	ADV
ijassa-1406	161	7	(	(	PUNCT
ijassa-1406	161	8	by	by	ADP
ijassa-1406	161	9	zero	zero	NUM
ijassa-1406	161	10	)	)	PUNCT
ijassa-1406	161	11	,	,	PUNCT
ijassa-1406	161	12	and	and	CCONJ
ijassa-1406	161	13	hence	hence	ADV
ijassa-1406	161	14	converges	converge	VERB
ijassa-1406	161	15	.	.	PUNCT
ijassa-1406	162	1	consider	consider	VERB
ijassa-1406	162	2	first	first	ADV
ijassa-1406	162	3	the	the	DET
ijassa-1406	162	4	case	case	NOUN
ijassa-1406	162	5	when	when	SCONJ
ijassa-1406	162	6	there	there	PRON
ijassa-1406	162	7	exists	exist	VERB
ijassa-1406	162	8	an	an	DET
ijassa-1406	162	9	infinite	infinite	ADJ
ijassa-1406	162	10	subsequence	subsequence	NOUN
ijassa-1406	162	11	{	{	PUNCT
ijassa-1406	162	12	ukj	ukj	NOUN
ijassa-1406	162	13	}	}	PUNCT
ijassa-1406	162	14	convergent	convergent	NOUN
ijassa-1406	162	15	to	to	ADP
ijassa-1406	162	16	some	some	DET
ijassa-1406	162	17	ū	ū	NOUN
ijassa-1406	162	18	,	,	PUNCT
ijassa-1406	162	19	and	and	CCONJ
ijassa-1406	162	20	such	such	ADJ
ijassa-1406	162	21	that	that	SCONJ
ijassa-1406	162	22	the	the	DET
ijassa-1406	162	23	semismooth	semismooth	NOUN
ijassa-1406	162	24	newton	newton	PROPN
ijassa-1406	162	25	direction	direction	NOUN
ijassa-1406	162	26	is	be	AUX
ijassa-1406	162	27	accepted	accept	VERB
ijassa-1406	162	28	by	by	ADP
ijassa-1406	162	29	algorithm	algorithm	NOUN
ijassa-1406	162	30	3.2	3.2	NUM
ijassa-1406	162	31	at	at	ADP
ijassa-1406	162	32	every	every	DET
ijassa-1406	162	33	point	point	NOUN
ijassa-1406	162	34	of	of	ADP
ijassa-1406	162	35	this	this	DET
ijassa-1406	162	36	subsequence	subsequence	NOUN
ijassa-1406	162	37	.	.	PUNCT
ijassa-1406	163	1	if	if	SCONJ
ijassa-1406	163	2	τ̄	τ̄	VERB
ijassa-1406	163	3	=	=	SYM
ijassa-1406	163	4	lim	lim	PROPN
ijassa-1406	163	5	sup	sup	NOUN
ijassa-1406	163	6	j→∞	j→∞	NUM
ijassa-1406	163	7	τkj	τkj	X
ijassa-1406	163	8	>	>	PUNCT
ijassa-1406	163	9	0	0	NUM
ijassa-1406	163	10	,	,	PUNCT
ijassa-1406	163	11	(	(	PUNCT
ijassa-1406	163	12	3.12	3.12	NUM
ijassa-1406	163	13	)	)	PUNCT
ijassa-1406	163	14	then	then	ADV
ijassa-1406	163	15	(	(	PUNCT
ijassa-1406	163	16	2.4	2.4	NUM
ijassa-1406	163	17	)	)	PUNCT
ijassa-1406	163	18	implies	imply	VERB
ijassa-1406	163	19	that	that	SCONJ
ijassa-1406	163	20	for	for	ADP
ijassa-1406	163	21	infinitely	infinitely	ADV
ijassa-1406	163	22	many	many	ADJ
ijassa-1406	163	23	indices	index	NOUN
ijassa-1406	163	24	kj	kj	PROPN
ijassa-1406	163	25	,	,	PUNCT
ijassa-1406	163	26	the	the	DET
ijassa-1406	163	27	residual	residual	ADJ
ijassa-1406	163	28	∥φ(ukj)∥	∥φ(ukj)∥	NOUN
ijassa-1406	163	29	is	be	AUX
ijassa-1406	163	30	reduced	reduce	VERB
ijassa-1406	163	31	at	at	ADP
ijassa-1406	163	32	least	least	ADJ
ijassa-1406	163	33	linearly	linearly	ADV
ijassa-1406	163	34	(	(	PUNCT
ijassa-1406	163	35	by	by	ADP
ijassa-1406	163	36	a	a	DET
ijassa-1406	163	37	factor	factor	NOUN
ijassa-1406	163	38	of	of	ADP
ijassa-1406	163	39	at	at	ADV
ijassa-1406	163	40	least	least	ADJ
ijassa-1406	163	41	(	(	PUNCT
ijassa-1406	163	42	1−	1−	NUM
ijassa-1406	163	43	στ̄/2	στ̄/2	PROPN
ijassa-1406	163	44	)	)	PUNCT
ijassa-1406	163	45	)	)	PUNCT
ijassa-1406	163	46	,	,	PUNCT
ijassa-1406	163	47	and	and	CCONJ
ijassa-1406	163	48	hence	hence	ADV
ijassa-1406	163	49	,	,	PUNCT
ijassa-1406	163	50	{	{	PUNCT
ijassa-1406	163	51	φ(ukj	φ(ukj	ADJ
ijassa-1406	163	52	)	)	PUNCT
ijassa-1406	163	53	}	}	PUNCT
ijassa-1406	163	54	→	→	SYM
ijassa-1406	163	55	0	0	PUNCT
ijassa-1406	163	56	as	as	SCONJ
ijassa-1406	163	57	j	j	PROPN
ijassa-1406	163	58	→	→	SYM
ijassa-1406	163	59	∞.	∞.	PROPN
ijassa-1406	163	60	since	since	SCONJ
ijassa-1406	163	61	{	{	PUNCT
ijassa-1406	163	62	∥φ(uk)∥	∥φ(uk)∥	NOUN
ijassa-1406	163	63	}	}	PUNCT
ijassa-1406	163	64	is	be	AUX
ijassa-1406	163	65	convergent	convergent	ADJ
ijassa-1406	163	66	,	,	PUNCT
ijassa-1406	163	67	we	we	PRON
ijassa-1406	163	68	conclude	conclude	VERB
ijassa-1406	163	69	that	that	SCONJ
ijassa-1406	163	70	(	(	PUNCT
ijassa-1406	163	71	3.11	3.11	NUM
ijassa-1406	163	72	)	)	PUNCT
ijassa-1406	163	73	holds	hold	VERB
ijassa-1406	163	74	.	.	PUNCT
ijassa-1406	164	1	copyright	copyright	NOUN
ijassa-1406	164	2	©	©	PROPN
ijassa-1406	164	3	2023	2023	NUM
ijassa-1406	164	4	assa	assa	NOUN
ijassa-1406	164	5	.	.	PUNCT
ijassa-1406	165	1	adv	adv	PROPN
ijassa-1406	165	2	syst	syst	PROPN
ijassa-1406	165	3	sci	sci	PROPN
ijassa-1406	165	4	appl	appl	PROPN
ijassa-1406	165	5	(	(	PUNCT
ijassa-1406	165	6	2023	2023	NUM
ijassa-1406	165	7	)	)	PUNCT
ijassa-1406	165	8	22	22	NUM
ijassa-1406	165	9	a.	a.	NOUN
ijassa-1406	165	10	izmailov	izmailov	NOUN
ijassa-1406	165	11	,	,	PUNCT
ijassa-1406	165	12	e.	e.	PROPN
ijassa-1406	165	13	uskov	uskov	PROPN
ijassa-1406	165	14	,	,	PUNCT
ijassa-1406	165	15	y.	y.	PROPN
ijassa-1406	165	16	zhibai	zhibai	PROPN
ijassa-1406	165	17	on	on	ADP
ijassa-1406	165	18	the	the	DET
ijassa-1406	165	19	other	other	ADJ
ijassa-1406	165	20	hand	hand	NOUN
ijassa-1406	165	21	,	,	PUNCT
ijassa-1406	165	22	if	if	SCONJ
ijassa-1406	165	23	(	(	PUNCT
ijassa-1406	165	24	3.12	3.12	NUM
ijassa-1406	165	25	)	)	PUNCT
ijassa-1406	165	26	is	be	AUX
ijassa-1406	165	27	not	not	PART
ijassa-1406	165	28	valid	valid	ADJ
ijassa-1406	165	29	,	,	PUNCT
ijassa-1406	165	30	then	then	ADV
ijassa-1406	165	31	lim	lim	PROPN
ijassa-1406	165	32	j→∞	j→∞	NOUN
ijassa-1406	165	33	τkj	τkj	PUNCT
ijassa-1406	166	1	=	=	SYM
ijassa-1406	166	2	0	0	NUM
ijassa-1406	166	3	,	,	PUNCT
ijassa-1406	166	4	(	(	PUNCT
ijassa-1406	166	5	3.13	3.13	NUM
ijassa-1406	166	6	)	)	PUNCT
ijassa-1406	166	7	implying	imply	VERB
ijassa-1406	166	8	that	that	SCONJ
ijassa-1406	166	9	for	for	ADP
ijassa-1406	166	10	each	each	DET
ijassa-1406	166	11	j	j	PROPN
ijassa-1406	166	12	large	large	ADJ
ijassa-1406	166	13	enough	enough	ADV
ijassa-1406	166	14	,	,	PUNCT
ijassa-1406	166	15	the	the	DET
ijassa-1406	166	16	initial	initial	ADJ
ijassa-1406	166	17	trial	trial	NOUN
ijassa-1406	166	18	stepsize	stepsize	NOUN
ijassa-1406	166	19	value	value	NOUN
ijassa-1406	166	20	had	have	AUX
ijassa-1406	166	21	been	be	AUX
ijassa-1406	166	22	reduced	reduce	VERB
ijassa-1406	166	23	at	at	ADP
ijassa-1406	166	24	least	least	ADJ
ijassa-1406	166	25	once	once	ADV
ijassa-1406	166	26	,	,	PUNCT
ijassa-1406	166	27	i.e.	i.e.	X
ijassa-1406	166	28	,	,	PUNCT
ijassa-1406	166	29	the	the	DET
ijassa-1406	166	30	value	value	NOUN
ijassa-1406	166	31	τ	τ	NOUN
ijassa-1406	166	32	=	=	SYM
ijassa-1406	166	33	τkj	τkj	X
ijassa-1406	166	34	/	/	SYM
ijassa-1406	166	35	θ	θ	NOUN
ijassa-1406	166	36	>	>	X
ijassa-1406	166	37	τkj	τkj	X
ijassa-1406	166	38	does	do	AUX
ijassa-1406	166	39	not	not	PART
ijassa-1406	166	40	satisfy	satisfy	VERB
ijassa-1406	166	41	(	(	PUNCT
ijassa-1406	166	42	2.4	2.4	NUM
ijassa-1406	166	43	)	)	PUNCT
ijassa-1406	166	44	.	.	PUNCT
ijassa-1406	167	1	since	since	SCONJ
ijassa-1406	167	2	(	(	PUNCT
ijassa-1406	167	3	2.4	2.4	NUM
ijassa-1406	167	4	)	)	PUNCT
ijassa-1406	167	5	is	be	AUX
ijassa-1406	167	6	equivalent	equivalent	ADJ
ijassa-1406	167	7	to	to	ADP
ijassa-1406	167	8	(	(	PUNCT
ijassa-1406	167	9	3.6	3.6	NUM
ijassa-1406	167	10	)	)	PUNCT
ijassa-1406	167	11	,	,	PUNCT
ijassa-1406	167	12	it	it	PRON
ijassa-1406	167	13	then	then	ADV
ijassa-1406	167	14	holds	hold	VERB
ijassa-1406	167	15	that	that	SCONJ
ijassa-1406	167	16	φ(ukj	φ(ukj	PROPN
ijassa-1406	167	17	+	+	NUM
ijassa-1406	167	18	τkjv	τkjv	ADJ
ijassa-1406	167	19	kj	kj	PROPN
ijassa-1406	167	20	/	/	PROPN
ijassa-1406	167	21	θ)−	θ)−	PROPN
ijassa-1406	167	22	φ(ukj	φ(ukj	PROPN
ijassa-1406	167	23	)	)	PUNCT
ijassa-1406	167	24	τkj	τkj	X
ijassa-1406	167	25	/	/	SYM
ijassa-1406	167	26	θ	θ	PROPN
ijassa-1406	167	27	>	>	X
ijassa-1406	167	28	σ(1−	σ(1−	PROPN
ijassa-1406	167	29	στkj/2)⟨φ′(uk	στkj/2)⟨φ′(uk	VERB
ijassa-1406	167	30	)	)	PUNCT
ijassa-1406	167	31	,	,	PUNCT
ijassa-1406	167	32	vk⟩.	vk⟩.	PROPN
ijassa-1406	167	33	(	(	PUNCT
ijassa-1406	167	34	3.14	3.14	NUM
ijassa-1406	167	35	)	)	PUNCT
ijassa-1406	167	36	observe	observe	VERB
ijassa-1406	167	37	that	that	SCONJ
ijassa-1406	167	38	according	accord	VERB
ijassa-1406	167	39	to	to	ADP
ijassa-1406	167	40	[	[	X
ijassa-1406	167	41	15	15	NUM
ijassa-1406	167	42	,	,	PUNCT
ijassa-1406	167	43	proposition	proposition	NOUN
ijassa-1406	167	44	5.5	5.5	NUM
ijassa-1406	167	45	]	]	PUNCT
ijassa-1406	167	46	,	,	PUNCT
ijassa-1406	167	47	φ	φ	PROPN
ijassa-1406	167	48	is	be	AUX
ijassa-1406	167	49	continuously	continuously	ADV
ijassa-1406	167	50	differentiable	differentiable	ADJ
ijassa-1406	167	51	on	on	ADP
ijassa-1406	167	52	rp	rp	NOUN
ijassa-1406	167	53	,	,	PUNCT
ijassa-1406	167	54	and	and	CCONJ
ijassa-1406	167	55	employing	employ	VERB
ijassa-1406	167	56	the	the	DET
ijassa-1406	167	57	mean	mean	ADJ
ijassa-1406	167	58	-	-	PUNCT
ijassa-1406	167	59	value	value	NOUN
ijassa-1406	167	60	theorem	theorem	NOUN
ijassa-1406	167	61	[	[	X
ijassa-1406	167	62	15	15	NUM
ijassa-1406	167	63	,	,	PUNCT
ijassa-1406	167	64	theorem	theorem	ADJ
ijassa-1406	167	65	a.10(a	a.10(a	PROPN
ijassa-1406	167	66	)	)	PUNCT
ijassa-1406	167	67	]	]	PUNCT
ijassa-1406	167	68	,	,	PUNCT
ijassa-1406	167	69	we	we	PRON
ijassa-1406	167	70	then	then	ADV
ijassa-1406	167	71	obtain	obtain	VERB
ijassa-1406	167	72	from	from	ADP
ijassa-1406	167	73	(	(	PUNCT
ijassa-1406	167	74	3.14	3.14	NUM
ijassa-1406	167	75	)	)	PUNCT
ijassa-1406	167	76	that	that	SCONJ
ijassa-1406	167	77	for	for	ADP
ijassa-1406	167	78	each	each	DET
ijassa-1406	167	79	j	j	NOUN
ijassa-1406	167	80	there	there	PRON
ijassa-1406	167	81	exists	exist	VERB
ijassa-1406	167	82	ωkj	ωkj	NOUN
ijassa-1406	167	83	∈	∈	PROPN
ijassa-1406	168	1	[	[	X
ijassa-1406	168	2	0	0	NUM
ijassa-1406	168	3	,	,	PUNCT
ijassa-1406	168	4	1	1	NUM
ijassa-1406	168	5	]	]	PUNCT
ijassa-1406	168	6	such	such	ADJ
ijassa-1406	168	7	that	that	SCONJ
ijassa-1406	168	8	⟨φ(ukj	⟨φ(ukj	PROPN
ijassa-1406	168	9	+	+	X
ijassa-1406	168	10	ωkjτkjv	ωkjτkjv	ADJ
ijassa-1406	168	11	kj	kj	PROPN
ijassa-1406	168	12	/	/	SYM
ijassa-1406	168	13	θ	θ	PROPN
ijassa-1406	168	14	)	)	PUNCT
ijassa-1406	168	15	,	,	PUNCT
ijassa-1406	168	16	vkj⟩	vkj⟩	VERB
ijassa-1406	168	17	>	>	X
ijassa-1406	168	18	σ(1−	σ(1−	PROPN
ijassa-1406	168	19	στkj/2)⟨φ′(uk	στkj/2)⟨φ′(uk	PROPN
ijassa-1406	168	20	)	)	PUNCT
ijassa-1406	168	21	,	,	PUNCT
ijassa-1406	168	22	vk⟩.	vk⟩.	PROPN
ijassa-1406	168	23	(	(	PUNCT
ijassa-1406	168	24	3.15	3.15	NUM
ijassa-1406	168	25	)	)	PUNCT
ijassa-1406	168	26	if	if	SCONJ
ijassa-1406	168	27	the	the	DET
ijassa-1406	168	28	sequence	sequence	NOUN
ijassa-1406	168	29	{	{	PUNCT
ijassa-1406	168	30	vkj	vkj	NOUN
ijassa-1406	168	31	}	}	PUNCT
ijassa-1406	168	32	of	of	ADP
ijassa-1406	168	33	the	the	DET
ijassa-1406	168	34	semismooth	semismooth	NOUN
ijassa-1406	168	35	newton	newton	PROPN
ijassa-1406	168	36	directions	direction	NOUN
ijassa-1406	168	37	is	be	AUX
ijassa-1406	168	38	unbounded	unbounde	VERB
ijassa-1406	168	39	,	,	PUNCT
ijassa-1406	168	40	condition	condition	NOUN
ijassa-1406	168	41	(	(	PUNCT
ijassa-1406	168	42	3.7	3.7	NUM
ijassa-1406	168	43	)	)	PUNCT
ijassa-1406	168	44	implies	imply	VERB
ijassa-1406	168	45	that	that	SCONJ
ijassa-1406	168	46	lim	lim	PROPN
ijassa-1406	168	47	inf	inf	PROPN
ijassa-1406	168	48	j→∞	j→∞	NOUN
ijassa-1406	168	49	∥φ(ukj)∥	∥φ(ukj)∥	NOUN
ijassa-1406	168	50	=	=	SYM
ijassa-1406	168	51	0	0	X
ijassa-1406	168	52	.	.	PUNCT
ijassa-1406	169	1	in	in	ADP
ijassa-1406	169	2	view	view	NOUN
ijassa-1406	169	3	of	of	ADP
ijassa-1406	169	4	convergence	convergence	NOUN
ijassa-1406	169	5	of	of	ADP
ijassa-1406	169	6	the	the	DET
ijassa-1406	169	7	sequence	sequence	NOUN
ijassa-1406	169	8	{	{	PUNCT
ijassa-1406	169	9	∥φ(uk)∥	∥φ(uk)∥	PROPN
ijassa-1406	169	10	}	}	PUNCT
ijassa-1406	169	11	,	,	PUNCT
ijassa-1406	169	12	this	this	PRON
ijassa-1406	169	13	again	again	ADV
ijassa-1406	169	14	implies	imply	VERB
ijassa-1406	169	15	(	(	PUNCT
ijassa-1406	169	16	3.11	3.11	NUM
ijassa-1406	169	17	)	)	PUNCT
ijassa-1406	169	18	.	.	PUNCT
ijassa-1406	170	1	therefore	therefore	ADV
ijassa-1406	170	2	,	,	PUNCT
ijassa-1406	170	3	it	it	PRON
ijassa-1406	170	4	remains	remain	VERB
ijassa-1406	170	5	to	to	PART
ijassa-1406	170	6	consider	consider	VERB
ijassa-1406	170	7	the	the	DET
ijassa-1406	170	8	case	case	NOUN
ijassa-1406	170	9	when	when	SCONJ
ijassa-1406	170	10	{	{	PUNCT
ijassa-1406	170	11	vkj	vkj	NOUN
ijassa-1406	170	12	}	}	PUNCT
ijassa-1406	170	13	is	be	AUX
ijassa-1406	170	14	bounded	bound	VERB
ijassa-1406	170	15	.	.	PUNCT
ijassa-1406	171	1	taking	take	VERB
ijassa-1406	171	2	a	a	DET
ijassa-1406	171	3	further	further	ADJ
ijassa-1406	171	4	subsequence	subsequence	NOUN
ijassa-1406	171	5	,	,	PUNCT
ijassa-1406	171	6	if	if	SCONJ
ijassa-1406	171	7	necessary	necessary	ADJ
ijassa-1406	171	8	,	,	PUNCT
ijassa-1406	171	9	we	we	PRON
ijassa-1406	171	10	may	may	AUX
ijassa-1406	171	11	assume	assume	VERB
ijassa-1406	171	12	that	that	SCONJ
ijassa-1406	171	13	{	{	PUNCT
ijassa-1406	171	14	vkj	vkj	NOUN
ijassa-1406	171	15	}	}	PUNCT
ijassa-1406	171	16	converges	converge	NOUN
ijassa-1406	171	17	to	to	ADP
ijassa-1406	171	18	some	some	DET
ijassa-1406	171	19	ṽ	ṽ	PROPN
ijassa-1406	171	20	,	,	PUNCT
ijassa-1406	171	21	and	and	CCONJ
ijassa-1406	171	22	therefore	therefore	ADV
ijassa-1406	171	23	,	,	PUNCT
ijassa-1406	171	24	by	by	ADP
ijassa-1406	171	25	(	(	PUNCT
ijassa-1406	171	26	3.5	3.5	NUM
ijassa-1406	171	27	)	)	PUNCT
ijassa-1406	171	28	,	,	PUNCT
ijassa-1406	171	29	⟨φ′(ū	⟨φ′(ū	PROPN
ijassa-1406	171	30	)	)	PUNCT
ijassa-1406	171	31	,	,	PUNCT
ijassa-1406	171	32	ṽ⟩	ṽ⟩	PROPN
ijassa-1406	171	33	=	=	SYM
ijassa-1406	171	34	−2φ′(ū	−2φ′(ū	PROPN
ijassa-1406	171	35	)	)	PUNCT
ijassa-1406	171	36	.	.	PUNCT
ijassa-1406	172	1	then	then	ADV
ijassa-1406	172	2	by	by	ADP
ijassa-1406	172	3	(	(	PUNCT
ijassa-1406	172	4	3.13	3.13	NUM
ijassa-1406	172	5	)	)	PUNCT
ijassa-1406	172	6	,	,	PUNCT
ijassa-1406	172	7	passing	pass	VERB
ijassa-1406	172	8	onto	onto	ADP
ijassa-1406	172	9	the	the	DET
ijassa-1406	172	10	limit	limit	NOUN
ijassa-1406	172	11	in	in	ADP
ijassa-1406	172	12	(	(	PUNCT
ijassa-1406	172	13	3.15	3.15	NUM
ijassa-1406	172	14	)	)	PUNCT
ijassa-1406	172	15	as	as	ADP
ijassa-1406	172	16	j	j	PROPN
ijassa-1406	172	17	→	→	SYM
ijassa-1406	172	18	∞	∞	PROPN
ijassa-1406	172	19	,	,	PUNCT
ijassa-1406	172	20	we	we	PRON
ijassa-1406	172	21	obtain	obtain	VERB
ijassa-1406	172	22	that	that	DET
ijassa-1406	172	23	−φ(ū	−φ(ū	PROPN
ijassa-1406	172	24	)	)	PUNCT
ijassa-1406	172	25	≥	≥	NOUN
ijassa-1406	172	26	−σφ(ū	−σφ(ū	NUM
ijassa-1406	172	27	)	)	PUNCT
ijassa-1406	172	28	,	,	PUNCT
ijassa-1406	172	29	which	which	PRON
ijassa-1406	172	30	is	be	AUX
ijassa-1406	172	31	only	only	ADV
ijassa-1406	172	32	possible	possible	ADJ
ijassa-1406	172	33	when	when	SCONJ
ijassa-1406	172	34	φ(ū	φ(ū	X
ijassa-1406	172	35	)	)	PUNCT
ijassa-1406	172	36	=	=	SYM
ijassa-1406	173	1	0	0	X
ijassa-1406	173	2	.	.	PUNCT
ijassa-1406	174	1	it	it	PRON
ijassa-1406	174	2	remains	remain	VERB
ijassa-1406	174	3	to	to	PART
ijassa-1406	174	4	consider	consider	VERB
ijassa-1406	174	5	the	the	DET
ijassa-1406	174	6	case	case	NOUN
ijassa-1406	174	7	when	when	SCONJ
ijassa-1406	174	8	there	there	PRON
ijassa-1406	174	9	exists	exist	VERB
ijassa-1406	174	10	an	an	DET
ijassa-1406	174	11	infinite	infinite	ADJ
ijassa-1406	174	12	subsequence	subsequence	NOUN
ijassa-1406	174	13	{	{	PUNCT
ijassa-1406	174	14	ukj	ukj	NOUN
ijassa-1406	174	15	}	}	PUNCT
ijassa-1406	174	16	convergent	convergent	NOUN
ijassa-1406	174	17	to	to	ADP
ijassa-1406	174	18	some	some	DET
ijassa-1406	174	19	ū	ū	NOUN
ijassa-1406	174	20	,	,	PUNCT
ijassa-1406	174	21	and	and	CCONJ
ijassa-1406	174	22	such	such	ADJ
ijassa-1406	174	23	that	that	SCONJ
ijassa-1406	174	24	the	the	DET
ijassa-1406	174	25	semismooth	semismooth	NOUN
ijassa-1406	174	26	newton	newton	PROPN
ijassa-1406	174	27	direction	direction	NOUN
ijassa-1406	174	28	is	be	AUX
ijassa-1406	174	29	not	not	PART
ijassa-1406	174	30	accepted	accept	VERB
ijassa-1406	174	31	by	by	ADP
ijassa-1406	174	32	algorithm	algorithm	NOUN
ijassa-1406	174	33	3.2	3.2	NUM
ijassa-1406	174	34	at	at	ADP
ijassa-1406	174	35	every	every	DET
ijassa-1406	174	36	point	point	NOUN
ijassa-1406	174	37	of	of	ADP
ijassa-1406	174	38	this	this	DET
ijassa-1406	174	39	subsequence	subsequence	NOUN
ijassa-1406	174	40	.	.	PUNCT
ijassa-1406	175	1	in	in	ADP
ijassa-1406	175	2	this	this	DET
ijassa-1406	175	3	case	case	NOUN
ijassa-1406	175	4	,	,	PUNCT
ijassa-1406	175	5	the	the	DET
ijassa-1406	175	6	iterates	iterate	NOUN
ijassa-1406	175	7	{	{	PUNCT
ijassa-1406	175	8	ukj+1	ukj+1	PRON
ijassa-1406	175	9	}	}	PUNCT
ijassa-1406	175	10	are	be	AUX
ijassa-1406	175	11	generated	generate	VERB
ijassa-1406	175	12	by	by	ADP
ijassa-1406	175	13	the	the	DET
ijassa-1406	175	14	gradient	gradient	ADJ
ijassa-1406	175	15	steps	step	NOUN
ijassa-1406	175	16	with	with	ADP
ijassa-1406	175	17	armijo	armijo	PROPN
ijassa-1406	175	18	linesearch	linesearch	NOUN
ijassa-1406	175	19	for	for	ADP
ijassa-1406	175	20	the	the	DET
ijassa-1406	175	21	continuously	continuously	ADV
ijassa-1406	175	22	differentiable	differentiable	ADJ
ijassa-1406	175	23	merit	merit	NOUN
ijassa-1406	175	24	function	function	PROPN
ijassa-1406	175	25	φ	φ	PROPN
ijassa-1406	175	26	.	.	PUNCT
ijassa-1406	176	1	then	then	ADV
ijassa-1406	176	2	by	by	ADP
ijassa-1406	176	3	standard	standard	ADJ
ijassa-1406	176	4	argument	argument	NOUN
ijassa-1406	176	5	(	(	PUNCT
ijassa-1406	176	6	see	see	VERB
ijassa-1406	176	7	,	,	PUNCT
ijassa-1406	176	8	e.g.	e.g.	ADV
ijassa-1406	176	9	,	,	PUNCT
ijassa-1406	176	10	[	[	X
ijassa-1406	176	11	2	2	NUM
ijassa-1406	176	12	,	,	PUNCT
ijassa-1406	176	13	proposition	proposition	NOUN
ijassa-1406	176	14	1.2.3	1.2.3	NUM
ijassa-1406	176	15	]	]	PUNCT
ijassa-1406	176	16	)	)	PUNCT
ijassa-1406	177	1	,	,	PUNCT
ijassa-1406	177	2	it	it	PRON
ijassa-1406	177	3	follows	follow	VERB
ijassa-1406	177	4	that	that	SCONJ
ijassa-1406	177	5	φ′(ū	φ′(ū	PROPN
ijassa-1406	177	6	)	)	PUNCT
ijassa-1406	177	7	=	=	SYM
ijassa-1406	177	8	0	0	NUM
ijassa-1406	177	9	,	,	PUNCT
ijassa-1406	177	10	and	and	CCONJ
ijassa-1406	177	11	according	accord	VERB
ijassa-1406	177	12	to	to	ADP
ijassa-1406	177	13	(	(	PUNCT
ijassa-1406	177	14	3.4	3.4	NUM
ijassa-1406	177	15	)	)	PUNCT
ijassa-1406	177	16	,	,	PUNCT
ijassa-1406	177	17	this	this	DET
ijassa-1406	177	18	yields	yield	NOUN
ijassa-1406	177	19	(	(	PUNCT
ijassa-1406	177	20	3.10	3.10	NUM
ijassa-1406	177	21	)	)	PUNCT
ijassa-1406	177	22	.	.	PUNCT
ijassa-1406	178	1	4	4	X
ijassa-1406	178	2	.	.	X
ijassa-1406	178	3	numerical	numerical	ADJ
ijassa-1406	178	4	results	result	NOUN
ijassa-1406	178	5	in	in	ADP
ijassa-1406	178	6	this	this	DET
ijassa-1406	178	7	section	section	NOUN
ijassa-1406	178	8	we	we	PRON
ijassa-1406	178	9	provide	provide	VERB
ijassa-1406	178	10	some	some	DET
ijassa-1406	178	11	numerical	numerical	ADJ
ijassa-1406	178	12	comparisons	comparison	NOUN
ijassa-1406	178	13	of	of	ADP
ijassa-1406	178	14	the	the	DET
ijassa-1406	178	15	algorithms	algorithm	NOUN
ijassa-1406	178	16	discussed	discuss	VERB
ijassa-1406	178	17	above	above	ADV
ijassa-1406	178	18	for	for	ADP
ijassa-1406	178	19	a	a	DET
ijassa-1406	178	20	collection	collection	NOUN
ijassa-1406	178	21	of	of	ADP
ijassa-1406	178	22	small	small	ADJ
ijassa-1406	178	23	ncps	ncps	PROPN
ijassa-1406	178	24	taken	take	VERB
ijassa-1406	178	25	from	from	ADP
ijassa-1406	178	26	[	[	X
ijassa-1406	178	27	19	19	NUM
ijassa-1406	178	28	]	]	PUNCT
ijassa-1406	178	29	,	,	PUNCT
ijassa-1406	178	30	and	and	CCONJ
ijassa-1406	178	31	for	for	ADP
ijassa-1406	178	32	some	some	DET
ijassa-1406	178	33	other	other	ADJ
ijassa-1406	178	34	examples	example	NOUN
ijassa-1406	178	35	of	of	ADP
ijassa-1406	178	36	ncps	ncps	PROPN
ijassa-1406	178	37	with	with	ADP
ijassa-1406	178	38	solutions	solution	NOUN
ijassa-1406	178	39	violating	violate	VERB
ijassa-1406	178	40	strict	strict	ADJ
ijassa-1406	178	41	complementarity	complementarity	NOUN
ijassa-1406	178	42	,	,	PUNCT
ijassa-1406	178	43	taken	take	VERB
ijassa-1406	178	44	from	from	ADP
ijassa-1406	178	45	various	various	ADJ
ijassa-1406	178	46	sources	source	NOUN
ijassa-1406	178	47	.	.	PUNCT
ijassa-1406	179	1	for	for	ADP
ijassa-1406	179	2	the	the	DET
ijassa-1406	179	3	former	former	ADJ
ijassa-1406	179	4	,	,	PUNCT
ijassa-1406	179	5	we	we	PRON
ijassa-1406	179	6	use	use	VERB
ijassa-1406	179	7	the	the	DET
ijassa-1406	179	8	identifiers	identifier	NOUN
ijassa-1406	179	9	of	of	ADP
ijassa-1406	179	10	the	the	DET
ijassa-1406	179	11	problems	problem	NOUN
ijassa-1406	179	12	adopted	adopt	VERB
ijassa-1406	179	13	in	in	ADP
ijassa-1406	179	14	[	[	X
ijassa-1406	179	15	19	19	NUM
ijassa-1406	179	16	]	]	PUNCT
ijassa-1406	179	17	,	,	PUNCT
ijassa-1406	179	18	while	while	SCONJ
ijassa-1406	179	19	the	the	DET
ijassa-1406	179	20	latter	latter	ADJ
ijassa-1406	179	21	are	be	AUX
ijassa-1406	179	22	cited	cite	VERB
ijassa-1406	179	23	as	as	SCONJ
ijassa-1406	179	24	they	they	PRON
ijassa-1406	179	25	appear	appear	VERB
ijassa-1406	179	26	in	in	ADP
ijassa-1406	179	27	the	the	DET
ijassa-1406	179	28	related	related	ADJ
ijassa-1406	179	29	references	reference	NOUN
ijassa-1406	179	30	.	.	PUNCT
ijassa-1406	180	1	for	for	ADP
ijassa-1406	180	2	each	each	PRON
ijassa-1406	180	3	of	of	ADP
ijassa-1406	180	4	these	these	DET
ijassa-1406	180	5	test	test	NOUN
ijassa-1406	180	6	problems	problem	NOUN
ijassa-1406	180	7	,	,	PUNCT
ijassa-1406	180	8	a	a	DET
ijassa-1406	180	9	solution	solution	NOUN
ijassa-1406	180	10	of	of	ADP
ijassa-1406	180	11	interest	interest	NOUN
ijassa-1406	180	12	ū	ū	NOUN
ijassa-1406	180	13	,	,	PUNCT
ijassa-1406	180	14	violating	violate	VERB
ijassa-1406	180	15	strict	strict	ADJ
ijassa-1406	180	16	complementarity	complementarity	NOUN
ijassa-1406	180	17	,	,	PUNCT
ijassa-1406	180	18	is	be	AUX
ijassa-1406	180	19	known	know	VERB
ijassa-1406	180	20	;	;	PUNCT
ijassa-1406	180	21	this	this	DET
ijassa-1406	180	22	information	information	NOUN
ijassa-1406	180	23	is	be	AUX
ijassa-1406	180	24	provided	provide	VERB
ijassa-1406	180	25	in	in	ADP
ijassa-1406	180	26	table	table	NOUN
ijassa-1406	180	27	3.1	3.1	NUM
ijassa-1406	180	28	.	.	PUNCT
ijassa-1406	181	1	the	the	DET
ijassa-1406	181	2	algorithms	algorithm	NOUN
ijassa-1406	181	3	being	be	AUX
ijassa-1406	181	4	tested	test	VERB
ijassa-1406	181	5	are	be	AUX
ijassa-1406	181	6	abbreviated	abbreviate	VERB
ijassa-1406	181	7	as	as	SCONJ
ijassa-1406	181	8	follows	follow	VERB
ijassa-1406	181	9	:	:	PUNCT
ijassa-1406	182	1	•	•	NUM
ijassa-1406	182	2	nm	nm	NOUN
ijassa-1406	182	3	is	be	AUX
ijassa-1406	182	4	algorithm	algorithm	NOUN
ijassa-1406	182	5	2.1	2.1	NUM
ijassa-1406	182	6	.	.	PUNCT
ijassa-1406	183	1	•	•	NUM
ijassa-1406	183	2	nm	nm	NOUN
ijassa-1406	183	3	-	-	PUNCT
ijassa-1406	183	4	ep	ep	ADJ
ijassa-1406	183	5	(	(	PUNCT
ijassa-1406	183	6	for	for	ADP
ijassa-1406	183	7	“	"	PUNCT
ijassa-1406	183	8	extrapolation	extrapolation	NOUN
ijassa-1406	183	9	”	"	PUNCT
ijassa-1406	183	10	)	)	PUNCT
ijassa-1406	183	11	is	be	AUX
ijassa-1406	183	12	algorithm	algorithm	NOUN
ijassa-1406	183	13	2.1	2.1	NUM
ijassa-1406	183	14	,	,	PUNCT
ijassa-1406	183	15	generating	generate	VERB
ijassa-1406	183	16	also	also	ADV
ijassa-1406	183	17	an	an	DET
ijassa-1406	183	18	auxiliary	auxiliary	ADJ
ijassa-1406	183	19	sequence	sequence	NOUN
ijassa-1406	183	20	{	{	PUNCT
ijassa-1406	183	21	ûk	ûk	PROPN
ijassa-1406	183	22	}	}	PUNCT
ijassa-1406	183	23	according	accord	VERB
ijassa-1406	183	24	to	to	ADP
ijassa-1406	183	25	(	(	PUNCT
ijassa-1406	183	26	2.5	2.5	NUM
ijassa-1406	183	27	)	)	PUNCT
ijassa-1406	183	28	.	.	PUNCT
ijassa-1406	184	1	copyright	copyright	NOUN
ijassa-1406	184	2	©	©	PROPN
ijassa-1406	184	3	2023	2023	NUM
ijassa-1406	184	4	assa	assa	NOUN
ijassa-1406	184	5	.	.	PUNCT
ijassa-1406	185	1	adv	adv	PROPN
ijassa-1406	185	2	syst	syst	PROPN
ijassa-1406	185	3	sci	sci	PROPN
ijassa-1406	185	4	appl	appl	PROPN
ijassa-1406	185	5	(	(	PUNCT
ijassa-1406	185	6	2023	2023	NUM
ijassa-1406	185	7	)	)	PUNCT
ijassa-1406	185	8	newton	newton	PROPN
ijassa-1406	185	9	method	method	NOUN
ijassa-1406	185	10	vs.	vs.	ADP
ijassa-1406	185	11	semismooth	semismooth	NOUN
ijassa-1406	185	12	newton	newton	PROPN
ijassa-1406	185	13	method	method	VERB
ijassa-1406	185	14	23	23	NUM
ijassa-1406	185	15	100	100	NUM
ijassa-1406	185	16	101	101	NUM
ijassa-1406	185	17	0	0	NUM
ijassa-1406	185	18	0.2	0.2	NUM
ijassa-1406	185	19	0.4	0.4	NUM
ijassa-1406	185	20	0.6	0.6	NUM
ijassa-1406	185	21	0.8	0.8	NUM
ijassa-1406	185	22	1	1	NUM
ijassa-1406	185	23	nm	nm	PRON
ijassa-1406	185	24	nm	nm	NOUN
ijassa-1406	185	25	-	-	ADJ
ijassa-1406	185	26	ep	ep	ADJ
ijassa-1406	185	27	snm	snm	PROPN
ijassa-1406	185	28	snm	snm	PROPN
ijassa-1406	185	29	-	-	PUNCT
ijassa-1406	185	30	ep	ep	PROPN
ijassa-1406	185	31	fig	fig	NOUN
ijassa-1406	185	32	.	.	PUNCT
ijassa-1406	186	1	3.1	3.1	NUM
ijassa-1406	186	2	.	.	PUNCT
ijassa-1406	186	3	single	single	ADJ
ijassa-1406	186	4	runs	run	NOUN
ijassa-1406	186	5	from	from	ADP
ijassa-1406	186	6	“	"	PUNCT
ijassa-1406	186	7	standard	standard	NOUN
ijassa-1406	186	8	”	"	PUNCT
ijassa-1406	186	9	starting	start	VERB
ijassa-1406	186	10	points	point	NOUN
ijassa-1406	186	11	.	.	PUNCT
ijassa-1406	187	1	100	100	NUM
ijassa-1406	187	2	101	101	NUM
ijassa-1406	187	3	0	0	NUM
ijassa-1406	187	4	0.2	0.2	NUM
ijassa-1406	187	5	0.4	0.4	NUM
ijassa-1406	187	6	0.6	0.6	NUM
ijassa-1406	187	7	0.8	0.8	NUM
ijassa-1406	187	8	1	1	NUM
ijassa-1406	187	9	nm	nm	PRON
ijassa-1406	187	10	nm	nm	NOUN
ijassa-1406	187	11	-	-	ADJ
ijassa-1406	187	12	ep	ep	ADJ
ijassa-1406	187	13	snm	snm	PROPN
ijassa-1406	187	14	snm	snm	PROPN
ijassa-1406	187	15	-	-	PUNCT
ijassa-1406	187	16	ep	ep	PROPN
ijassa-1406	187	17	fig	fig	NOUN
ijassa-1406	187	18	.	.	PUNCT
ijassa-1406	188	1	3.2	3.2	NUM
ijassa-1406	188	2	.	.	PUNCT
ijassa-1406	189	1	multiple	multiple	ADJ
ijassa-1406	189	2	runs	run	NOUN
ijassa-1406	189	3	from	from	ADP
ijassa-1406	189	4	random	random	ADJ
ijassa-1406	189	5	starting	starting	NOUN
ijassa-1406	189	6	points	point	NOUN
ijassa-1406	189	7	.	.	PUNCT
ijassa-1406	190	1	copyright	copyright	NOUN
ijassa-1406	190	2	©	©	PROPN
ijassa-1406	190	3	2023	2023	NUM
ijassa-1406	190	4	assa	assa	NOUN
ijassa-1406	190	5	.	.	PUNCT
ijassa-1406	191	1	adv	adv	PROPN
ijassa-1406	191	2	syst	syst	PROPN
ijassa-1406	191	3	sci	sci	PROPN
ijassa-1406	191	4	appl	appl	PROPN
ijassa-1406	191	5	(	(	PUNCT
ijassa-1406	191	6	2023	2023	NUM
ijassa-1406	191	7	)	)	PUNCT
ijassa-1406	191	8	24	24	NUM
ijassa-1406	191	9	a.	a.	NOUN
ijassa-1406	191	10	izmailov	izmailov	NOUN
ijassa-1406	191	11	,	,	PUNCT
ijassa-1406	191	12	e.	e.	PROPN
ijassa-1406	191	13	uskov	uskov	PROPN
ijassa-1406	191	14	,	,	PUNCT
ijassa-1406	191	15	y.	y.	PROPN
ijassa-1406	191	16	zhibai	zhibai	PROPN
ijassa-1406	191	17	•	•	PROPN
ijassa-1406	191	18	snm	snm	PROPN
ijassa-1406	191	19	is	be	AUX
ijassa-1406	191	20	algorithm	algorithm	NOUN
ijassa-1406	191	21	3.1	3.1	NUM
ijassa-1406	191	22	.	.	PUNCT
ijassa-1406	191	23	•	•	NUM
ijassa-1406	191	24	snm	snm	PROPN
ijassa-1406	191	25	-	-	PUNCT
ijassa-1406	191	26	ep	ep	PROPN
ijassa-1406	191	27	is	be	AUX
ijassa-1406	191	28	algorithm	algorithm	NOUN
ijassa-1406	191	29	3.1	3.1	NUM
ijassa-1406	191	30	,	,	PUNCT
ijassa-1406	191	31	generating	generate	VERB
ijassa-1406	191	32	also	also	ADV
ijassa-1406	191	33	an	an	DET
ijassa-1406	191	34	auxiliary	auxiliary	ADJ
ijassa-1406	191	35	sequence	sequence	NOUN
ijassa-1406	191	36	{	{	PUNCT
ijassa-1406	191	37	ûk	ûk	PROPN
ijassa-1406	191	38	}	}	PUNCT
ijassa-1406	191	39	according	accord	VERB
ijassa-1406	191	40	to	to	ADP
ijassa-1406	191	41	(	(	PUNCT
ijassa-1406	191	42	2.5	2.5	NUM
ijassa-1406	191	43	)	)	PUNCT
ijassa-1406	191	44	.	.	PUNCT
ijassa-1406	192	1	all	all	DET
ijassa-1406	192	2	algorithms	algorithm	NOUN
ijassa-1406	192	3	were	be	AUX
ijassa-1406	192	4	run	run	VERB
ijassa-1406	192	5	with	with	ADP
ijassa-1406	192	6	with	with	ADP
ijassa-1406	192	7	parameter	parameter	NOUN
ijassa-1406	192	8	values	value	NOUN
ijassa-1406	192	9	σ	σ	X
ijassa-1406	193	1	=	=	PUNCT
ijassa-1406	193	2	0.01	0.01	NUM
ijassa-1406	193	3	and	and	CCONJ
ijassa-1406	193	4	θ	θ	NOUN
ijassa-1406	193	5	=	=	SYM
ijassa-1406	193	6	0.5	0.5	NUM
ijassa-1406	193	7	.	.	PUNCT
ijassa-1406	194	1	runs	run	NOUN
ijassa-1406	194	2	of	of	ADP
ijassa-1406	194	3	nm	nm	NOUN
ijassa-1406	194	4	and	and	CCONJ
ijassa-1406	194	5	snm	snm	PROPN
ijassa-1406	194	6	were	be	AUX
ijassa-1406	194	7	terminate	terminate	NOUN
ijassa-1406	194	8	with	with	ADP
ijassa-1406	194	9	success	success	NOUN
ijassa-1406	194	10	declared	declare	VERB
ijassa-1406	194	11	once	once	ADV
ijassa-1406	194	12	an	an	DET
ijassa-1406	194	13	iterate	iterate	NOUN
ijassa-1406	194	14	uk	uk	PROPN
ijassa-1406	194	15	was	be	AUX
ijassa-1406	194	16	generated	generate	VERB
ijassa-1406	194	17	satisfying	satisfy	VERB
ijassa-1406	194	18	∥φ(uk)∥	∥φ(uk)∥	PROPN
ijassa-1406	194	19	≤	≤	NOUN
ijassa-1406	194	20	10−11	10−11	NUM
ijassa-1406	194	21	.	.	PUNCT
ijassa-1406	195	1	for	for	ADP
ijassa-1406	195	2	nm	nm	PROPN
ijassa-1406	195	3	-	-	PUNCT
ijassa-1406	195	4	ep	ep	ADJ
ijassa-1406	195	5	and	and	CCONJ
ijassa-1406	195	6	snm	snm	PROPN
ijassa-1406	195	7	-	-	PUNCT
ijassa-1406	195	8	ep	ep	PROPN
ijassa-1406	195	9	,	,	PUNCT
ijassa-1406	195	10	for	for	ADP
ijassa-1406	195	11	k	k	PROPN
ijassa-1406	195	12	=	=	SYM
ijassa-1406	195	13	1	1	NUM
ijassa-1406	195	14	,	,	PUNCT
ijassa-1406	195	15	2	2	NUM
ijassa-1406	195	16	,	,	PUNCT
ijassa-1406	195	17	.	.	PUNCT
ijassa-1406	195	18	.	.	PUNCT
ijassa-1406	195	19	.	.	PUNCT
ijassa-1406	196	1	,	,	PUNCT
ijassa-1406	196	2	we	we	PRON
ijassa-1406	196	3	first	first	ADV
ijassa-1406	196	4	generated	generate	VERB
ijassa-1406	196	5	ûk	ûk	PROPN
ijassa-1406	196	6	according	accord	VERB
ijassa-1406	196	7	to	to	ADP
ijassa-1406	196	8	(	(	PUNCT
ijassa-1406	196	9	2.5	2.5	NUM
ijassa-1406	196	10	)	)	PUNCT
ijassa-1406	196	11	,	,	PUNCT
ijassa-1406	196	12	and	and	CCONJ
ijassa-1406	196	13	terminated	terminate	VERB
ijassa-1406	196	14	the	the	DET
ijassa-1406	196	15	run	run	NOUN
ijassa-1406	196	16	with	with	ADP
ijassa-1406	196	17	success	success	NOUN
ijassa-1406	196	18	if	if	SCONJ
ijassa-1406	196	19	∥φ(ûk)∥	∥φ(ûk)∥	ADP
ijassa-1406	196	20	≤	≤	NUM
ijassa-1406	196	21	10−11	10−11	NUM
ijassa-1406	196	22	.	.	PUNCT
ijassa-1406	197	1	(	(	PUNCT
ijassa-1406	197	2	4.1	4.1	NUM
ijassa-1406	197	3	)	)	PUNCT
ijassa-1406	197	4	convergence	convergence	NOUN
ijassa-1406	197	5	to	to	ADP
ijassa-1406	197	6	the	the	DET
ijassa-1406	197	7	solution	solution	NOUN
ijassa-1406	197	8	of	of	ADP
ijassa-1406	197	9	interest	interest	NOUN
ijassa-1406	197	10	ū	ū	NOUN
ijassa-1406	197	11	was	be	AUX
ijassa-1406	197	12	declared	declare	VERB
ijassa-1406	197	13	when	when	SCONJ
ijassa-1406	197	14	,	,	PUNCT
ijassa-1406	197	15	at	at	ADP
ijassa-1406	197	16	successful	successful	ADJ
ijassa-1406	197	17	termination	termination	NOUN
ijassa-1406	197	18	,	,	PUNCT
ijassa-1406	197	19	we	we	PRON
ijassa-1406	197	20	had	have	AUX
ijassa-1406	197	21	∥uk	∥uk	VERB
ijassa-1406	197	22	−	−	PROPN
ijassa-1406	197	23	ū∥	ū∥	PROPN
ijassa-1406	197	24	≤	≤	PROPN
ijassa-1406	197	25	10−3	10−3	NUM
ijassa-1406	197	26	(	(	PUNCT
ijassa-1406	197	27	with	with	ADP
ijassa-1406	197	28	uk	uk	PROPN
ijassa-1406	197	29	replaced	replace	VERB
ijassa-1406	197	30	by	by	ADP
ijassa-1406	197	31	ûk	ûk	PROPN
ijassa-1406	197	32	for	for	ADP
ijassa-1406	197	33	nm	nm	PROPN
ijassa-1406	197	34	-	-	ADJ
ijassa-1406	197	35	ep	ep	ADJ
ijassa-1406	197	36	and	and	CCONJ
ijassa-1406	197	37	snm	snm	PROPN
ijassa-1406	197	38	-	-	PUNCT
ijassa-1406	197	39	ep	ep	PROPN
ijassa-1406	197	40	when	when	SCONJ
ijassa-1406	197	41	termination	termination	NOUN
ijassa-1406	197	42	happened	happen	VERB
ijassa-1406	197	43	because	because	SCONJ
ijassa-1406	197	44	of	of	ADP
ijassa-1406	197	45	(	(	PUNCT
ijassa-1406	197	46	4.1	4.1	NUM
ijassa-1406	197	47	)	)	PUNCT
ijassa-1406	197	48	)	)	PUNCT
ijassa-1406	197	49	.	.	PUNCT
ijassa-1406	198	1	if	if	SCONJ
ijassa-1406	198	2	successful	successful	ADJ
ijassa-1406	198	3	termination	termination	NOUN
ijassa-1406	198	4	did	do	AUX
ijassa-1406	198	5	not	not	PART
ijassa-1406	198	6	occur	occur	VERB
ijassa-1406	198	7	after	after	ADP
ijassa-1406	198	8	50	50	NUM
ijassa-1406	198	9	iterations	iteration	NOUN
ijassa-1406	198	10	,	,	PUNCT
ijassa-1406	198	11	or	or	CCONJ
ijassa-1406	198	12	the	the	DET
ijassa-1406	198	13	backtracking	backtrack	VERB
ijassa-1406	198	14	procedures	procedure	NOUN
ijassa-1406	198	15	in	in	ADP
ijassa-1406	198	16	steps	step	NOUN
ijassa-1406	198	17	3	3	NUM
ijassa-1406	198	18	of	of	ADP
ijassa-1406	198	19	algorithms	algorithms	NOUN
ijassa-1406	198	20	2.1	2.1	NUM
ijassa-1406	198	21	and	and	CCONJ
ijassa-1406	198	22	3.1	3.1	NUM
ijassa-1406	198	23	produced	produce	VERB
ijassa-1406	198	24	a	a	DET
ijassa-1406	198	25	trial	trial	NOUN
ijassa-1406	198	26	value	value	NOUN
ijassa-1406	198	27	τ	τ	X
ijassa-1406	198	28	such	such	ADJ
ijassa-1406	198	29	that	that	SCONJ
ijassa-1406	198	30	τ∥vk∥	τ∥vk∥	NOUN
ijassa-1406	198	31	≤	≤	NOUN
ijassa-1406	198	32	10−10	10−10	NUM
ijassa-1406	198	33	,	,	PUNCT
ijassa-1406	198	34	the	the	DET
ijassa-1406	198	35	process	process	NOUN
ijassa-1406	198	36	was	be	AUX
ijassa-1406	198	37	terminated	terminate	VERB
ijassa-1406	198	38	with	with	ADP
ijassa-1406	198	39	failure	failure	NOUN
ijassa-1406	198	40	declaring	declare	VERB
ijassa-1406	198	41	that	that	SCONJ
ijassa-1406	198	42	the	the	DET
ijassa-1406	198	43	step	step	NOUN
ijassa-1406	198	44	became	become	VERB
ijassa-1406	198	45	too	too	ADV
ijassa-1406	198	46	short	short	ADJ
ijassa-1406	198	47	to	to	PART
ijassa-1406	198	48	proceed	proceed	VERB
ijassa-1406	198	49	.	.	PUNCT
ijassa-1406	199	1	all	all	DET
ijassa-1406	199	2	problems	problem	NOUN
ijassa-1406	199	3	in	in	ADP
ijassa-1406	199	4	[	[	X
ijassa-1406	199	5	19	19	NUM
ijassa-1406	199	6	]	]	PUNCT
ijassa-1406	199	7	are	be	AUX
ijassa-1406	199	8	supplied	supply	VERB
ijassa-1406	199	9	with	with	ADP
ijassa-1406	199	10	“	"	PUNCT
ijassa-1406	199	11	recommended	recommend	VERB
ijassa-1406	199	12	”	"	PUNCT
ijassa-1406	199	13	starting	start	VERB
ijassa-1406	199	14	points	point	NOUN
ijassa-1406	199	15	.	.	PUNCT
ijassa-1406	200	1	for	for	ADP
ijassa-1406	200	2	each	each	PRON
ijassa-1406	200	3	of	of	ADP
ijassa-1406	200	4	the	the	DET
ijassa-1406	200	5	other	other	ADJ
ijassa-1406	200	6	test	test	NOUN
ijassa-1406	200	7	problems	problem	NOUN
ijassa-1406	200	8	being	be	AUX
ijassa-1406	200	9	used	use	VERB
ijassa-1406	200	10	,	,	PUNCT
ijassa-1406	200	11	we	we	PRON
ijassa-1406	200	12	have	have	AUX
ijassa-1406	200	13	also	also	ADV
ijassa-1406	200	14	selected	select	VERB
ijassa-1406	200	15	some	some	DET
ijassa-1406	200	16	starting	starting	NOUN
ijassa-1406	200	17	point	point	NOUN
ijassa-1406	200	18	,	,	PUNCT
ijassa-1406	200	19	trying	try	VERB
ijassa-1406	200	20	to	to	PART
ijassa-1406	200	21	keep	keep	VERB
ijassa-1406	200	22	our	our	PRON
ijassa-1406	200	23	choices	choice	NOUN
ijassa-1406	200	24	reasonably	reasonably	ADV
ijassa-1406	200	25	generic	generic	ADJ
ijassa-1406	200	26	.	.	PUNCT
ijassa-1406	201	1	information	information	NOUN
ijassa-1406	201	2	on	on	ADP
ijassa-1406	201	3	“	"	PUNCT
ijassa-1406	201	4	standard	standard	NOUN
ijassa-1406	201	5	”	"	PUNCT
ijassa-1406	201	6	starting	start	VERB
ijassa-1406	201	7	points	point	NOUN
ijassa-1406	201	8	u0	u0	ADJ
ijassa-1406	201	9	and	and	CCONJ
ijassa-1406	201	10	solutions	solution	NOUN
ijassa-1406	201	11	of	of	ADP
ijassa-1406	201	12	interest	interest	NOUN
ijassa-1406	201	13	ū	ū	NOUN
ijassa-1406	201	14	is	be	AUX
ijassa-1406	201	15	collected	collect	VERB
ijassa-1406	201	16	in	in	ADP
ijassa-1406	201	17	table	table	NOUN
ijassa-1406	201	18	3.1	3.1	NUM
ijassa-1406	201	19	.	.	PUNCT
ijassa-1406	202	1	in	in	ADP
ijassa-1406	202	2	the	the	DET
ijassa-1406	202	3	first	first	ADJ
ijassa-1406	202	4	part	part	NOUN
ijassa-1406	202	5	of	of	ADP
ijassa-1406	202	6	the	the	DET
ijassa-1406	202	7	experiments	experiment	NOUN
ijassa-1406	202	8	,	,	PUNCT
ijassa-1406	202	9	for	for	ADP
ijassa-1406	202	10	each	each	DET
ijassa-1406	202	11	test	test	NOUN
ijassa-1406	202	12	problem	problem	NOUN
ijassa-1406	202	13	,	,	PUNCT
ijassa-1406	202	14	we	we	PRON
ijassa-1406	202	15	have	have	AUX
ijassa-1406	202	16	performed	perform	VERB
ijassa-1406	202	17	a	a	DET
ijassa-1406	202	18	single	single	ADJ
ijassa-1406	202	19	run	run	NOUN
ijassa-1406	202	20	of	of	ADP
ijassa-1406	202	21	each	each	DET
ijassa-1406	202	22	algorithm	algorithm	NOUN
ijassa-1406	202	23	using	use	VERB
ijassa-1406	202	24	the	the	DET
ijassa-1406	202	25	specified	specified	ADJ
ijassa-1406	202	26	“	"	PUNCT
ijassa-1406	202	27	standard	standard	NOUN
ijassa-1406	202	28	”	"	PUNCT
ijassa-1406	202	29	starting	starting	NOUN
ijassa-1406	202	30	point	point	NOUN
ijassa-1406	202	31	.	.	PUNCT
ijassa-1406	203	1	the	the	DET
ijassa-1406	203	2	results	result	NOUN
ijassa-1406	203	3	(	(	PUNCT
ijassa-1406	203	4	iteration	iteration	NOUN
ijassa-1406	203	5	counts	count	VERB
ijassa-1406	203	6	until	until	ADP
ijassa-1406	203	7	successful	successful	ADJ
ijassa-1406	203	8	termination	termination	NOUN
ijassa-1406	203	9	)	)	PUNCT
ijassa-1406	203	10	are	be	AUX
ijassa-1406	203	11	reported	report	VERB
ijassa-1406	203	12	in	in	ADP
ijassa-1406	203	13	table	table	NOUN
ijassa-1406	203	14	3.2	3.2	NUM
ijassa-1406	203	15	;	;	PUNCT
ijassa-1406	203	16	cases	case	NOUN
ijassa-1406	203	17	of	of	ADP
ijassa-1406	203	18	failure	failure	NOUN
ijassa-1406	203	19	are	be	AUX
ijassa-1406	203	20	shown	show	VERB
ijassa-1406	203	21	as	as	ADP
ijassa-1406	203	22	“	"	PUNCT
ijassa-1406	203	23	–	–	PUNCT
ijassa-1406	203	24	”	"	PUNCT
ijassa-1406	203	25	.	.	PUNCT
ijassa-1406	204	1	information	information	NOUN
ijassa-1406	204	2	in	in	ADP
ijassa-1406	204	3	table	table	NOUN
ijassa-1406	204	4	3.2	3.2	NUM
ijassa-1406	204	5	is	be	AUX
ijassa-1406	204	6	further	far	ADV
ijassa-1406	204	7	summarized	summarize	VERB
ijassa-1406	204	8	in	in	ADP
ijassa-1406	204	9	figure	figure	NOUN
ijassa-1406	204	10	3.1	3.1	NUM
ijassa-1406	204	11	in	in	ADP
ijassa-1406	204	12	the	the	DET
ijassa-1406	204	13	form	form	NOUN
ijassa-1406	204	14	of	of	ADP
ijassa-1406	204	15	performance	performance	NOUN
ijassa-1406	204	16	profile	profile	NOUN
ijassa-1406	204	17	,	,	PUNCT
ijassa-1406	204	18	proposed	propose	VERB
ijassa-1406	204	19	in	in	ADP
ijassa-1406	204	20	[	[	X
ijassa-1406	204	21	4	4	NUM
ijassa-1406	204	22	]	]	PUNCT
ijassa-1406	204	23	.	.	PUNCT
ijassa-1406	205	1	the	the	DET
ijassa-1406	205	2	value	value	NOUN
ijassa-1406	205	3	of	of	ADP
ijassa-1406	205	4	any	any	DET
ijassa-1406	205	5	function	function	NOUN
ijassa-1406	205	6	whose	whose	DET
ijassa-1406	205	7	graph	graph	NOUN
ijassa-1406	205	8	is	be	AUX
ijassa-1406	205	9	presented	present	VERB
ijassa-1406	205	10	in	in	ADP
ijassa-1406	205	11	the	the	DET
ijassa-1406	205	12	figure	figure	NOUN
ijassa-1406	205	13	at	at	ADP
ijassa-1406	205	14	a	a	DET
ijassa-1406	205	15	point	point	NOUN
ijassa-1406	205	16	t	t	NOUN
ijassa-1406	205	17	of	of	ADP
ijassa-1406	205	18	the	the	DET
ijassa-1406	205	19	horizontal	horizontal	ADJ
ijassa-1406	205	20	axis	axis	NOUN
ijassa-1406	205	21	corresponds	correspond	VERB
ijassa-1406	205	22	to	to	ADP
ijassa-1406	205	23	the	the	DET
ijassa-1406	205	24	portion	portion	NOUN
ijassa-1406	205	25	of	of	ADP
ijassa-1406	205	26	test	test	NOUN
ijassa-1406	205	27	problems	problem	NOUN
ijassa-1406	205	28	for	for	ADP
ijassa-1406	205	29	with	with	ADP
ijassa-1406	205	30	the	the	DET
ijassa-1406	205	31	result	result	NOUN
ijassa-1406	205	32	(	(	PUNCT
ijassa-1406	205	33	in	in	ADP
ijassa-1406	205	34	our	our	PRON
ijassa-1406	205	35	case	case	NOUN
ijassa-1406	205	36	,	,	PUNCT
ijassa-1406	205	37	the	the	DET
ijassa-1406	205	38	iteration	iteration	NOUN
ijassa-1406	205	39	count	count	NOUN
ijassa-1406	205	40	)	)	PUNCT
ijassa-1406	205	41	of	of	ADP
ijassa-1406	205	42	the	the	DET
ijassa-1406	205	43	algorithm	algorithm	NOUN
ijassa-1406	205	44	associated	associate	VERB
ijassa-1406	205	45	with	with	ADP
ijassa-1406	205	46	this	this	DET
ijassa-1406	205	47	graph	graph	NOUN
ijassa-1406	205	48	was	be	AUX
ijassa-1406	205	49	no	no	ADV
ijassa-1406	205	50	more	more	ADJ
ijassa-1406	205	51	than	than	ADP
ijassa-1406	205	52	t	t	PROPN
ijassa-1406	205	53	times	time	NOUN
ijassa-1406	205	54	worse	bad	ADJ
ijassa-1406	205	55	than	than	ADP
ijassa-1406	205	56	the	the	DET
ijassa-1406	205	57	best	good	ADJ
ijassa-1406	205	58	result	result	NOUN
ijassa-1406	205	59	among	among	ADP
ijassa-1406	205	60	all	all	DET
ijassa-1406	205	61	the	the	DET
ijassa-1406	205	62	algorithms	algorithm	NOUN
ijassa-1406	205	63	being	be	AUX
ijassa-1406	205	64	tested	test	VERB
ijassa-1406	205	65	(	(	PUNCT
ijassa-1406	205	66	the	the	DET
ijassa-1406	205	67	result	result	NOUN
ijassa-1406	205	68	of	of	ADP
ijassa-1406	205	69	a	a	DET
ijassa-1406	205	70	failure	failure	NOUN
ijassa-1406	205	71	is	be	AUX
ijassa-1406	205	72	regarded	regard	VERB
ijassa-1406	205	73	infinitely	infinitely	ADV
ijassa-1406	205	74	many	many	ADJ
ijassa-1406	205	75	times	time	NOUN
ijassa-1406	205	76	worse	bad	ADJ
ijassa-1406	205	77	than	than	ADP
ijassa-1406	205	78	any	any	DET
ijassa-1406	205	79	result	result	NOUN
ijassa-1406	205	80	)	)	PUNCT
ijassa-1406	205	81	.	.	PUNCT
ijassa-1406	206	1	in	in	ADP
ijassa-1406	206	2	the	the	DET
ijassa-1406	206	3	second	second	ADJ
ijassa-1406	206	4	part	part	NOUN
ijassa-1406	206	5	of	of	ADP
ijassa-1406	206	6	the	the	DET
ijassa-1406	206	7	experiments	experiment	NOUN
ijassa-1406	206	8	,	,	PUNCT
ijassa-1406	206	9	for	for	ADP
ijassa-1406	206	10	each	each	DET
ijassa-1406	206	11	test	test	NOUN
ijassa-1406	206	12	problem	problem	NOUN
ijassa-1406	206	13	,	,	PUNCT
ijassa-1406	206	14	we	we	PRON
ijassa-1406	206	15	have	have	AUX
ijassa-1406	206	16	performed	perform	VERB
ijassa-1406	206	17	1000	1000	NUM
ijassa-1406	206	18	runs	run	NOUN
ijassa-1406	206	19	of	of	ADP
ijassa-1406	206	20	each	each	DET
ijassa-1406	206	21	algorithm	algorithm	NOUN
ijassa-1406	206	22	from	from	ADP
ijassa-1406	206	23	randomly	randomly	ADV
ijassa-1406	206	24	generated	generate	VERB
ijassa-1406	206	25	starting	start	VERB
ijassa-1406	206	26	points	point	NOUN
ijassa-1406	206	27	with	with	ADP
ijassa-1406	206	28	uniform	uniform	ADJ
ijassa-1406	206	29	distribution	distribution	NOUN
ijassa-1406	206	30	in	in	ADP
ijassa-1406	206	31	the	the	DET
ijassa-1406	206	32	cubic	cubic	ADJ
ijassa-1406	206	33	neighborhood	neighborhood	NOUN
ijassa-1406	206	34	of	of	ADP
ijassa-1406	206	35	the	the	DET
ijassa-1406	206	36	solution	solution	NOUN
ijassa-1406	206	37	of	of	ADP
ijassa-1406	206	38	interest	interest	NOUN
ijassa-1406	206	39	,	,	PUNCT
ijassa-1406	206	40	with	with	ADP
ijassa-1406	206	41	the	the	DET
ijassa-1406	206	42	half	half	ADJ
ijassa-1406	206	43	-	-	PUNCT
ijassa-1406	206	44	edge	edge	NOUN
ijassa-1406	206	45	of	of	ADP
ijassa-1406	206	46	the	the	DET
ijassa-1406	206	47	cube	cube	NOUN
ijassa-1406	206	48	equal	equal	ADJ
ijassa-1406	206	49	to	to	ADP
ijassa-1406	206	50	1	1	NUM
ijassa-1406	206	51	.	.	PUNCT
ijassa-1406	207	1	in	in	ADP
ijassa-1406	207	2	table	table	NOUN
ijassa-1406	207	3	3.3	3.3	NUM
ijassa-1406	207	4	,	,	PUNCT
ijassa-1406	207	5	we	we	PRON
ijassa-1406	207	6	report	report	VERB
ijassa-1406	207	7	the	the	DET
ijassa-1406	207	8	percentage	percentage	NOUN
ijassa-1406	207	9	of	of	ADP
ijassa-1406	207	10	successful	successful	ADJ
ijassa-1406	207	11	runs	run	NOUN
ijassa-1406	207	12	,	,	PUNCT
ijassa-1406	207	13	the	the	DET
ijassa-1406	207	14	average	average	ADJ
ijassa-1406	207	15	iteration	iteration	NOUN
ijassa-1406	207	16	count	count	NOUN
ijassa-1406	207	17	over	over	ADP
ijassa-1406	207	18	successful	successful	ADJ
ijassa-1406	207	19	runs	run	NOUN
ijassa-1406	207	20	,	,	PUNCT
ijassa-1406	207	21	and	and	CCONJ
ijassa-1406	207	22	the	the	DET
ijassa-1406	207	23	average	average	ADJ
ijassa-1406	207	24	distance	distance	NOUN
ijassa-1406	207	25	to	to	ADP
ijassa-1406	207	26	the	the	DET
ijassa-1406	207	27	solution	solution	NOUN
ijassa-1406	207	28	of	of	ADP
ijassa-1406	207	29	interest	interest	NOUN
ijassa-1406	207	30	over	over	ADP
ijassa-1406	207	31	cases	case	NOUN
ijassa-1406	207	32	when	when	SCONJ
ijassa-1406	207	33	convergence	convergence	NOUN
ijassa-1406	207	34	to	to	ADP
ijassa-1406	207	35	such	such	ADJ
ijassa-1406	207	36	solution	solution	NOUN
ijassa-1406	207	37	was	be	AUX
ijassa-1406	207	38	detected	detect	VERB
ijassa-1406	207	39	(	(	PUNCT
ijassa-1406	207	40	separated	separate	VERB
ijassa-1406	207	41	by	by	ADP
ijassa-1406	207	42	slashes	slash	NOUN
ijassa-1406	207	43	)	)	PUNCT
ijassa-1406	207	44	.	.	PUNCT
ijassa-1406	208	1	the	the	DET
ijassa-1406	208	2	cases	case	NOUN
ijassa-1406	208	3	when	when	SCONJ
ijassa-1406	208	4	there	there	PRON
ijassa-1406	208	5	were	be	VERB
ijassa-1406	208	6	no	no	DET
ijassa-1406	208	7	successful	successful	ADJ
ijassa-1406	208	8	runs	run	NOUN
ijassa-1406	208	9	are	be	AUX
ijassa-1406	208	10	still	still	ADV
ijassa-1406	208	11	marked	mark	VERB
ijassa-1406	208	12	by	by	ADP
ijassa-1406	208	13	“	"	PUNCT
ijassa-1406	208	14	–	–	PUNCT
ijassa-1406	208	15	”	"	PUNCT
ijassa-1406	208	16	.	.	PUNCT
ijassa-1406	209	1	the	the	DET
ijassa-1406	209	2	corresponding	correspond	VERB
ijassa-1406	209	3	performance	performance	NOUN
ijassa-1406	209	4	profile	profile	NOUN
ijassa-1406	209	5	in	in	ADP
ijassa-1406	209	6	figure	figure	NOUN
ijassa-1406	209	7	3.2	3.2	NUM
ijassa-1406	209	8	is	be	AUX
ijassa-1406	209	9	an	an	DET
ijassa-1406	209	10	adaptation	adaptation	NOUN
ijassa-1406	209	11	of	of	ADP
ijassa-1406	209	12	the	the	DET
ijassa-1406	209	13	original	original	ADJ
ijassa-1406	209	14	proposal	proposal	NOUN
ijassa-1406	209	15	in	in	ADP
ijassa-1406	209	16	[	[	X
ijassa-1406	209	17	4	4	NUM
ijassa-1406	209	18	]	]	PUNCT
ijassa-1406	209	19	to	to	ADP
ijassa-1406	209	20	the	the	DET
ijassa-1406	209	21	case	case	NOUN
ijassa-1406	209	22	of	of	ADP
ijassa-1406	209	23	multiple	multiple	ADJ
ijassa-1406	209	24	runs	run	NOUN
ijassa-1406	209	25	for	for	ADP
ijassa-1406	209	26	each	each	DET
ijassa-1406	209	27	test	test	NOUN
ijassa-1406	209	28	problem	problem	NOUN
ijassa-1406	209	29	,	,	PUNCT
ijassa-1406	209	30	suggested	suggest	VERB
ijassa-1406	209	31	in	in	ADP
ijassa-1406	209	32	[	[	X
ijassa-1406	209	33	16	16	NUM
ijassa-1406	209	34	]	]	PUNCT
ijassa-1406	209	35	.	.	PUNCT
ijassa-1406	210	1	the	the	DET
ijassa-1406	210	2	failures	failure	NOUN
ijassa-1406	210	3	for	for	ADP
ijassa-1406	210	4	dis64	dis64	NOUN
ijassa-1406	210	5	and	and	CCONJ
ijassa-1406	210	6	[	[	X
ijassa-1406	210	7	1	1	NUM
ijassa-1406	210	8	,	,	PUNCT
ijassa-1406	210	9	example	example	NOUN
ijassa-1406	210	10	3.1	3.1	NUM
ijassa-1406	210	11	]	]	PUNCT
ijassa-1406	210	12	happen	happen	VERB
ijassa-1406	210	13	at	at	ADP
ijassa-1406	210	14	steps	step	NOUN
ijassa-1406	210	15	2	2	NUM
ijassa-1406	210	16	of	of	ADP
ijassa-1406	210	17	both	both	PRON
ijassa-1406	210	18	algorithms	algorithm	NOUN
ijassa-1406	210	19	2.1	2.1	NUM
ijassa-1406	210	20	and	and	CCONJ
ijassa-1406	210	21	3.1	3.1	NUM
ijassa-1406	210	22	because	because	SCONJ
ijassa-1406	210	23	the	the	DET
ijassa-1406	210	24	jacobians	jacobian	NOUN
ijassa-1406	210	25	of	of	ADP
ijassa-1406	210	26	the	the	DET
ijassa-1406	210	27	corresponding	correspond	VERB
ijassa-1406	210	28	φ	φ	PROPN
ijassa-1406	210	29	at	at	ADP
ijassa-1406	210	30	u0	u0	PROPN
ijassa-1406	210	31	are	be	AUX
ijassa-1406	210	32	singular	singular	ADJ
ijassa-1406	210	33	,	,	PUNCT
ijassa-1406	210	34	and	and	CCONJ
ijassa-1406	210	35	the	the	DET
ijassa-1406	210	36	iteration	iteration	NOUN
ijassa-1406	210	37	equation	equation	NOUN
ijassa-1406	210	38	can	can	AUX
ijassa-1406	210	39	not	not	PART
ijassa-1406	210	40	be	be	AUX
ijassa-1406	210	41	solved	solve	VERB
ijassa-1406	210	42	.	.	PUNCT
ijassa-1406	211	1	generally	generally	ADV
ijassa-1406	211	2	,	,	PUNCT
ijassa-1406	211	3	this	this	PRON
ijassa-1406	211	4	is	be	AUX
ijassa-1406	211	5	a	a	DET
ijassa-1406	211	6	typical	typical	ADJ
ijassa-1406	211	7	reason	reason	NOUN
ijassa-1406	211	8	of	of	ADP
ijassa-1406	211	9	failures	failure	NOUN
ijassa-1406	211	10	encountered	encounter	VERB
ijassa-1406	211	11	in	in	ADP
ijassa-1406	211	12	these	these	DET
ijassa-1406	211	13	experiments	experiment	NOUN
ijassa-1406	211	14	.	.	PUNCT
ijassa-1406	212	1	there	there	PRON
ijassa-1406	212	2	are	be	VERB
ijassa-1406	212	3	also	also	ADV
ijassa-1406	212	4	some	some	DET
ijassa-1406	212	5	rare	rare	ADJ
ijassa-1406	212	6	cases	case	NOUN
ijassa-1406	212	7	when	when	SCONJ
ijassa-1406	212	8	failure	failure	NOUN
ijassa-1406	212	9	was	be	AUX
ijassa-1406	212	10	declared	declare	VERB
ijassa-1406	212	11	because	because	SCONJ
ijassa-1406	212	12	of	of	ADP
ijassa-1406	212	13	too	too	ADV
ijassa-1406	212	14	short	short	ADJ
ijassa-1406	212	15	steps	step	NOUN
ijassa-1406	212	16	(	(	PUNCT
ijassa-1406	212	17	for	for	ADP
ijassa-1406	212	18	quarquad	quarquad	NOUN
ijassa-1406	212	19	and	and	CCONJ
ijassa-1406	212	20	doubleknot	doubleknot	VERB
ijassa-1406	212	21	)	)	PUNCT
ijassa-1406	212	22	,	,	PUNCT
ijassa-1406	212	23	or	or	CCONJ
ijassa-1406	212	24	when	when	SCONJ
ijassa-1406	212	25	the	the	DET
ijassa-1406	212	26	iteration	iteration	NOUN
ijassa-1406	212	27	limit	limit	NOUN
ijassa-1406	212	28	was	be	AUX
ijassa-1406	212	29	achieved	achieve	VERB
ijassa-1406	212	30	.	.	PUNCT
ijassa-1406	213	1	another	another	DET
ijassa-1406	213	2	observation	observation	NOUN
ijassa-1406	213	3	is	be	AUX
ijassa-1406	213	4	that	that	SCONJ
ijassa-1406	213	5	the	the	DET
ijassa-1406	213	6	full	full	ADJ
ijassa-1406	213	7	step	step	NOUN
ijassa-1406	213	8	of	of	ADP
ijassa-1406	213	9	nm	nm	PRON
ijassa-1406	213	10	was	be	AUX
ijassa-1406	213	11	always	always	ADV
ijassa-1406	213	12	asymptotically	asymptotically	ADV
ijassa-1406	213	13	accepted	accept	VERB
ijassa-1406	213	14	in	in	ADP
ijassa-1406	213	15	these	these	DET
ijassa-1406	213	16	experiments	experiment	NOUN
ijassa-1406	213	17	,	,	PUNCT
ijassa-1406	213	18	while	while	SCONJ
ijassa-1406	213	19	for	for	ADP
ijassa-1406	213	20	snm	snm	PROPN
ijassa-1406	213	21	,	,	PUNCT
ijassa-1406	213	22	there	there	PRON
ijassa-1406	213	23	were	be	VERB
ijassa-1406	213	24	runs	run	NOUN
ijassa-1406	213	25	with	with	ADP
ijassa-1406	213	26	the	the	DET
ijassa-1406	213	27	last	last	ADJ
ijassa-1406	213	28	step	step	NOUN
ijassa-1406	213	29	before	before	ADP
ijassa-1406	213	30	successful	successful	ADJ
ijassa-1406	213	31	termination	termination	NOUN
ijassa-1406	213	32	using	use	VERB
ijassa-1406	213	33	τk	τk	ADP
ijassa-1406	213	34	<	<	X
ijassa-1406	213	35	1	1	NUM
ijassa-1406	213	36	.	.	PUNCT
ijassa-1406	213	37	looking	look	VERB
ijassa-1406	213	38	at	at	ADP
ijassa-1406	213	39	the	the	DET
ijassa-1406	213	40	results	result	NOUN
ijassa-1406	213	41	of	of	ADP
ijassa-1406	213	42	the	the	DET
ijassa-1406	213	43	experiments	experiment	NOUN
ijassa-1406	213	44	,	,	PUNCT
ijassa-1406	213	45	one	one	PRON
ijassa-1406	213	46	can	can	AUX
ijassa-1406	213	47	conclude	conclude	VERB
ijassa-1406	213	48	that	that	SCONJ
ijassa-1406	213	49	nm	nm	NOUN
ijassa-1406	213	50	is	be	AUX
ijassa-1406	213	51	definitely	definitely	ADV
ijassa-1406	213	52	outperformed	outperform	VERB
ijassa-1406	213	53	in	in	ADP
ijassa-1406	213	54	terms	term	NOUN
ijassa-1406	213	55	of	of	ADP
ijassa-1406	213	56	efficiency	efficiency	NOUN
ijassa-1406	213	57	by	by	ADP
ijassa-1406	213	58	any	any	PRON
ijassa-1406	213	59	of	of	ADP
ijassa-1406	213	60	the	the	DET
ijassa-1406	213	61	concurrent	concurrent	ADJ
ijassa-1406	213	62	algorithms	algorithm	NOUN
ijassa-1406	213	63	,	,	PUNCT
ijassa-1406	213	64	and	and	CCONJ
ijassa-1406	213	65	the	the	DET
ijassa-1406	213	66	reason	reason	NOUN
ijassa-1406	213	67	for	for	ADP
ijassa-1406	213	68	copyright	copyright	NOUN
ijassa-1406	213	69	©	©	PROPN
ijassa-1406	213	70	2023	2023	NUM
ijassa-1406	213	71	assa	assa	NOUN
ijassa-1406	213	72	.	.	PUNCT
ijassa-1406	214	1	adv	adv	PROPN
ijassa-1406	214	2	syst	syst	PROPN
ijassa-1406	214	3	sci	sci	PROPN
ijassa-1406	214	4	appl	appl	PROPN
ijassa-1406	214	5	(	(	PUNCT
ijassa-1406	214	6	2023	2023	NUM
ijassa-1406	214	7	)	)	PUNCT
ijassa-1406	214	8	newton	newton	PROPN
ijassa-1406	214	9	method	method	NOUN
ijassa-1406	214	10	vs.	vs.	ADP
ijassa-1406	214	11	semismooth	semismooth	NOUN
ijassa-1406	214	12	newton	newton	PROPN
ijassa-1406	214	13	method	method	PROPN
ijassa-1406	214	14	25	25	NUM
ijassa-1406	214	15	that	that	PRON
ijassa-1406	214	16	must	must	AUX
ijassa-1406	214	17	be	be	AUX
ijassa-1406	214	18	precisely	precisely	ADV
ijassa-1406	214	19	the	the	DET
ijassa-1406	214	20	slow	slow	ADJ
ijassa-1406	214	21	(	(	PUNCT
ijassa-1406	214	22	linear	linear	ADJ
ijassa-1406	214	23	,	,	PUNCT
ijassa-1406	214	24	at	at	ADP
ijassa-1406	214	25	best	good	ADJ
ijassa-1406	214	26	)	)	PUNCT
ijassa-1406	214	27	convergence	convergence	NOUN
ijassa-1406	214	28	to	to	ADP
ijassa-1406	214	29	so	so	ADV
ijassa-1406	214	30	-	-	PUNCT
ijassa-1406	214	31	called	call	VERB
ijassa-1406	214	32	critical	critical	ADJ
ijassa-1406	214	33	solutions	solution	NOUN
ijassa-1406	214	34	,	,	PUNCT
ijassa-1406	214	35	established	establish	VERB
ijassa-1406	214	36	in	in	ADP
ijassa-1406	214	37	[	[	X
ijassa-1406	214	38	9–11	9–11	NOUN
ijassa-1406	214	39	,	,	PUNCT
ijassa-1406	214	40	13	13	NUM
ijassa-1406	214	41	]	]	PUNCT
ijassa-1406	214	42	for	for	ADP
ijassa-1406	214	43	newton	newton	NOUN
ijassa-1406	214	44	-	-	PUNCT
ijassa-1406	214	45	type	type	NOUN
ijassa-1406	214	46	methods	method	NOUN
ijassa-1406	214	47	in	in	ADP
ijassa-1406	214	48	the	the	DET
ijassa-1406	214	49	twice	twice	ADV
ijassa-1406	214	50	differentiable	differentiable	ADJ
ijassa-1406	214	51	case	case	NOUN
ijassa-1406	214	52	.	.	PUNCT
ijassa-1406	215	1	this	this	PRON
ijassa-1406	215	2	might	might	AUX
ijassa-1406	215	3	give	give	VERB
ijassa-1406	215	4	an	an	DET
ijassa-1406	215	5	impression	impression	NOUN
ijassa-1406	215	6	that	that	SCONJ
ijassa-1406	215	7	the	the	DET
ijassa-1406	215	8	use	use	NOUN
ijassa-1406	215	9	of	of	ADP
ijassa-1406	215	10	the	the	DET
ijassa-1406	215	11	fischer	fischer	NOUN
ijassa-1406	215	12	–	–	PUNCT
ijassa-1406	215	13	burmeister	burmeister	NOUN
ijassa-1406	215	14	complementarity	complementarity	NOUN
ijassa-1406	215	15	function	function	NOUN
ijassa-1406	215	16	and	and	CCONJ
ijassa-1406	215	17	semismooth	semismooth	PROPN
ijassa-1406	215	18	newton	newton	PROPN
ijassa-1406	215	19	-	-	PUNCT
ijassa-1406	215	20	type	type	NOUN
ijassa-1406	215	21	methods	method	NOUN
ijassa-1406	215	22	is	be	AUX
ijassa-1406	215	23	definitely	definitely	ADV
ijassa-1406	215	24	preferable	preferable	ADJ
ijassa-1406	215	25	with	with	ADP
ijassa-1406	215	26	respect	respect	NOUN
ijassa-1406	215	27	to	to	ADP
ijassa-1406	215	28	the	the	DET
ijassa-1406	215	29	smooth	smooth	ADJ
ijassa-1406	215	30	complementarity	complementarity	NOUN
ijassa-1406	215	31	function	function	NOUN
ijassa-1406	215	32	and	and	CCONJ
ijassa-1406	215	33	usual	usual	ADJ
ijassa-1406	215	34	newton	newton	NOUN
ijassa-1406	215	35	-	-	PUNCT
ijassa-1406	215	36	type	type	NOUN
ijassa-1406	215	37	methods	method	NOUN
ijassa-1406	215	38	.	.	PUNCT
ijassa-1406	216	1	indeed	indeed	ADV
ijassa-1406	216	2	,	,	PUNCT
ijassa-1406	216	3	it	it	PRON
ijassa-1406	216	4	appears	appear	VERB
ijassa-1406	216	5	that	that	SCONJ
ijassa-1406	216	6	attraction	attraction	NOUN
ijassa-1406	216	7	to	to	ADP
ijassa-1406	216	8	any	any	DET
ijassa-1406	216	9	special	special	ADJ
ijassa-1406	216	10	(	(	PUNCT
ijassa-1406	216	11	“	"	PUNCT
ijassa-1406	216	12	critical	critical	ADJ
ijassa-1406	216	13	”	"	PUNCT
ijassa-1406	216	14	)	)	PUNCT
ijassa-1406	216	15	singular	singular	ADJ
ijassa-1406	216	16	solutions	solution	NOUN
ijassa-1406	216	17	and	and	CCONJ
ijassa-1406	216	18	the	the	DET
ijassa-1406	216	19	related	relate	VERB
ijassa-1406	216	20	special	special	ADJ
ijassa-1406	216	21	convergence	convergence	NOUN
ijassa-1406	216	22	pattern	pattern	NOUN
ijassa-1406	216	23	show	show	VERB
ijassa-1406	216	24	up	up	ADP
ijassa-1406	216	25	in	in	ADP
ijassa-1406	216	26	a	a	DET
ijassa-1406	216	27	much	much	ADV
ijassa-1406	216	28	less	less	ADV
ijassa-1406	216	29	persistent	persistent	ADJ
ijassa-1406	216	30	way	way	NOUN
ijassa-1406	216	31	for	for	ADP
ijassa-1406	216	32	nonsmooth	nonsmooth	NOUN
ijassa-1406	216	33	equations	equation	NOUN
ijassa-1406	216	34	.	.	PUNCT
ijassa-1406	217	1	nevertheless	nevertheless	ADV
ijassa-1406	217	2	,	,	PUNCT
ijassa-1406	217	3	passing	pass	VERB
ijassa-1406	217	4	from	from	ADP
ijassa-1406	217	5	snm	snm	PROPN
ijassa-1406	217	6	to	to	ADP
ijassa-1406	217	7	snm	snm	PROPN
ijassa-1406	217	8	-	-	PUNCT
ijassa-1406	217	9	ep	ep	PROPN
ijassa-1406	217	10	makes	make	VERB
ijassa-1406	217	11	the	the	DET
ijassa-1406	217	12	efficiency	efficiency	NOUN
ijassa-1406	217	13	somewhat	somewhat	ADV
ijassa-1406	217	14	higher	higher	ADV
ijassa-1406	217	15	,	,	PUNCT
ijassa-1406	217	16	even	even	ADV
ijassa-1406	217	17	though	though	SCONJ
ijassa-1406	217	18	there	there	PRON
ijassa-1406	217	19	currently	currently	ADV
ijassa-1406	217	20	exists	exist	VERB
ijassa-1406	217	21	no	no	DET
ijassa-1406	217	22	any	any	DET
ijassa-1406	217	23	theory	theory	NOUN
ijassa-1406	217	24	supporting	support	VERB
ijassa-1406	217	25	this	this	DET
ijassa-1406	217	26	behavior	behavior	NOUN
ijassa-1406	217	27	.	.	PUNCT
ijassa-1406	218	1	observe	observe	VERB
ijassa-1406	218	2	,	,	PUNCT
ijassa-1406	218	3	however	however	ADV
ijassa-1406	218	4	,	,	PUNCT
ijassa-1406	218	5	that	that	SCONJ
ijassa-1406	218	6	the	the	DET
ijassa-1406	218	7	impact	impact	NOUN
ijassa-1406	218	8	of	of	ADP
ijassa-1406	218	9	extrapolation	extrapolation	NOUN
ijassa-1406	218	10	on	on	ADP
ijassa-1406	218	11	the	the	DET
ijassa-1406	218	12	newton	newton	PROPN
ijassa-1406	218	13	method	method	NOUN
ijassa-1406	218	14	is	be	AUX
ijassa-1406	218	15	even	even	ADV
ijassa-1406	218	16	more	more	ADV
ijassa-1406	218	17	evident	evident	ADJ
ijassa-1406	218	18	:	:	PUNCT
ijassa-1406	218	19	nm	nm	ADJ
ijassa-1406	218	20	-	-	PUNCT
ijassa-1406	218	21	ep	ep	ADJ
ijassa-1406	218	22	outperforms	outperform	VERB
ijassa-1406	218	23	snm	snm	PROPN
ijassa-1406	218	24	in	in	ADP
ijassa-1406	218	25	terms	term	NOUN
ijassa-1406	218	26	of	of	ADP
ijassa-1406	218	27	efficiency	efficiency	NOUN
ijassa-1406	218	28	,	,	PUNCT
ijassa-1406	218	29	and	and	CCONJ
ijassa-1406	218	30	is	be	AUX
ijassa-1406	218	31	demonstrated	demonstrate	VERB
ijassa-1406	218	32	performance	performance	NOUN
ijassa-1406	218	33	similar	similar	ADJ
ijassa-1406	218	34	to	to	ADP
ijassa-1406	218	35	that	that	PRON
ijassa-1406	218	36	of	of	ADP
ijassa-1406	218	37	snm	snm	PROPN
ijassa-1406	218	38	-	-	PUNCT
ijassa-1406	218	39	ep	ep	PROPN
ijassa-1406	218	40	.	.	PUNCT
ijassa-1406	219	1	all	all	ADV
ijassa-1406	219	2	in	in	ADP
ijassa-1406	219	3	all	all	PRON
ijassa-1406	219	4	,	,	PUNCT
ijassa-1406	219	5	nm	nm	ADJ
ijassa-1406	219	6	-	-	ADJ
ijassa-1406	219	7	ep	ep	ADJ
ijassa-1406	219	8	demonstrates	demonstrate	VERB
ijassa-1406	219	9	a	a	DET
ijassa-1406	219	10	concurrent	concurrent	ADJ
ijassa-1406	219	11	behavior	behavior	NOUN
ijassa-1406	219	12	when	when	SCONJ
ijassa-1406	219	13	compared	compare	VERB
ijassa-1406	219	14	with	with	ADP
ijassa-1406	219	15	snm	snm	PROPN
ijassa-1406	219	16	and	and	CCONJ
ijassa-1406	219	17	snm	snm	PROPN
ijassa-1406	219	18	-	-	PUNCT
ijassa-1406	219	19	ep	ep	PROPN
ijassa-1406	219	20	,	,	PUNCT
ijassa-1406	219	21	even	even	ADV
ijassa-1406	219	22	though	though	SCONJ
ijassa-1406	219	23	nm	nm	PRON
ijassa-1406	219	24	evidently	evidently	ADV
ijassa-1406	219	25	suffers	suffer	VERB
ijassa-1406	219	26	from	from	ADP
ijassa-1406	219	27	the	the	DET
ijassa-1406	219	28	negative	negative	ADJ
ijassa-1406	219	29	effect	effect	NOUN
ijassa-1406	219	30	of	of	ADP
ijassa-1406	219	31	critical	critical	ADJ
ijassa-1406	219	32	solutions	solution	NOUN
ijassa-1406	219	33	on	on	ADP
ijassa-1406	219	34	its	its	PRON
ijassa-1406	219	35	convergence	convergence	NOUN
ijassa-1406	219	36	rate	rate	NOUN
ijassa-1406	219	37	.	.	PUNCT
ijassa-1406	220	1	5	5	X
ijassa-1406	220	2	.	.	X
ijassa-1406	220	3	concluding	conclude	VERB
ijassa-1406	220	4	remarks	remark	NOUN
ijassa-1406	220	5	in	in	ADP
ijassa-1406	220	6	this	this	DET
ijassa-1406	220	7	paper	paper	NOUN
ijassa-1406	220	8	,	,	PUNCT
ijassa-1406	220	9	we	we	PRON
ijassa-1406	220	10	provided	provide	VERB
ijassa-1406	220	11	a	a	DET
ijassa-1406	220	12	numerical	numerical	ADJ
ijassa-1406	220	13	comparison	comparison	NOUN
ijassa-1406	220	14	of	of	ADP
ijassa-1406	220	15	two	two	NUM
ijassa-1406	220	16	approaches	approach	NOUN
ijassa-1406	220	17	to	to	ADP
ijassa-1406	220	18	numerical	numerical	ADJ
ijassa-1406	220	19	solution	solution	NOUN
ijassa-1406	220	20	of	of	ADP
ijassa-1406	220	21	nonlinear	nonlinear	ADJ
ijassa-1406	220	22	complementarity	complementarity	NOUN
ijassa-1406	220	23	problems	problem	NOUN
ijassa-1406	220	24	,	,	PUNCT
ijassa-1406	220	25	one	one	NUM
ijassa-1406	220	26	employing	employ	VERB
ijassa-1406	220	27	a	a	DET
ijassa-1406	220	28	smooth	smooth	ADJ
ijassa-1406	220	29	complementarity	complementarity	NOUN
ijassa-1406	220	30	function	function	NOUN
ijassa-1406	220	31	,	,	PUNCT
ijassa-1406	220	32	while	while	SCONJ
ijassa-1406	220	33	another	another	DET
ijassa-1406	220	34	one	one	NOUN
ijassa-1406	220	35	making	make	VERB
ijassa-1406	220	36	use	use	NOUN
ijassa-1406	220	37	of	of	ADP
ijassa-1406	220	38	the	the	DET
ijassa-1406	220	39	(	(	PUNCT
ijassa-1406	220	40	nonsmooth	nonsmooth	NOUN
ijassa-1406	220	41	)	)	PUNCT
ijassa-1406	220	42	fischer	fischer	NOUN
ijassa-1406	220	43	–	–	PUNCT
ijassa-1406	220	44	burmeister	burmeister	NOUN
ijassa-1406	220	45	complementarity	complementarity	NOUN
ijassa-1406	220	46	function	function	NOUN
ijassa-1406	220	47	.	.	PUNCT
ijassa-1406	221	1	the	the	DET
ijassa-1406	221	2	results	result	NOUN
ijassa-1406	221	3	obtained	obtain	VERB
ijassa-1406	221	4	demonstrate	demonstrate	VERB
ijassa-1406	221	5	that	that	SCONJ
ijassa-1406	221	6	even	even	ADV
ijassa-1406	221	7	in	in	ADP
ijassa-1406	221	8	the	the	DET
ijassa-1406	221	9	presence	presence	NOUN
ijassa-1406	221	10	of	of	ADP
ijassa-1406	221	11	solutions	solution	NOUN
ijassa-1406	221	12	violating	violate	VERB
ijassa-1406	221	13	strict	strict	ADJ
ijassa-1406	221	14	complementarity	complementarity	NOUN
ijassa-1406	221	15	,	,	PUNCT
ijassa-1406	221	16	the	the	DET
ijassa-1406	221	17	first	first	ADJ
ijassa-1406	221	18	approach	approach	NOUN
ijassa-1406	221	19	may	may	AUX
ijassa-1406	221	20	still	still	ADV
ijassa-1406	221	21	be	be	AUX
ijassa-1406	221	22	fully	fully	ADV
ijassa-1406	221	23	competitive	competitive	ADJ
ijassa-1406	221	24	if	if	SCONJ
ijassa-1406	221	25	equipped	equip	VERB
ijassa-1406	221	26	with	with	ADP
ijassa-1406	221	27	the	the	DET
ijassa-1406	221	28	simplest	simple	ADJ
ijassa-1406	221	29	extrapolation	extrapolation	NOUN
ijassa-1406	221	30	procedure	procedure	NOUN
ijassa-1406	221	31	intended	intend	VERB
ijassa-1406	221	32	for	for	ADP
ijassa-1406	221	33	acceleration	acceleration	NOUN
ijassa-1406	221	34	of	of	ADP
ijassa-1406	221	35	convergence	convergence	NOUN
ijassa-1406	221	36	to	to	ADP
ijassa-1406	221	37	such	such	ADJ
ijassa-1406	221	38	solutions	solution	NOUN
ijassa-1406	221	39	.	.	PUNCT
ijassa-1406	222	1	theoretical	theoretical	ADJ
ijassa-1406	222	2	justification	justification	NOUN
ijassa-1406	222	3	of	of	ADP
ijassa-1406	222	4	the	the	DET
ijassa-1406	222	5	effects	effect	NOUN
ijassa-1406	222	6	demonstrated	demonstrate	VERB
ijassa-1406	222	7	in	in	ADP
ijassa-1406	222	8	this	this	DET
ijassa-1406	222	9	work	work	NOUN
ijassa-1406	222	10	will	will	AUX
ijassa-1406	222	11	be	be	AUX
ijassa-1406	222	12	a	a	DET
ijassa-1406	222	13	subject	subject	NOUN
ijassa-1406	222	14	of	of	ADP
ijassa-1406	222	15	future	future	ADJ
ijassa-1406	222	16	research	research	NOUN
ijassa-1406	222	17	.	.	PUNCT
ijassa-1406	223	1	acknowledgements	acknowledgement	NOUN
ijassa-1406	223	2	this	this	DET
ijassa-1406	223	3	research	research	NOUN
ijassa-1406	223	4	was	be	AUX
ijassa-1406	223	5	supported	support	VERB
ijassa-1406	223	6	by	by	ADP
ijassa-1406	223	7	the	the	DET
ijassa-1406	223	8	russian	russian	PROPN
ijassa-1406	223	9	science	science	PROPN
ijassa-1406	223	10	foundation	foundation	PROPN
ijassa-1406	223	11	grant	grant	VERB
ijassa-1406	223	12	23	23	NUM
ijassa-1406	223	13	-	-	SYM
ijassa-1406	223	14	11	11	NUM
ijassa-1406	223	15	-	-	PUNCT
ijassa-1406	223	16	20020	20020	NUM
ijassa-1406	223	17	(	(	PUNCT
ijassa-1406	223	18	https://rscf.ru/en/project/23-11-20020/	https://rscf.ru/en/project/23-11-20020/	PROPN
ijassa-1406	223	19	)	)	PUNCT
ijassa-1406	223	20	.	.	PUNCT
ijassa-1406	224	1	references	reference	NOUN
ijassa-1406	224	2	1	1	NUM
ijassa-1406	224	3	.	.	PUNCT
ijassa-1406	225	1	arutyunov	arutyunov	PROPN
ijassa-1406	225	2	,	,	PUNCT
ijassa-1406	225	3	a.v	a.v	PROPN
ijassa-1406	225	4	.	.	PROPN
ijassa-1406	225	5	&	&	CCONJ
ijassa-1406	225	6	izmailov	izmailov	PROPN
ijassa-1406	225	7	,	,	PUNCT
ijassa-1406	225	8	a.f	a.f	PROPN
ijassa-1406	225	9	.	.	PROPN
ijassa-1406	225	10	(	(	PUNCT
ijassa-1406	225	11	2018	2018	NUM
ijassa-1406	225	12	)	)	PUNCT
ijassa-1406	225	13	stability	stability	NOUN
ijassa-1406	225	14	of	of	ADP
ijassa-1406	225	15	possibly	possibly	ADV
ijassa-1406	225	16	nonisolated	nonisolate	VERB
ijassa-1406	225	17	solutions	solution	NOUN
ijassa-1406	225	18	of	of	ADP
ijassa-1406	225	19	constrained	constrained	ADJ
ijassa-1406	225	20	equations	equation	NOUN
ijassa-1406	225	21	with	with	ADP
ijassa-1406	225	22	applications	application	NOUN
ijassa-1406	225	23	to	to	ADP
ijassa-1406	225	24	complementarity	complementarity	NOUN
ijassa-1406	225	25	and	and	CCONJ
ijassa-1406	225	26	equilibrium	equilibrium	NOUN
ijassa-1406	225	27	problems	problem	NOUN
ijassa-1406	225	28	.	.	PUNCT
ijassa-1406	226	1	set	set	NOUN
ijassa-1406	226	2	-	-	PUNCT
ijassa-1406	226	3	valued	value	VERB
ijassa-1406	226	4	var	var	NOUN
ijassa-1406	226	5	.	.	PUNCT
ijassa-1406	227	1	anal	anal	PROPN
ijassa-1406	227	2	.	.	PROPN
ijassa-1406	227	3	,	,	PUNCT
ijassa-1406	227	4	26	26	NUM
ijassa-1406	227	5	,	,	PUNCT
ijassa-1406	227	6	327–352	327–352	NUM
ijassa-1406	227	7	.	.	NOUN
ijassa-1406	228	1	2	2	NUM
ijassa-1406	228	2	.	.	X
ijassa-1406	228	3	bertsekas	bertsekas	PROPN
ijassa-1406	228	4	,	,	PUNCT
ijassa-1406	228	5	d.p	d.p	PROPN
ijassa-1406	228	6	.	.	PROPN
ijassa-1406	229	1	(	(	PUNCT
ijassa-1406	229	2	1999	1999	NUM
ijassa-1406	229	3	)	)	PUNCT
ijassa-1406	229	4	nonlinear	nonlinear	ADJ
ijassa-1406	229	5	programming	programming	NOUN
ijassa-1406	229	6	.	.	PUNCT
ijassa-1406	230	1	2nd	2nd	PROPN
ijassa-1406	230	2	edition	edition	PROPN
ijassa-1406	230	3	.	.	PUNCT
ijassa-1406	231	1	belmont	belmont	PROPN
ijassa-1406	231	2	:	:	PUNCT
ijassa-1406	231	3	athena	athena	PROPN
ijassa-1406	231	4	.	.	PUNCT
ijassa-1406	232	1	3	3	X
ijassa-1406	232	2	.	.	X
ijassa-1406	232	3	daryina	daryina	PROPN
ijassa-1406	232	4	,	,	PUNCT
ijassa-1406	232	5	a.n	a.n	PROPN
ijassa-1406	232	6	.	.	PROPN
ijassa-1406	232	7	&	&	CCONJ
ijassa-1406	232	8	izmailov	izmailov	PROPN
ijassa-1406	232	9	,	,	PUNCT
ijassa-1406	232	10	a.f	a.f	PROPN
ijassa-1406	232	11	.	.	PROPN
ijassa-1406	233	1	(	(	PUNCT
ijassa-1406	233	2	2004	2004	NUM
ijassa-1406	233	3	)	)	PUNCT
ijassa-1406	234	1	on	on	ADP
ijassa-1406	234	2	identification	identification	NOUN
ijassa-1406	234	3	of	of	ADP
ijassa-1406	234	4	active	active	ADJ
ijassa-1406	234	5	indices	index	NOUN
ijassa-1406	234	6	in	in	ADP
ijassa-1406	234	7	mixed	mixed	ADJ
ijassa-1406	234	8	complementarity	complementarity	NOUN
ijassa-1406	234	9	problems	problem	NOUN
ijassa-1406	234	10	.	.	PUNCT
ijassa-1406	235	1	in	in	ADP
ijassa-1406	235	2	:	:	PUNCT
ijassa-1406	235	3	bereznev	bereznev	PROPN
ijassa-1406	235	4	,	,	PUNCT
ijassa-1406	235	5	v.a	v.a	PROPN
ijassa-1406	235	6	.	.	PROPN
ijassa-1406	235	7	(	(	PUNCT
ijassa-1406	235	8	ed	ed	NOUN
ijassa-1406	235	9	.	.	PUNCT
ijassa-1406	235	10	)	)	PUNCT
ijassa-1406	235	11	,	,	PUNCT
ijassa-1406	235	12	questions	question	NOUN
ijassa-1406	235	13	of	of	ADP
ijassa-1406	235	14	modelling	modelling	NOUN
ijassa-1406	235	15	and	and	CCONJ
ijassa-1406	235	16	analysis	analysis	NOUN
ijassa-1406	235	17	in	in	ADP
ijassa-1406	235	18	decision	decision	NOUN
ijassa-1406	235	19	making	make	VERB
ijassa-1406	235	20	problems	problem	NOUN
ijassa-1406	235	21	.	.	PUNCT
ijassa-1406	236	1	ccas	ccas	PROPN
ijassa-1406	236	2	,	,	PUNCT
ijassa-1406	236	3	moscow	moscow	PROPN
ijassa-1406	236	4	,	,	PUNCT
ijassa-1406	236	5	72–87	72–87	NUM
ijassa-1406	236	6	.	.	PUNCT
ijassa-1406	237	1	4	4	NUM
ijassa-1406	237	2	.	.	X
ijassa-1406	237	3	dolan	dolan	PROPN
ijassa-1406	237	4	,	,	PUNCT
ijassa-1406	237	5	e.d	e.d	PROPN
ijassa-1406	237	6	.	.	PROPN
ijassa-1406	237	7	&	&	CCONJ
ijassa-1406	237	8	more	more	ADJ
ijassa-1406	237	9	,	,	PUNCT
ijassa-1406	237	10	j.j	j.j	PROPN
ijassa-1406	237	11	.	.	PROPN
ijassa-1406	237	12	(	(	PUNCT
ijassa-1406	237	13	2002	2002	NUM
ijassa-1406	237	14	)	)	PUNCT
ijassa-1406	237	15	benchmarking	benchmarke	VERB
ijassa-1406	237	16	optimization	optimization	NOUN
ijassa-1406	237	17	software	software	NOUN
ijassa-1406	237	18	with	with	ADP
ijassa-1406	237	19	performance	performance	NOUN
ijassa-1406	237	20	profiles	profile	NOUN
ijassa-1406	237	21	.	.	PUNCT
ijassa-1406	238	1	math	math	NOUN
ijassa-1406	238	2	.	.	PUNCT
ijassa-1406	239	1	program	program	PROPN
ijassa-1406	239	2	.	.	PUNCT
ijassa-1406	239	3	,	,	PUNCT
ijassa-1406	239	4	91	91	NUM
ijassa-1406	239	5	,	,	PUNCT
ijassa-1406	239	6	201–213	201–213	NUM
ijassa-1406	239	7	.	.	NOUN
ijassa-1406	240	1	5	5	NUM
ijassa-1406	240	2	.	.	X
ijassa-1406	240	3	fischer	fischer	PROPN
ijassa-1406	240	4	,	,	PUNCT
ijassa-1406	240	5	a.	a.	PROPN
ijassa-1406	240	6	,	,	PUNCT
ijassa-1406	240	7	izmailov	izmailov	PROPN
ijassa-1406	240	8	,	,	PUNCT
ijassa-1406	240	9	a.f	a.f	PROPN
ijassa-1406	240	10	.	.	PROPN
ijassa-1406	240	11	&	&	CCONJ
ijassa-1406	240	12	jelitte	jelitte	PROPN
ijassa-1406	240	13	,	,	PUNCT
ijassa-1406	240	14	m.	m.	NOUN
ijassa-1406	240	15	(	(	PUNCT
ijassa-1406	240	16	2021	2021	NUM
ijassa-1406	240	17	)	)	PUNCT
ijassa-1406	240	18	newton	newton	NOUN
ijassa-1406	240	19	-	-	PUNCT
ijassa-1406	240	20	type	type	NOUN
ijassa-1406	240	21	methods	method	NOUN
ijassa-1406	240	22	near	near	ADP
ijassa-1406	240	23	critical	critical	ADJ
ijassa-1406	240	24	solutions	solution	NOUN
ijassa-1406	240	25	of	of	ADP
ijassa-1406	240	26	piecewise	piecewise	NOUN
ijassa-1406	240	27	smooth	smooth	ADJ
ijassa-1406	240	28	nonlinear	nonlinear	ADJ
ijassa-1406	240	29	equations	equation	NOUN
ijassa-1406	240	30	.	.	PUNCT
ijassa-1406	241	1	comput	comput	NOUN
ijassa-1406	241	2	.	.	PUNCT
ijassa-1406	242	1	optim	optim	PROPN
ijassa-1406	242	2	.	.	PUNCT
ijassa-1406	243	1	appl	appl	PROPN
ijassa-1406	243	2	.	.	PROPN
ijassa-1406	243	3	,	,	PUNCT
ijassa-1406	243	4	80	80	NUM
ijassa-1406	243	5	,	,	PUNCT
ijassa-1406	243	6	587	587	NUM
ijassa-1406	243	7	–	–	PUNCT
ijassa-1406	243	8	615	615	NUM
ijassa-1406	243	9	.	.	NOUN
ijassa-1406	244	1	6	6	NUM
ijassa-1406	244	2	.	.	X
ijassa-1406	245	1	fischer	fischer	PROPN
ijassa-1406	245	2	,	,	PUNCT
ijassa-1406	245	3	a.	a.	PROPN
ijassa-1406	245	4	,	,	PUNCT
ijassa-1406	245	5	izmailov	izmailov	PROPN
ijassa-1406	245	6	,	,	PUNCT
ijassa-1406	245	7	a.f	a.f	PROPN
ijassa-1406	245	8	.	.	PROPN
ijassa-1406	245	9	&	&	CCONJ
ijassa-1406	245	10	solodov	solodov	PROPN
ijassa-1406	245	11	,	,	PUNCT
ijassa-1406	245	12	m.v	m.v	PROPN
ijassa-1406	245	13	.	.	PROPN
ijassa-1406	245	14	(	(	PUNCT
ijassa-1406	245	15	2019	2019	NUM
ijassa-1406	245	16	)	)	PUNCT
ijassa-1406	245	17	local	local	ADJ
ijassa-1406	245	18	attractors	attractor	NOUN
ijassa-1406	245	19	of	of	ADP
ijassa-1406	245	20	newton	newton	NOUN
ijassa-1406	245	21	-	-	PUNCT
ijassa-1406	245	22	type	type	NOUN
ijassa-1406	245	23	methods	method	NOUN
ijassa-1406	245	24	for	for	ADP
ijassa-1406	245	25	constrained	constrained	ADJ
ijassa-1406	245	26	equations	equation	NOUN
ijassa-1406	245	27	and	and	CCONJ
ijassa-1406	245	28	complementarity	complementarity	NOUN
ijassa-1406	245	29	problems	problem	NOUN
ijassa-1406	245	30	with	with	ADP
ijassa-1406	245	31	nonisolated	nonisolated	ADJ
ijassa-1406	245	32	solutions	solution	NOUN
ijassa-1406	245	33	.	.	PUNCT
ijassa-1406	246	1	j.	j.	PROPN
ijassa-1406	246	2	optim	optim	PROPN
ijassa-1406	246	3	.	.	PUNCT
ijassa-1406	247	1	theory	theory	NOUN
ijassa-1406	247	2	appl	appl	PROPN
ijassa-1406	247	3	.	.	PROPN
ijassa-1406	247	4	,	,	PUNCT
ijassa-1406	247	5	180	180	NUM
ijassa-1406	247	6	,	,	PUNCT
ijassa-1406	247	7	140–169	140–169	NUM
ijassa-1406	247	8	.	.	NOUN
ijassa-1406	248	1	7	7	NUM
ijassa-1406	248	2	.	.	X
ijassa-1406	248	3	fischer	fischer	PROPN
ijassa-1406	248	4	,	,	PUNCT
ijassa-1406	248	5	a.	a.	PROPN
ijassa-1406	248	6	,	,	PUNCT
ijassa-1406	248	7	izmailov	izmailov	PROPN
ijassa-1406	248	8	,	,	PUNCT
ijassa-1406	248	9	a.f	a.f	PROPN
ijassa-1406	248	10	.	.	PROPN
ijassa-1406	248	11	&	&	CCONJ
ijassa-1406	248	12	solodov	solodov	PROPN
ijassa-1406	248	13	,	,	PUNCT
ijassa-1406	248	14	m.v	m.v	PROPN
ijassa-1406	248	15	.	.	PROPN
ijassa-1406	248	16	(	(	PUNCT
ijassa-1406	248	17	2021	2021	NUM
ijassa-1406	248	18	)	)	PUNCT
ijassa-1406	248	19	accelerating	accelerate	VERB
ijassa-1406	248	20	convergence	convergence	NOUN
ijassa-1406	248	21	of	of	ADP
ijassa-1406	248	22	the	the	DET
ijassa-1406	248	23	globalized	globalized	ADJ
ijassa-1406	248	24	newton	newton	PROPN
ijassa-1406	248	25	method	method	NOUN
ijassa-1406	248	26	to	to	ADP
ijassa-1406	248	27	critical	critical	ADJ
ijassa-1406	248	28	solutions	solution	NOUN
ijassa-1406	248	29	of	of	ADP
ijassa-1406	248	30	nonlinear	nonlinear	ADJ
ijassa-1406	248	31	equations	equation	NOUN
ijassa-1406	248	32	.	.	PUNCT
ijassa-1406	249	1	comput	comput	NOUN
ijassa-1406	249	2	.	.	PUNCT
ijassa-1406	250	1	optim	optim	PROPN
ijassa-1406	250	2	.	.	PUNCT
ijassa-1406	251	1	appl	appl	PROPN
ijassa-1406	251	2	.	.	PROPN
ijassa-1406	251	3	,	,	PUNCT
ijassa-1406	251	4	78	78	NUM
ijassa-1406	251	5	,	,	PUNCT
ijassa-1406	251	6	273–286	273–286	NUM
ijassa-1406	251	7	.	.	PUNCT
ijassa-1406	252	1	copyright	copyright	NOUN
ijassa-1406	252	2	©	©	PROPN
ijassa-1406	252	3	2023	2023	NUM
ijassa-1406	252	4	assa	assa	NOUN
ijassa-1406	252	5	.	.	PUNCT
ijassa-1406	253	1	adv	adv	PROPN
ijassa-1406	253	2	syst	syst	PROPN
ijassa-1406	253	3	sci	sci	PROPN
ijassa-1406	253	4	appl	appl	PROPN
ijassa-1406	253	5	(	(	PUNCT
ijassa-1406	253	6	2023	2023	NUM
ijassa-1406	253	7	)	)	PUNCT
ijassa-1406	253	8	https://rscf.ru/en/project/23-11-20020/	https://rscf.ru/en/project/23-11-20020/	PROPN
ijassa-1406	253	9	26	26	NUM
ijassa-1406	253	10	a.	a.	NOUN
ijassa-1406	253	11	izmailov	izmailov	NOUN
ijassa-1406	253	12	,	,	PUNCT
ijassa-1406	253	13	e.	e.	PROPN
ijassa-1406	253	14	uskov	uskov	PROPN
ijassa-1406	253	15	,	,	PUNCT
ijassa-1406	253	16	y.	y.	PROPN
ijassa-1406	253	17	zhibai	zhibai	PROPN
ijassa-1406	253	18	8	8	NUM
ijassa-1406	253	19	.	.	PUNCT
ijassa-1406	254	1	fischer	fischer	PROPN
ijassa-1406	254	2	,	,	PUNCT
ijassa-1406	254	3	a.	a.	PROPN
ijassa-1406	254	4	,	,	PUNCT
ijassa-1406	254	5	izmailov	izmailov	PROPN
ijassa-1406	254	6	,	,	PUNCT
ijassa-1406	254	7	a.f	a.f	PROPN
ijassa-1406	254	8	.	.	PROPN
ijassa-1406	254	9	&	&	CCONJ
ijassa-1406	254	10	solodov	solodov	PROPN
ijassa-1406	254	11	,	,	PUNCT
ijassa-1406	254	12	m.v	m.v	PROPN
ijassa-1406	254	13	.	.	PROPN
ijassa-1406	254	14	(	(	PUNCT
ijassa-1406	254	15	2021	2021	NUM
ijassa-1406	254	16	)	)	PUNCT
ijassa-1406	254	17	unit	unit	NOUN
ijassa-1406	254	18	stepsize	stepsize	NOUN
ijassa-1406	254	19	for	for	ADP
ijassa-1406	254	20	the	the	DET
ijassa-1406	254	21	newton	newton	PROPN
ijassa-1406	254	22	method	method	NOUN
ijassa-1406	254	23	close	close	ADV
ijassa-1406	254	24	to	to	ADP
ijassa-1406	254	25	critical	critical	ADJ
ijassa-1406	254	26	solutions	solution	NOUN
ijassa-1406	254	27	.	.	PUNCT
ijassa-1406	255	1	math	math	NOUN
ijassa-1406	255	2	.	.	PUNCT
ijassa-1406	256	1	program	program	PROPN
ijassa-1406	256	2	.	.	PUNCT
ijassa-1406	256	3	,	,	PUNCT
ijassa-1406	256	4	187	187	NUM
ijassa-1406	256	5	,	,	PUNCT
ijassa-1406	256	6	697–721	697–721	NUM
ijassa-1406	256	7	.	.	NOUN
ijassa-1406	257	1	9	9	NUM
ijassa-1406	257	2	.	.	X
ijassa-1406	257	3	griewank	griewank	PROPN
ijassa-1406	257	4	,	,	PUNCT
ijassa-1406	257	5	a.	a.	NOUN
ijassa-1406	257	6	(	(	PUNCT
ijassa-1406	257	7	1980	1980	NUM
ijassa-1406	257	8	)	)	PUNCT
ijassa-1406	257	9	analysis	analysis	NOUN
ijassa-1406	257	10	and	and	CCONJ
ijassa-1406	257	11	modification	modification	NOUN
ijassa-1406	257	12	of	of	ADP
ijassa-1406	257	13	mewton	mewton	PROPN
ijassa-1406	257	14	’s	’s	PART
ijassa-1406	257	15	method	method	NOUN
ijassa-1406	257	16	at	at	ADP
ijassa-1406	257	17	singularities	singularity	NOUN
ijassa-1406	257	18	.	.	PUNCT
ijassa-1406	258	1	phd	phd	NOUN
ijassa-1406	258	2	thesis	thesis	NOUN
ijassa-1406	258	3	.	.	PUNCT
ijassa-1406	259	1	australian	australian	ADJ
ijassa-1406	259	2	national	national	PROPN
ijassa-1406	259	3	university	university	PROPN
ijassa-1406	259	4	,	,	PUNCT
ijassa-1406	259	5	canberra	canberra	PROPN
ijassa-1406	259	6	.	.	PUNCT
ijassa-1406	260	1	10	10	NUM
ijassa-1406	260	2	.	.	X
ijassa-1406	260	3	griewank	griewank	PROPN
ijassa-1406	260	4	,	,	PUNCT
ijassa-1406	260	5	a.	a.	NOUN
ijassa-1406	260	6	(	(	PUNCT
ijassa-1406	260	7	1980	1980	NUM
ijassa-1406	260	8	)	)	PUNCT
ijassa-1406	260	9	starlike	starlike	NOUN
ijassa-1406	260	10	domains	domain	NOUN
ijassa-1406	260	11	of	of	ADP
ijassa-1406	260	12	convergence	convergence	NOUN
ijassa-1406	260	13	for	for	ADP
ijassa-1406	260	14	newton	newton	PROPN
ijassa-1406	260	15	’s	’s	PART
ijassa-1406	260	16	method	method	NOUN
ijassa-1406	260	17	at	at	ADP
ijassa-1406	260	18	singularities	singularity	NOUN
ijassa-1406	260	19	.	.	PUNCT
ijassa-1406	261	1	numer	numer	PROPN
ijassa-1406	261	2	.	.	PUNCT
ijassa-1406	261	3	math	math	PROPN
ijassa-1406	261	4	.	.	PUNCT
ijassa-1406	261	5	,	,	PUNCT
ijassa-1406	261	6	35	35	NUM
ijassa-1406	261	7	,	,	PUNCT
ijassa-1406	261	8	95–111	95–111	NUM
ijassa-1406	261	9	.	.	NOUN
ijassa-1406	261	10	11	11	NUM
ijassa-1406	261	11	.	.	X
ijassa-1406	261	12	griewank	griewank	PROPN
ijassa-1406	261	13	,	,	PUNCT
ijassa-1406	261	14	a.	a.	NOUN
ijassa-1406	261	15	(	(	PUNCT
ijassa-1406	261	16	1985	1985	NUM
ijassa-1406	261	17	)	)	PUNCT
ijassa-1406	261	18	on	on	ADP
ijassa-1406	261	19	solving	solve	VERB
ijassa-1406	261	20	nonlinear	nonlinear	ADJ
ijassa-1406	261	21	equations	equation	NOUN
ijassa-1406	261	22	with	with	ADP
ijassa-1406	261	23	simple	simple	ADJ
ijassa-1406	261	24	singularities	singularity	NOUN
ijassa-1406	261	25	or	or	CCONJ
ijassa-1406	261	26	nearly	nearly	ADV
ijassa-1406	261	27	singular	singular	ADJ
ijassa-1406	261	28	solutions	solution	NOUN
ijassa-1406	261	29	.	.	PUNCT
ijassa-1406	262	1	siam	siam	PROPN
ijassa-1406	262	2	rev	rev	PROPN
ijassa-1406	262	3	.	.	PROPN
ijassa-1406	262	4	,	,	PUNCT
ijassa-1406	262	5	27	27	NUM
ijassa-1406	262	6	,	,	PUNCT
ijassa-1406	262	7	537–563	537–563	NUM
ijassa-1406	262	8	.	.	PUNCT
ijassa-1406	263	1	12	12	NUM
ijassa-1406	263	2	.	.	PUNCT
ijassa-1406	264	1	izmailov	izmailov	PROPN
ijassa-1406	264	2	,	,	PUNCT
ijassa-1406	264	3	a.f	a.f	PROPN
ijassa-1406	264	4	.	.	PROPN
ijassa-1406	264	5	&	&	CCONJ
ijassa-1406	264	6	kurennoy	kurennoy	PROPN
ijassa-1406	264	7	,	,	PUNCT
ijassa-1406	264	8	a.s	a.s	PROPN
ijassa-1406	264	9	.	.	PROPN
ijassa-1406	264	10	(	(	PUNCT
ijassa-1406	264	11	2014	2014	NUM
ijassa-1406	264	12	)	)	PUNCT
ijassa-1406	264	13	on	on	ADP
ijassa-1406	264	14	regularity	regularity	NOUN
ijassa-1406	264	15	conditions	condition	NOUN
ijassa-1406	264	16	for	for	ADP
ijassa-1406	264	17	complementarity	complementarity	NOUN
ijassa-1406	264	18	problems	problem	NOUN
ijassa-1406	264	19	.	.	PUNCT
ijassa-1406	265	1	comput	comput	NOUN
ijassa-1406	265	2	.	.	PUNCT
ijassa-1406	266	1	optim	optim	PROPN
ijassa-1406	266	2	.	.	PUNCT
ijassa-1406	267	1	appl	appl	PROPN
ijassa-1406	267	2	.	.	PROPN
ijassa-1406	267	3	,	,	PUNCT
ijassa-1406	267	4	57	57	NUM
ijassa-1406	267	5	,	,	PUNCT
ijassa-1406	267	6	667–684	667–684	NUM
ijassa-1406	267	7	.	.	NOUN
ijassa-1406	268	1	13	13	NUM
ijassa-1406	268	2	.	.	PUNCT
ijassa-1406	269	1	izmailov	izmailov	PROPN
ijassa-1406	269	2	,	,	PUNCT
ijassa-1406	269	3	a.f	a.f	PROPN
ijassa-1406	269	4	.	.	PROPN
ijassa-1406	269	5	kurennoy	kurennoy	PROPN
ijassa-1406	269	6	,	,	PUNCT
ijassa-1406	269	7	a.s	a.s	PROPN
ijassa-1406	269	8	.	.	PROPN
ijassa-1406	269	9	&	&	CCONJ
ijassa-1406	269	10	solodov	solodov	PROPN
ijassa-1406	269	11	,	,	PUNCT
ijassa-1406	269	12	m.v	m.v	PROPN
ijassa-1406	269	13	.	.	PROPN
ijassa-1406	270	1	(	(	PUNCT
ijassa-1406	270	2	2018	2018	NUM
ijassa-1406	270	3	)	)	PUNCT
ijassa-1406	270	4	critical	critical	ADJ
ijassa-1406	270	5	solutions	solution	NOUN
ijassa-1406	270	6	of	of	ADP
ijassa-1406	270	7	nonlinear	nonlinear	ADJ
ijassa-1406	270	8	equations	equation	NOUN
ijassa-1406	270	9	:	:	PUNCT
ijassa-1406	270	10	local	local	ADJ
ijassa-1406	270	11	attraction	attraction	NOUN
ijassa-1406	270	12	for	for	ADP
ijassa-1406	270	13	newton	newton	NOUN
ijassa-1406	270	14	-	-	PUNCT
ijassa-1406	270	15	type	type	NOUN
ijassa-1406	270	16	methods	method	NOUN
ijassa-1406	270	17	.	.	PUNCT
ijassa-1406	271	1	math	math	NOUN
ijassa-1406	271	2	.	.	PUNCT
ijassa-1406	272	1	program	program	PROPN
ijassa-1406	272	2	.	.	PUNCT
ijassa-1406	272	3	,	,	PUNCT
ijassa-1406	272	4	167	167	NUM
ijassa-1406	272	5	,	,	PUNCT
ijassa-1406	272	6	355–379	355–379	NUM
ijassa-1406	272	7	.	.	PUNCT
ijassa-1406	273	1	14	14	NUM
ijassa-1406	273	2	.	.	PUNCT
ijassa-1406	274	1	izmailov	izmailov	PROPN
ijassa-1406	274	2	,	,	PUNCT
ijassa-1406	274	3	a.f	a.f	PROPN
ijassa-1406	274	4	.	.	PROPN
ijassa-1406	274	5	&	&	CCONJ
ijassa-1406	274	6	solodov	solodov	PROPN
ijassa-1406	274	7	,	,	PUNCT
ijassa-1406	274	8	m.v	m.v	PROPN
ijassa-1406	274	9	.	.	PROPN
ijassa-1406	275	1	(	(	PUNCT
ijassa-1406	275	2	2001	2001	NUM
ijassa-1406	275	3	)	)	PUNCT
ijassa-1406	275	4	error	error	NOUN
ijassa-1406	275	5	bounds	bound	VERB
ijassa-1406	275	6	for	for	ADP
ijassa-1406	275	7	2	2	NUM
ijassa-1406	275	8	-	-	PUNCT
ijassa-1406	275	9	regular	regular	ADJ
ijassa-1406	275	10	mappings	mapping	NOUN
ijassa-1406	275	11	with	with	ADP
ijassa-1406	275	12	lipschitzian	lipschitzian	ADJ
ijassa-1406	275	13	derivatives	derivative	NOUN
ijassa-1406	275	14	and	and	CCONJ
ijassa-1406	275	15	their	their	PRON
ijassa-1406	275	16	applications	application	NOUN
ijassa-1406	275	17	.	.	PUNCT
ijassa-1406	276	1	math	math	NOUN
ijassa-1406	276	2	.	.	PUNCT
ijassa-1406	277	1	program	program	PROPN
ijassa-1406	277	2	.	.	PUNCT
ijassa-1406	277	3	,	,	PUNCT
ijassa-1406	277	4	89	89	NUM
ijassa-1406	277	5	,	,	PUNCT
ijassa-1406	277	6	413–435	413–435	NUM
ijassa-1406	277	7	.	.	NOUN
ijassa-1406	277	8	15	15	NUM
ijassa-1406	278	1	.	.	X
ijassa-1406	278	2	izmailov	izmailov	PROPN
ijassa-1406	278	3	,	,	PUNCT
ijassa-1406	278	4	a.f	a.f	PROPN
ijassa-1406	278	5	.	.	PROPN
ijassa-1406	278	6	&	&	CCONJ
ijassa-1406	278	7	solodov	solodov	PROPN
ijassa-1406	278	8	,	,	PUNCT
ijassa-1406	278	9	m.v	m.v	PROPN
ijassa-1406	278	10	.	.	PROPN
ijassa-1406	279	1	(	(	PUNCT
ijassa-1406	279	2	2014	2014	NUM
ijassa-1406	279	3	)	)	PUNCT
ijassa-1406	279	4	newton	newton	NOUN
ijassa-1406	279	5	-	-	PUNCT
ijassa-1406	279	6	type	type	NOUN
ijassa-1406	279	7	methods	method	NOUN
ijassa-1406	279	8	for	for	ADP
ijassa-1406	279	9	optimization	optimization	NOUN
ijassa-1406	279	10	and	and	CCONJ
ijassa-1406	279	11	variational	variational	ADJ
ijassa-1406	279	12	problems	problem	NOUN
ijassa-1406	279	13	.	.	PUNCT
ijassa-1406	280	1	springer	springer	NOUN
ijassa-1406	280	2	series	series	PROPN
ijassa-1406	280	3	in	in	ADP
ijassa-1406	280	4	operations	operation	NOUN
ijassa-1406	280	5	research	research	NOUN
ijassa-1406	280	6	and	and	CCONJ
ijassa-1406	280	7	financial	financial	ADJ
ijassa-1406	280	8	engineering	engineering	NOUN
ijassa-1406	280	9	.	.	PUNCT
ijassa-1406	281	1	cham	cham	PROPN
ijassa-1406	281	2	:	:	PUNCT
ijassa-1406	281	3	springer	springer	NOUN
ijassa-1406	281	4	.	.	PUNCT
ijassa-1406	282	1	16	16	NUM
ijassa-1406	282	2	.	.	PUNCT
ijassa-1406	283	1	izmailov	izmailov	PROPN
ijassa-1406	283	2	,	,	PUNCT
ijassa-1406	283	3	a.f	a.f	PROPN
ijassa-1406	283	4	.	.	PROPN
ijassa-1406	283	5	,	,	PUNCT
ijassa-1406	283	6	solodov	solodov	PROPN
ijassa-1406	283	7	,	,	PUNCT
ijassa-1406	283	8	m.v	m.v	PROPN
ijassa-1406	283	9	.	.	PROPN
ijassa-1406	283	10	&	&	CCONJ
ijassa-1406	283	11	uskov	uskov	PROPN
ijassa-1406	283	12	,	,	PUNCT
ijassa-1406	283	13	e.i	e.i	PROPN
ijassa-1406	283	14	.	.	PROPN
ijassa-1406	283	15	(	(	PUNCT
ijassa-1406	283	16	2015	2015	NUM
ijassa-1406	283	17	)	)	PUNCT
ijassa-1406	283	18	combining	combine	VERB
ijassa-1406	283	19	stabilized	stabilize	VERB
ijassa-1406	283	20	sqp	sqp	NOUN
ijassa-1406	283	21	with	with	ADP
ijassa-1406	283	22	the	the	DET
ijassa-1406	283	23	augmented	augment	VERB
ijassa-1406	283	24	lagrangian	lagrangian	ADJ
ijassa-1406	283	25	algorithm	algorithm	NOUN
ijassa-1406	283	26	comput	comput	NOUN
ijassa-1406	283	27	.	.	PUNCT
ijassa-1406	284	1	optim	optim	PROPN
ijassa-1406	284	2	.	.	PUNCT
ijassa-1406	284	3	appl	appl	PROPN
ijassa-1406	284	4	.	.	PROPN
ijassa-1406	284	5	,	,	PUNCT
ijassa-1406	284	6	62	62	NUM
ijassa-1406	284	7	,	,	PUNCT
ijassa-1406	284	8	405–429	405–429	NUM
ijassa-1406	284	9	.	.	NOUN
ijassa-1406	284	10	17	17	NUM
ijassa-1406	284	11	.	.	PUNCT
ijassa-1406	285	1	kanzow	kanzow	PROPN
ijassa-1406	285	2	,	,	PUNCT
ijassa-1406	285	3	c.	c.	PROPN
ijassa-1406	285	4	(	(	PUNCT
ijassa-1406	285	5	1994	1994	NUM
ijassa-1406	285	6	)	)	PUNCT
ijassa-1406	285	7	some	some	DET
ijassa-1406	285	8	equation	equation	NOUN
ijassa-1406	285	9	-	-	PUNCT
ijassa-1406	285	10	based	base	VERB
ijassa-1406	285	11	methods	method	NOUN
ijassa-1406	285	12	for	for	ADP
ijassa-1406	285	13	the	the	DET
ijassa-1406	285	14	nonlinear	nonlinear	ADJ
ijassa-1406	285	15	complementarity	complementarity	NOUN
ijassa-1406	285	16	problem	problem	NOUN
ijassa-1406	285	17	.	.	PUNCT
ijassa-1406	286	1	optim	optim	ADJ
ijassa-1406	286	2	.	.	PUNCT
ijassa-1406	287	1	methods	method	NOUN
ijassa-1406	287	2	software	software	NOUN
ijassa-1406	287	3	,	,	PUNCT
ijassa-1406	287	4	3	3	NUM
ijassa-1406	287	5	,	,	PUNCT
ijassa-1406	287	6	327–340	327–340	NUM
ijassa-1406	287	7	.	.	PUNCT
ijassa-1406	288	1	18	18	NUM
ijassa-1406	288	2	.	.	X
ijassa-1406	288	3	mangasarian	mangasarian	PROPN
ijassa-1406	288	4	,	,	PUNCT
ijassa-1406	288	5	o.l	o.l	PROPN
ijassa-1406	288	6	.	.	PROPN
ijassa-1406	288	7	(	(	PUNCT
ijassa-1406	288	8	1976	1976	NUM
ijassa-1406	288	9	)	)	PUNCT
ijassa-1406	288	10	equivalence	equivalence	NOUN
ijassa-1406	288	11	of	of	ADP
ijassa-1406	288	12	the	the	DET
ijassa-1406	288	13	complementarity	complementarity	NOUN
ijassa-1406	288	14	problem	problem	NOUN
ijassa-1406	288	15	to	to	ADP
ijassa-1406	288	16	a	a	DET
ijassa-1406	288	17	system	system	NOUN
ijassa-1406	288	18	of	of	ADP
ijassa-1406	288	19	nonlinear	nonlinear	ADJ
ijassa-1406	288	20	equations	equation	NOUN
ijassa-1406	288	21	.	.	PUNCT
ijassa-1406	289	1	siam	siam	PROPN
ijassa-1406	289	2	j.	j.	PROPN
ijassa-1406	289	3	appl	appl	PROPN
ijassa-1406	289	4	.	.	PROPN
ijassa-1406	289	5	math	math	PROPN
ijassa-1406	289	6	.	.	PUNCT
ijassa-1406	289	7	,	,	PUNCT
ijassa-1406	289	8	31	31	NUM
ijassa-1406	289	9	,	,	PUNCT
ijassa-1406	289	10	89–92	89–92	NUM
ijassa-1406	289	11	.	.	PUNCT
ijassa-1406	290	1	19	19	NUM
ijassa-1406	290	2	.	.	PUNCT
ijassa-1406	291	1	oberlin	oberlin	PROPN
ijassa-1406	291	2	,	,	PUNCT
ijassa-1406	291	3	c.	c.	PROPN
ijassa-1406	291	4	&	&	CCONJ
ijassa-1406	291	5	wright	wright	PROPN
ijassa-1406	291	6	,	,	PUNCT
ijassa-1406	291	7	s.j	s.j	PROPN
ijassa-1406	291	8	.	.	PROPN
ijassa-1406	291	9	(	(	PUNCT
ijassa-1406	291	10	2009	2009	NUM
ijassa-1406	291	11	)	)	PUNCT
ijassa-1406	291	12	an	an	DET
ijassa-1406	291	13	accelerated	accelerate	VERB
ijassa-1406	291	14	newton	newton	PROPN
ijassa-1406	291	15	method	method	NOUN
ijassa-1406	291	16	for	for	ADP
ijassa-1406	291	17	equations	equation	NOUN
ijassa-1406	291	18	with	with	ADP
ijassa-1406	291	19	semismooth	semismooth	NOUN
ijassa-1406	291	20	jacobians	jacobian	NOUN
ijassa-1406	291	21	and	and	CCONJ
ijassa-1406	291	22	nonlinear	nonlinear	ADJ
ijassa-1406	291	23	complementarity	complementarity	NOUN
ijassa-1406	291	24	problems	problem	NOUN
ijassa-1406	291	25	.	.	PUNCT
ijassa-1406	292	1	math	math	NOUN
ijassa-1406	292	2	.	.	PUNCT
ijassa-1406	293	1	program	program	PROPN
ijassa-1406	293	2	.	.	PUNCT
ijassa-1406	293	3	,	,	PUNCT
ijassa-1406	293	4	117	117	NUM
ijassa-1406	293	5	,	,	PUNCT
ijassa-1406	293	6	355–386	355–386	NUM
ijassa-1406	293	7	.	.	PUNCT
ijassa-1406	294	1	copyright	copyright	NOUN
ijassa-1406	294	2	©	©	PROPN
ijassa-1406	294	3	2023	2023	NUM
ijassa-1406	294	4	assa	assa	NOUN
ijassa-1406	294	5	.	.	PUNCT
ijassa-1406	295	1	adv	adv	PROPN
ijassa-1406	295	2	syst	syst	PROPN
ijassa-1406	295	3	sci	sci	PROPN
ijassa-1406	295	4	appl	appl	PROPN
ijassa-1406	295	5	(	(	PUNCT
ijassa-1406	295	6	2023	2023	NUM
ijassa-1406	295	7	)	)	PUNCT
ijassa-1406	295	8	newton	newton	PROPN
ijassa-1406	295	9	method	method	NOUN
ijassa-1406	295	10	vs.	vs.	ADP
ijassa-1406	295	11	semismooth	semismooth	NOUN
ijassa-1406	295	12	newton	newton	PROPN
ijassa-1406	295	13	method	method	VERB
ijassa-1406	295	14	27	27	NUM
ijassa-1406	295	15	test	test	NOUN
ijassa-1406	295	16	problems	problem	NOUN
ijassa-1406	295	17	u0	u0	ADJ
ijassa-1406	295	18	ū	ū	NOUN
ijassa-1406	295	19	quarp	quarp	NOUN
ijassa-1406	295	20	0.9	0.9	NUM
ijassa-1406	295	21	1	1	NUM
ijassa-1406	295	22	dis61	dis61	NOUN
ijassa-1406	295	23	(	(	PUNCT
ijassa-1406	295	24	0.2	0.2	NUM
ijassa-1406	295	25	,	,	PUNCT
ijassa-1406	295	26	0.85	0.85	NUM
ijassa-1406	295	27	)	)	PUNCT
ijassa-1406	295	28	(	(	PUNCT
ijassa-1406	295	29	0	0	NUM
ijassa-1406	295	30	,	,	PUNCT
ijassa-1406	295	31	(	(	PUNCT
ijassa-1406	295	32	√	√	NUM
ijassa-1406	295	33	5−	5−	NUM
ijassa-1406	295	34	1)/2	1)/2	NUM
ijassa-1406	295	35	)	)	PUNCT
ijassa-1406	295	36	quarquad	quarquad	NOUN
ijassa-1406	295	37	,	,	PUNCT
ijassa-1406	295	38	1	1	NUM
ijassa-1406	295	39	(	(	PUNCT
ijassa-1406	295	40	0.1	0.1	NUM
ijassa-1406	295	41	,	,	PUNCT
ijassa-1406	295	42	0.9	0.9	NUM
ijassa-1406	295	43	)	)	PUNCT
ijassa-1406	295	44	(	(	PUNCT
ijassa-1406	295	45	0	0	NUM
ijassa-1406	295	46	,	,	PUNCT
ijassa-1406	295	47	1	1	NUM
ijassa-1406	295	48	)	)	PUNCT
ijassa-1406	295	49	quarquad	quarquad	NOUN
ijassa-1406	295	50	,	,	PUNCT
ijassa-1406	295	51	2	2	NUM
ijassa-1406	295	52	(	(	PUNCT
ijassa-1406	295	53	0.9	0.9	NUM
ijassa-1406	295	54	,	,	PUNCT
ijassa-1406	295	55	0.9	0.9	NUM
ijassa-1406	295	56	)	)	PUNCT
ijassa-1406	295	57	(	(	PUNCT
ijassa-1406	295	58	1	1	NUM
ijassa-1406	295	59	,	,	PUNCT
ijassa-1406	295	60	0	0	NUM
ijassa-1406	295	61	)	)	PUNCT
ijassa-1406	295	62	affknot1	affknot1	X
ijassa-1406	296	1	(	(	PUNCT
ijassa-1406	296	2	0.9	0.9	NUM
ijassa-1406	296	3	,	,	PUNCT
ijassa-1406	296	4	0.1	0.1	NUM
ijassa-1406	296	5	)	)	PUNCT
ijassa-1406	296	6	(	(	PUNCT
ijassa-1406	296	7	0	0	NUM
ijassa-1406	296	8	,	,	PUNCT
ijassa-1406	296	9	1	1	NUM
ijassa-1406	296	10	)	)	PUNCT
ijassa-1406	296	11	affknot2	affknot2	NOUN
ijassa-1406	296	12	(	(	PUNCT
ijassa-1406	296	13	0.5	0.5	NUM
ijassa-1406	296	14	,	,	PUNCT
ijassa-1406	296	15	0.5	0.5	NUM
ijassa-1406	296	16	)	)	PUNCT
ijassa-1406	296	17	(	(	PUNCT
ijassa-1406	296	18	0	0	NUM
ijassa-1406	296	19	,	,	PUNCT
ijassa-1406	296	20	1	1	NUM
ijassa-1406	296	21	)	)	PUNCT
ijassa-1406	296	22	quadknot	quadknot	NOUN
ijassa-1406	296	23	(	(	PUNCT
ijassa-1406	296	24	0.5	0.5	NUM
ijassa-1406	296	25	,	,	PUNCT
ijassa-1406	296	26	0.5	0.5	NUM
ijassa-1406	296	27	)	)	PUNCT
ijassa-1406	296	28	(	(	PUNCT
ijassa-1406	296	29	0	0	NUM
ijassa-1406	296	30	,	,	PUNCT
ijassa-1406	296	31	1	1	NUM
ijassa-1406	296	32	)	)	PUNCT
ijassa-1406	296	33	munson4	munson4	NOUN
ijassa-1406	296	34	(	(	PUNCT
ijassa-1406	296	35	0	0	NUM
ijassa-1406	296	36	,	,	PUNCT
ijassa-1406	296	37	0	0	NUM
ijassa-1406	296	38	)	)	PUNCT
ijassa-1406	296	39	(	(	PUNCT
ijassa-1406	296	40	1	1	NUM
ijassa-1406	296	41	,	,	PUNCT
ijassa-1406	296	42	1	1	X
ijassa-1406	296	43	)	)	PUNCT
ijassa-1406	296	44	dis64	dis64	NOUN
ijassa-1406	296	45	(	(	PUNCT
ijassa-1406	296	46	2	2	NUM
ijassa-1406	296	47	,	,	PUNCT
ijassa-1406	296	48	4	4	NUM
ijassa-1406	296	49	)	)	PUNCT
ijassa-1406	296	50	(	(	PUNCT
ijassa-1406	296	51	0	0	NUM
ijassa-1406	296	52	,	,	PUNCT
ijassa-1406	296	53	0	0	NUM
ijassa-1406	296	54	)	)	PUNCT
ijassa-1406	296	55	ne	ne	NOUN
ijassa-1406	296	56	-	-	ADJ
ijassa-1406	296	57	hard	hard	ADJ
ijassa-1406	296	58	(	(	PUNCT
ijassa-1406	296	59	10	10	NUM
ijassa-1406	296	60	,	,	PUNCT
ijassa-1406	296	61	1	1	NUM
ijassa-1406	296	62	,	,	PUNCT
ijassa-1406	296	63	10	10	NUM
ijassa-1406	296	64	)	)	PUNCT
ijassa-1406	296	65	(	(	PUNCT
ijassa-1406	296	66	0	0	NUM
ijassa-1406	296	67	,	,	PUNCT
ijassa-1406	296	68	0	0	NUM
ijassa-1406	296	69	,	,	PUNCT
ijassa-1406	296	70	√	√	NOUN
ijassa-1406	296	71	200	200	NUM
ijassa-1406	296	72	)	)	PUNCT
ijassa-1406	296	73	doubleknot	doubleknot	NOUN
ijassa-1406	296	74	(	(	PUNCT
ijassa-1406	296	75	0.5	0.5	NUM
ijassa-1406	296	76	,	,	PUNCT
ijassa-1406	296	77	0.5	0.5	NUM
ijassa-1406	296	78	,	,	PUNCT
ijassa-1406	296	79	0.5	0.5	NUM
ijassa-1406	296	80	,	,	PUNCT
ijassa-1406	296	81	0.5	0.5	NUM
ijassa-1406	296	82	)	)	PUNCT
ijassa-1406	296	83	(	(	PUNCT
ijassa-1406	296	84	1	1	NUM
ijassa-1406	296	85	,	,	PUNCT
ijassa-1406	296	86	0	0	NUM
ijassa-1406	296	87	,	,	PUNCT
ijassa-1406	296	88	0	0	NUM
ijassa-1406	296	89	,	,	PUNCT
ijassa-1406	296	90	1	1	NUM
ijassa-1406	296	91	)	)	PUNCT
ijassa-1406	296	92	quad1	quad1	NOUN
ijassa-1406	296	93	,	,	PUNCT
ijassa-1406	296	94	1	1	NUM
ijassa-1406	296	95	(	(	PUNCT
ijassa-1406	296	96	0.9	0.9	NUM
ijassa-1406	296	97	,	,	PUNCT
ijassa-1406	296	98	-0.1	-0.1	PROPN
ijassa-1406	296	99	)	)	PUNCT
ijassa-1406	296	100	(	(	PUNCT
ijassa-1406	296	101	1	1	NUM
ijassa-1406	296	102	,	,	PUNCT
ijassa-1406	296	103	0	0	NUM
ijassa-1406	296	104	)	)	PUNCT
ijassa-1406	296	105	quad1	quad1	NOUN
ijassa-1406	296	106	,	,	PUNCT
ijassa-1406	296	107	2	2	NUM
ijassa-1406	296	108	(	(	PUNCT
ijassa-1406	296	109	0.9	0.9	NUM
ijassa-1406	296	110	,	,	PUNCT
ijassa-1406	296	111	0.1	0.1	NUM
ijassa-1406	296	112	)	)	PUNCT
ijassa-1406	296	113	(	(	PUNCT
ijassa-1406	296	114	1	1	NUM
ijassa-1406	296	115	,	,	PUNCT
ijassa-1406	296	116	0	0	NUM
ijassa-1406	296	117	)	)	PUNCT
ijassa-1406	296	118	quad2	quad2	ADJ
ijassa-1406	296	119	,	,	PUNCT
ijassa-1406	296	120	1	1	NUM
ijassa-1406	296	121	(	(	PUNCT
ijassa-1406	296	122	-1	-1	ADJ
ijassa-1406	296	123	,	,	PUNCT
ijassa-1406	296	124	-1	-1	PUNCT
ijassa-1406	296	125	)	)	PUNCT
ijassa-1406	296	126	(	(	PUNCT
ijassa-1406	296	127	0	0	NUM
ijassa-1406	296	128	,	,	PUNCT
ijassa-1406	296	129	0	0	NUM
ijassa-1406	296	130	)	)	PUNCT
ijassa-1406	296	131	quad2	quad2	ADJ
ijassa-1406	296	132	,	,	PUNCT
ijassa-1406	296	133	2	2	NUM
ijassa-1406	296	134	(	(	PUNCT
ijassa-1406	296	135	1	1	NUM
ijassa-1406	296	136	,	,	PUNCT
ijassa-1406	296	137	1	1	NUM
ijassa-1406	296	138	)	)	PUNCT
ijassa-1406	296	139	(	(	PUNCT
ijassa-1406	296	140	0	0	NUM
ijassa-1406	296	141	,	,	PUNCT
ijassa-1406	296	142	0	0	NUM
ijassa-1406	296	143	)	)	PUNCT
ijassa-1406	296	144	quarn	quarn	VERB
ijassa-1406	296	145	0.9	0.9	NUM
ijassa-1406	296	146	1	1	NUM
ijassa-1406	296	147	[	[	X
ijassa-1406	296	148	1	1	NUM
ijassa-1406	296	149	,	,	PUNCT
ijassa-1406	296	150	example	example	NOUN
ijassa-1406	296	151	3.1	3.1	NUM
ijassa-1406	296	152	]	]	SYM
ijassa-1406	296	153	(	(	PUNCT
ijassa-1406	296	154	-0.5	-0.5	X
ijassa-1406	296	155	,	,	PUNCT
ijassa-1406	296	156	-0.9	-0.9	NOUN
ijassa-1406	296	157	)	)	PUNCT
ijassa-1406	296	158	(	(	PUNCT
ijassa-1406	296	159	0	0	NUM
ijassa-1406	296	160	,	,	PUNCT
ijassa-1406	296	161	0	0	NUM
ijassa-1406	296	162	)	)	PUNCT
ijassa-1406	297	1	[	[	X
ijassa-1406	297	2	1	1	NUM
ijassa-1406	297	3	,	,	PUNCT
ijassa-1406	297	4	example	example	NOUN
ijassa-1406	297	5	3.2	3.2	NUM
ijassa-1406	297	6	]	]	PUNCT
ijassa-1406	297	7	(	(	PUNCT
ijassa-1406	297	8	-0.5	-0.5	X
ijassa-1406	297	9	,	,	PUNCT
ijassa-1406	297	10	-0.5	-0.5	NUM
ijassa-1406	297	11	)	)	PUNCT
ijassa-1406	297	12	(	(	PUNCT
ijassa-1406	297	13	0	0	NUM
ijassa-1406	297	14	,	,	PUNCT
ijassa-1406	297	15	0	0	NUM
ijassa-1406	297	16	)	)	PUNCT
ijassa-1406	298	1	[	[	X
ijassa-1406	298	2	1	1	NUM
ijassa-1406	298	3	,	,	PUNCT
ijassa-1406	298	4	example	example	NOUN
ijassa-1406	298	5	3.3	3.3	NUM
ijassa-1406	298	6	]	]	PUNCT
ijassa-1406	298	7	,	,	PUNCT
ijassa-1406	298	8	1	1	NUM
ijassa-1406	298	9	(	(	PUNCT
ijassa-1406	298	10	-0.9	-0.9	NOUN
ijassa-1406	298	11	,	,	PUNCT
ijassa-1406	298	12	0.5	0.5	NUM
ijassa-1406	298	13	)	)	PUNCT
ijassa-1406	298	14	(	(	PUNCT
ijassa-1406	298	15	0	0	NUM
ijassa-1406	298	16	,	,	PUNCT
ijassa-1406	298	17	0	0	NUM
ijassa-1406	298	18	)	)	PUNCT
ijassa-1406	299	1	[	[	X
ijassa-1406	299	2	1	1	NUM
ijassa-1406	299	3	,	,	PUNCT
ijassa-1406	299	4	example	example	NOUN
ijassa-1406	299	5	3.3	3.3	NUM
ijassa-1406	299	6	]	]	PUNCT
ijassa-1406	299	7	,	,	PUNCT
ijassa-1406	299	8	2	2	NUM
ijassa-1406	299	9	(	(	PUNCT
ijassa-1406	299	10	0.9	0.9	NUM
ijassa-1406	299	11	,	,	PUNCT
ijassa-1406	299	12	-0.9	-0.9	NOUN
ijassa-1406	299	13	)	)	PUNCT
ijassa-1406	299	14	(	(	PUNCT
ijassa-1406	299	15	1	1	NUM
ijassa-1406	299	16	,	,	PUNCT
ijassa-1406	299	17	0	0	NUM
ijassa-1406	299	18	)	)	PUNCT
ijassa-1406	300	1	[	[	X
ijassa-1406	300	2	1	1	NUM
ijassa-1406	300	3	,	,	PUNCT
ijassa-1406	300	4	example	example	NOUN
ijassa-1406	300	5	3.4	3.4	NUM
ijassa-1406	300	6	]	]	PUNCT
ijassa-1406	300	7	(	(	PUNCT
ijassa-1406	300	8	1.9	1.9	NUM
ijassa-1406	300	9	,	,	PUNCT
ijassa-1406	300	10	-0.5	-0.5	NUM
ijassa-1406	300	11	)	)	PUNCT
ijassa-1406	300	12	(	(	PUNCT
ijassa-1406	300	13	1	1	NUM
ijassa-1406	300	14	,	,	PUNCT
ijassa-1406	300	15	0	0	NUM
ijassa-1406	300	16	)	)	PUNCT
ijassa-1406	301	1	[	[	X
ijassa-1406	301	2	3	3	NUM
ijassa-1406	301	3	,	,	PUNCT
ijassa-1406	301	4	example	example	NOUN
ijassa-1406	301	5	6	6	NUM
ijassa-1406	301	6	]	]	PUNCT
ijassa-1406	301	7	(	(	PUNCT
ijassa-1406	301	8	0.9	0.9	NUM
ijassa-1406	301	9	,	,	PUNCT
ijassa-1406	301	10	0.1	0.1	NUM
ijassa-1406	301	11	)	)	PUNCT
ijassa-1406	301	12	(	(	PUNCT
ijassa-1406	301	13	0	0	NUM
ijassa-1406	301	14	,	,	PUNCT
ijassa-1406	301	15	0	0	NUM
ijassa-1406	301	16	)	)	PUNCT
ijassa-1406	302	1	[	[	X
ijassa-1406	302	2	3	3	NUM
ijassa-1406	302	3	,	,	PUNCT
ijassa-1406	302	4	example	example	NOUN
ijassa-1406	302	5	7	7	NUM
ijassa-1406	302	6	]	]	PUNCT
ijassa-1406	302	7	(	(	PUNCT
ijassa-1406	302	8	0.9	0.9	NUM
ijassa-1406	302	9	,	,	PUNCT
ijassa-1406	302	10	0.1	0.1	NUM
ijassa-1406	302	11	)	)	PUNCT
ijassa-1406	302	12	(	(	PUNCT
ijassa-1406	302	13	0	0	NUM
ijassa-1406	302	14	,	,	PUNCT
ijassa-1406	302	15	0	0	NUM
ijassa-1406	302	16	)	)	PUNCT
ijassa-1406	303	1	[	[	X
ijassa-1406	303	2	3	3	NUM
ijassa-1406	303	3	,	,	PUNCT
ijassa-1406	303	4	example	example	NOUN
ijassa-1406	303	5	8	8	NUM
ijassa-1406	303	6	]	]	PUNCT
ijassa-1406	303	7	(	(	PUNCT
ijassa-1406	303	8	1.9	1.9	NUM
ijassa-1406	303	9	,	,	PUNCT
ijassa-1406	303	10	0.9	0.9	NUM
ijassa-1406	303	11	)	)	PUNCT
ijassa-1406	303	12	(	(	PUNCT
ijassa-1406	303	13	0	0	NUM
ijassa-1406	303	14	,	,	PUNCT
ijassa-1406	303	15	1	1	NUM
ijassa-1406	303	16	)	)	PUNCT
ijassa-1406	304	1	[	[	X
ijassa-1406	304	2	3	3	NUM
ijassa-1406	304	3	,	,	PUNCT
ijassa-1406	304	4	example	example	NOUN
ijassa-1406	304	5	9	9	NUM
ijassa-1406	304	6	]	]	PUNCT
ijassa-1406	304	7	(	(	PUNCT
ijassa-1406	304	8	0.9	0.9	NUM
ijassa-1406	304	9	,	,	PUNCT
ijassa-1406	304	10	0.9	0.9	NUM
ijassa-1406	304	11	)	)	PUNCT
ijassa-1406	304	12	(	(	PUNCT
ijassa-1406	304	13	0	0	NUM
ijassa-1406	304	14	,	,	PUNCT
ijassa-1406	304	15	0	0	NUM
ijassa-1406	304	16	)	)	PUNCT
ijassa-1406	305	1	[	[	X
ijassa-1406	305	2	5	5	NUM
ijassa-1406	305	3	,	,	PUNCT
ijassa-1406	305	4	example	example	NOUN
ijassa-1406	305	5	1	1	NUM
ijassa-1406	305	6	]	]	SYM
ijassa-1406	305	7	-0.9	-0.9	NOUN
ijassa-1406	305	8	0	0	PUNCT
ijassa-1406	306	1	[	[	X
ijassa-1406	306	2	5	5	NUM
ijassa-1406	306	3	,	,	PUNCT
ijassa-1406	306	4	example	example	NOUN
ijassa-1406	306	5	3	3	NUM
ijassa-1406	306	6	]	]	PUNCT
ijassa-1406	306	7	,	,	PUNCT
ijassa-1406	306	8	1	1	NUM
ijassa-1406	306	9	(	(	PUNCT
ijassa-1406	306	10	0.9	0.9	NUM
ijassa-1406	306	11	,	,	PUNCT
ijassa-1406	306	12	0.1	0.1	NUM
ijassa-1406	306	13	)	)	PUNCT
ijassa-1406	306	14	(	(	PUNCT
ijassa-1406	306	15	0	0	NUM
ijassa-1406	306	16	,	,	PUNCT
ijassa-1406	306	17	1	1	NUM
ijassa-1406	306	18	)	)	PUNCT
ijassa-1406	307	1	[	[	X
ijassa-1406	307	2	5	5	NUM
ijassa-1406	307	3	,	,	PUNCT
ijassa-1406	307	4	example	example	NOUN
ijassa-1406	307	5	3	3	NUM
ijassa-1406	307	6	]	]	PUNCT
ijassa-1406	307	7	,	,	PUNCT
ijassa-1406	307	8	2	2	NUM
ijassa-1406	307	9	(	(	PUNCT
ijassa-1406	307	10	-0.9	-0.9	NOUN
ijassa-1406	307	11	,	,	PUNCT
ijassa-1406	307	12	0.5	0.5	NUM
ijassa-1406	307	13	)	)	PUNCT
ijassa-1406	307	14	(	(	PUNCT
ijassa-1406	307	15	0	0	NUM
ijassa-1406	307	16	,	,	PUNCT
ijassa-1406	307	17	0	0	NUM
ijassa-1406	307	18	)	)	PUNCT
ijassa-1406	308	1	[	[	X
ijassa-1406	308	2	6	6	NUM
ijassa-1406	308	3	,	,	PUNCT
ijassa-1406	308	4	example	example	NOUN
ijassa-1406	308	5	4.2	4.2	NUM
ijassa-1406	308	6	]	]	PUNCT
ijassa-1406	308	7	(	(	PUNCT
ijassa-1406	308	8	0.9	0.9	NUM
ijassa-1406	308	9	,	,	PUNCT
ijassa-1406	308	10	0.9	0.9	NUM
ijassa-1406	308	11	)	)	PUNCT
ijassa-1406	308	12	(	(	PUNCT
ijassa-1406	308	13	0	0	NUM
ijassa-1406	308	14	,	,	PUNCT
ijassa-1406	308	15	0	0	NUM
ijassa-1406	308	16	)	)	PUNCT
ijassa-1406	309	1	[	[	X
ijassa-1406	309	2	6	6	NUM
ijassa-1406	309	3	,	,	PUNCT
ijassa-1406	309	4	example	example	NOUN
ijassa-1406	309	5	4.3	4.3	NUM
ijassa-1406	309	6	]	]	PUNCT
ijassa-1406	309	7	(	(	PUNCT
ijassa-1406	309	8	0.9	0.9	NUM
ijassa-1406	309	9	,	,	PUNCT
ijassa-1406	309	10	0.9	0.9	NUM
ijassa-1406	309	11	)	)	PUNCT
ijassa-1406	309	12	(	(	PUNCT
ijassa-1406	309	13	0	0	NUM
ijassa-1406	309	14	,	,	PUNCT
ijassa-1406	309	15	0	0	NUM
ijassa-1406	309	16	)	)	PUNCT
ijassa-1406	310	1	[	[	X
ijassa-1406	310	2	12	12	NUM
ijassa-1406	310	3	,	,	PUNCT
ijassa-1406	310	4	example	example	NOUN
ijassa-1406	310	5	3.4	3.4	NUM
ijassa-1406	310	6	]	]	SYM
ijassa-1406	310	7	0.9	0.9	NUM
ijassa-1406	310	8	0	0	NUM
ijassa-1406	311	1	[	[	X
ijassa-1406	311	2	12	12	NUM
ijassa-1406	311	3	,	,	PUNCT
ijassa-1406	311	4	example	example	NOUN
ijassa-1406	311	5	3.5	3.5	NUM
ijassa-1406	311	6	]	]	PUNCT
ijassa-1406	311	7	(	(	PUNCT
ijassa-1406	311	8	0.9	0.9	NUM
ijassa-1406	311	9	,	,	PUNCT
ijassa-1406	311	10	0.9	0.9	NUM
ijassa-1406	311	11	)	)	PUNCT
ijassa-1406	311	12	(	(	PUNCT
ijassa-1406	311	13	0	0	NUM
ijassa-1406	311	14	,	,	PUNCT
ijassa-1406	311	15	0	0	NUM
ijassa-1406	311	16	)	)	PUNCT
ijassa-1406	312	1	[	[	X
ijassa-1406	312	2	14	14	NUM
ijassa-1406	312	3	,	,	PUNCT
ijassa-1406	312	4	example	example	NOUN
ijassa-1406	312	5	1	1	NUM
ijassa-1406	312	6	]	]	PUNCT
ijassa-1406	312	7	(	(	PUNCT
ijassa-1406	312	8	0.9	0.9	NUM
ijassa-1406	312	9	,	,	PUNCT
ijassa-1406	312	10	0.9	0.9	NUM
ijassa-1406	312	11	)	)	PUNCT
ijassa-1406	312	12	(	(	PUNCT
ijassa-1406	312	13	0	0	NUM
ijassa-1406	312	14	,	,	PUNCT
ijassa-1406	312	15	1	1	NUM
ijassa-1406	312	16	)	)	PUNCT
ijassa-1406	313	1	[	[	X
ijassa-1406	313	2	14	14	NUM
ijassa-1406	313	3	,	,	PUNCT
ijassa-1406	313	4	example	example	NOUN
ijassa-1406	313	5	2	2	NUM
ijassa-1406	313	6	]	]	PUNCT
ijassa-1406	313	7	(	(	PUNCT
ijassa-1406	313	8	0.9	0.9	NUM
ijassa-1406	313	9	,	,	PUNCT
ijassa-1406	313	10	0.1	0.1	NUM
ijassa-1406	313	11	)	)	PUNCT
ijassa-1406	313	12	(	(	PUNCT
ijassa-1406	313	13	0	0	NUM
ijassa-1406	313	14	,	,	PUNCT
ijassa-1406	313	15	0	0	NUM
ijassa-1406	313	16	)	)	PUNCT
ijassa-1406	313	17	table	table	NOUN
ijassa-1406	313	18	3.1	3.1	NUM
ijassa-1406	313	19	.	.	PUNCT
ijassa-1406	314	1	“	"	PUNCT
ijassa-1406	314	2	standard	standard	NOUN
ijassa-1406	314	3	”	"	PUNCT
ijassa-1406	314	4	starting	start	VERB
ijassa-1406	314	5	points	point	NOUN
ijassa-1406	314	6	and	and	CCONJ
ijassa-1406	314	7	solutions	solution	NOUN
ijassa-1406	314	8	.	.	PUNCT
ijassa-1406	315	1	copyright	copyright	NOUN
ijassa-1406	315	2	©	©	PROPN
ijassa-1406	315	3	2023	2023	NUM
ijassa-1406	315	4	assa	assa	NOUN
ijassa-1406	315	5	.	.	PUNCT
ijassa-1406	316	1	adv	adv	PROPN
ijassa-1406	316	2	syst	syst	PROPN
ijassa-1406	316	3	sci	sci	PROPN
ijassa-1406	316	4	appl	appl	PROPN
ijassa-1406	316	5	(	(	PUNCT
ijassa-1406	316	6	2023	2023	NUM
ijassa-1406	316	7	)	)	PUNCT
ijassa-1406	316	8	28	28	NUM
ijassa-1406	316	9	a.	a.	NOUN
ijassa-1406	316	10	izmailov	izmailov	NOUN
ijassa-1406	316	11	,	,	PUNCT
ijassa-1406	316	12	e.	e.	PROPN
ijassa-1406	316	13	uskov	uskov	PROPN
ijassa-1406	316	14	,	,	PUNCT
ijassa-1406	316	15	y.	y.	PROPN
ijassa-1406	316	16	zhibai	zhibai	PROPN
ijassa-1406	316	17	test	test	NOUN
ijassa-1406	316	18	problems	problem	NOUN
ijassa-1406	316	19	nm	nm	ADP
ijassa-1406	316	20	nm	nm	NOUN
ijassa-1406	316	21	-	-	ADJ
ijassa-1406	316	22	ep	ep	ADJ
ijassa-1406	316	23	snm	snm	PROPN
ijassa-1406	316	24	snm	snm	PROPN
ijassa-1406	316	25	-	-	PUNCT
ijassa-1406	316	26	ep	ep	PROPN
ijassa-1406	316	27	quarp	quarp	NOUN
ijassa-1406	316	28	15	15	NUM
ijassa-1406	316	29	14	14	NUM
ijassa-1406	316	30	15	15	NUM
ijassa-1406	316	31	13	13	NUM
ijassa-1406	316	32	dis61	dis61	NOUN
ijassa-1406	316	33	19	19	NUM
ijassa-1406	316	34	10	10	NUM
ijassa-1406	316	35	18	18	NUM
ijassa-1406	316	36	12	12	NUM
ijassa-1406	316	37	quarquad	quarquad	NOUN
ijassa-1406	316	38	,	,	PUNCT
ijassa-1406	316	39	1	1	NUM
ijassa-1406	316	40	16	16	NUM
ijassa-1406	316	41	8	8	NUM
ijassa-1406	316	42	4	4	NUM
ijassa-1406	316	43	4	4	NUM
ijassa-1406	316	44	quarquad	quarquad	NOUN
ijassa-1406	316	45	,	,	PUNCT
ijassa-1406	316	46	2	2	NUM
ijassa-1406	316	47	18	18	NUM
ijassa-1406	316	48	17	17	NUM
ijassa-1406	316	49	17	17	NUM
ijassa-1406	316	50	15	15	NUM
ijassa-1406	316	51	affknot1	affknot1	NOUN
ijassa-1406	316	52	20	20	NUM
ijassa-1406	316	53	2	2	NUM
ijassa-1406	316	54	6	6	NUM
ijassa-1406	316	55	6	6	NUM
ijassa-1406	316	56	affknot2	affknot2	NOUN
ijassa-1406	316	57	18	18	NUM
ijassa-1406	316	58	1	1	NUM
ijassa-1406	316	59	1	1	NUM
ijassa-1406	316	60	1	1	NUM
ijassa-1406	316	61	quadknot	quadknot	NOUN
ijassa-1406	316	62	18	18	NUM
ijassa-1406	316	63	9	9	NUM
ijassa-1406	316	64	16	16	NUM
ijassa-1406	316	65	11	11	NUM
ijassa-1406	316	66	munson4	munson4	NOUN
ijassa-1406	316	67	19	19	NUM
ijassa-1406	316	68	10	10	NUM
ijassa-1406	316	69	20	20	NUM
ijassa-1406	316	70	8	8	NUM
ijassa-1406	316	71	dis64	dis64	NOUN
ijassa-1406	316	72	–	–	PUNCT
ijassa-1406	316	73	–	–	PUNCT
ijassa-1406	316	74	–	–	PUNCT
ijassa-1406	316	75	–	–	PUNCT
ijassa-1406	316	76	ne	ne	VERB
ijassa-1406	316	77	-	-	ADJ
ijassa-1406	316	78	hard	hard	ADJ
ijassa-1406	316	79	25	25	NUM
ijassa-1406	316	80	16	16	NUM
ijassa-1406	316	81	7	7	NUM
ijassa-1406	316	82	7	7	NUM
ijassa-1406	316	83	doubleknot	doubleknot	NOUN
ijassa-1406	316	84	21	21	NUM
ijassa-1406	316	85	11	11	NUM
ijassa-1406	316	86	8	8	NUM
ijassa-1406	316	87	8	8	NUM
ijassa-1406	316	88	quad1	quad1	NOUN
ijassa-1406	316	89	15	15	NUM
ijassa-1406	316	90	5	5	NUM
ijassa-1406	316	91	12	12	NUM
ijassa-1406	316	92	12	12	NUM
ijassa-1406	316	93	quad2	quad2	NOUN
ijassa-1406	316	94	20	20	NUM
ijassa-1406	316	95	9	9	NUM
ijassa-1406	316	96	18	18	NUM
ijassa-1406	316	97	18	18	NUM
ijassa-1406	316	98	quarn	quarn	NOUN
ijassa-1406	316	99	15	15	NUM
ijassa-1406	316	100	14	14	NUM
ijassa-1406	316	101	15	15	NUM
ijassa-1406	316	102	13	13	NUM
ijassa-1406	317	1	[	[	X
ijassa-1406	317	2	1	1	NUM
ijassa-1406	317	3	,	,	PUNCT
ijassa-1406	317	4	example	example	NOUN
ijassa-1406	317	5	3.1	3.1	NUM
ijassa-1406	317	6	]	]	PUNCT
ijassa-1406	317	7	–	–	PUNCT
ijassa-1406	317	8	–	–	PUNCT
ijassa-1406	317	9	–	–	PUNCT
ijassa-1406	317	10	–	–	PUNCT
ijassa-1406	317	11	[	[	X
ijassa-1406	317	12	1	1	NUM
ijassa-1406	317	13	,	,	PUNCT
ijassa-1406	317	14	example	example	NOUN
ijassa-1406	317	15	3.2	3.2	NUM
ijassa-1406	317	16	]	]	SYM
ijassa-1406	317	17	18	18	NUM
ijassa-1406	317	18	9	9	NUM
ijassa-1406	317	19	4	4	NUM
ijassa-1406	317	20	4	4	NUM
ijassa-1406	318	1	[	[	SYM
ijassa-1406	318	2	1	1	NUM
ijassa-1406	318	3	,	,	PUNCT
ijassa-1406	318	4	example	example	NOUN
ijassa-1406	318	5	3.3	3.3	NUM
ijassa-1406	318	6	]	]	PUNCT
ijassa-1406	318	7	,	,	PUNCT
ijassa-1406	318	8	1	1	NUM
ijassa-1406	318	9	20	20	NUM
ijassa-1406	318	10	11	11	NUM
ijassa-1406	318	11	7	7	NUM
ijassa-1406	318	12	7	7	NUM
ijassa-1406	319	1	[	[	X
ijassa-1406	319	2	1	1	NUM
ijassa-1406	319	3	,	,	PUNCT
ijassa-1406	319	4	example	example	NOUN
ijassa-1406	319	5	3.3	3.3	NUM
ijassa-1406	319	6	]	]	PUNCT
ijassa-1406	319	7	,	,	PUNCT
ijassa-1406	319	8	2	2	NUM
ijassa-1406	319	9	19	19	NUM
ijassa-1406	319	10	5	5	NUM
ijassa-1406	319	11	5	5	NUM
ijassa-1406	319	12	5	5	NUM
ijassa-1406	320	1	[	[	X
ijassa-1406	320	2	1	1	NUM
ijassa-1406	320	3	,	,	PUNCT
ijassa-1406	320	4	example	example	NOUN
ijassa-1406	320	5	3.4	3.4	NUM
ijassa-1406	320	6	]	]	SYM
ijassa-1406	320	7	20	20	NUM
ijassa-1406	320	8	11	11	NUM
ijassa-1406	320	9	18	18	NUM
ijassa-1406	320	10	6	6	NUM
ijassa-1406	320	11	[	[	X
ijassa-1406	320	12	3	3	NUM
ijassa-1406	320	13	,	,	PUNCT
ijassa-1406	320	14	example	example	NOUN
ijassa-1406	320	15	6	6	NUM
ijassa-1406	320	16	]	]	SYM
ijassa-1406	320	17	19	19	NUM
ijassa-1406	320	18	1	1	NUM
ijassa-1406	320	19	1	1	NUM
ijassa-1406	320	20	1	1	NUM
ijassa-1406	321	1	[	[	X
ijassa-1406	321	2	3	3	NUM
ijassa-1406	321	3	,	,	PUNCT
ijassa-1406	321	4	example	example	NOUN
ijassa-1406	321	5	7	7	NUM
ijassa-1406	321	6	]	]	SYM
ijassa-1406	321	7	19	19	NUM
ijassa-1406	321	8	1	1	NUM
ijassa-1406	321	9	1	1	NUM
ijassa-1406	321	10	1	1	NUM
ijassa-1406	322	1	[	[	X
ijassa-1406	322	2	3	3	NUM
ijassa-1406	322	3	,	,	PUNCT
ijassa-1406	322	4	example	example	NOUN
ijassa-1406	322	5	8	8	NUM
ijassa-1406	322	6	]	]	SYM
ijassa-1406	322	7	20	20	NUM
ijassa-1406	322	8	11	11	NUM
ijassa-1406	322	9	18	18	NUM
ijassa-1406	322	10	13	13	NUM
ijassa-1406	323	1	[	[	X
ijassa-1406	323	2	3	3	NUM
ijassa-1406	323	3	,	,	PUNCT
ijassa-1406	323	4	example	example	NOUN
ijassa-1406	323	5	9	9	NUM
ijassa-1406	323	6	]	]	SYM
ijassa-1406	323	7	19	19	NUM
ijassa-1406	323	8	1	1	NUM
ijassa-1406	323	9	1	1	NUM
ijassa-1406	323	10	1	1	NUM
ijassa-1406	324	1	[	[	X
ijassa-1406	324	2	5	5	NUM
ijassa-1406	324	3	,	,	PUNCT
ijassa-1406	324	4	example	example	NOUN
ijassa-1406	324	5	1	1	NUM
ijassa-1406	324	6	]	]	SYM
ijassa-1406	324	7	19	19	NUM
ijassa-1406	324	8	8	8	NUM
ijassa-1406	324	9	17	17	NUM
ijassa-1406	324	10	17	17	NUM
ijassa-1406	324	11	[	[	X
ijassa-1406	324	12	5	5	NUM
ijassa-1406	324	13	,	,	PUNCT
ijassa-1406	324	14	example	example	NOUN
ijassa-1406	324	15	3	3	NUM
ijassa-1406	324	16	]	]	PUNCT
ijassa-1406	324	17	,	,	PUNCT
ijassa-1406	324	18	1	1	NUM
ijassa-1406	324	19	21	21	NUM
ijassa-1406	324	20	16	16	NUM
ijassa-1406	324	21	5	5	NUM
ijassa-1406	324	22	5	5	NUM
ijassa-1406	325	1	[	[	X
ijassa-1406	325	2	5	5	NUM
ijassa-1406	325	3	,	,	PUNCT
ijassa-1406	325	4	example	example	NOUN
ijassa-1406	325	5	3	3	NUM
ijassa-1406	325	6	]	]	PUNCT
ijassa-1406	325	7	,	,	PUNCT
ijassa-1406	325	8	2	2	NUM
ijassa-1406	325	9	19	19	NUM
ijassa-1406	325	10	10	10	NUM
ijassa-1406	325	11	18	18	NUM
ijassa-1406	325	12	18	18	NUM
ijassa-1406	326	1	[	[	SYM
ijassa-1406	326	2	6	6	NUM
ijassa-1406	326	3	,	,	PUNCT
ijassa-1406	326	4	example	example	NOUN
ijassa-1406	326	5	4.2	4.2	NUM
ijassa-1406	326	6	]	]	SYM
ijassa-1406	326	7	19	19	NUM
ijassa-1406	326	8	1	1	NUM
ijassa-1406	326	9	1	1	NUM
ijassa-1406	326	10	1	1	NUM
ijassa-1406	327	1	[	[	X
ijassa-1406	327	2	6	6	NUM
ijassa-1406	327	3	,	,	PUNCT
ijassa-1406	327	4	example	example	NOUN
ijassa-1406	327	5	4.3	4.3	NUM
ijassa-1406	327	6	]	]	SYM
ijassa-1406	327	7	19	19	NUM
ijassa-1406	327	8	9	9	NUM
ijassa-1406	327	9	5	5	NUM
ijassa-1406	327	10	5	5	NUM
ijassa-1406	328	1	[	[	X
ijassa-1406	328	2	12	12	NUM
ijassa-1406	328	3	,	,	PUNCT
ijassa-1406	328	4	example	example	NOUN
ijassa-1406	328	5	3.4	3.4	NUM
ijassa-1406	328	6	]	]	SYM
ijassa-1406	328	7	19	19	NUM
ijassa-1406	328	8	1	1	NUM
ijassa-1406	328	9	1	1	NUM
ijassa-1406	328	10	1	1	NUM
ijassa-1406	329	1	[	[	X
ijassa-1406	329	2	12	12	NUM
ijassa-1406	329	3	,	,	PUNCT
ijassa-1406	329	4	example	example	NOUN
ijassa-1406	329	5	3.5	3.5	NUM
ijassa-1406	329	6	]	]	SYM
ijassa-1406	329	7	20	20	NUM
ijassa-1406	329	8	1	1	NUM
ijassa-1406	329	9	1	1	NUM
ijassa-1406	329	10	1	1	NUM
ijassa-1406	329	11	[	[	X
ijassa-1406	329	12	14	14	NUM
ijassa-1406	329	13	,	,	PUNCT
ijassa-1406	329	14	example	example	NOUN
ijassa-1406	329	15	1	1	NUM
ijassa-1406	329	16	]	]	SYM
ijassa-1406	329	17	19	19	NUM
ijassa-1406	329	18	7	7	NUM
ijassa-1406	329	19	15	15	NUM
ijassa-1406	329	20	4	4	NUM
ijassa-1406	330	1	[	[	X
ijassa-1406	330	2	14	14	NUM
ijassa-1406	330	3	,	,	PUNCT
ijassa-1406	330	4	example	example	NOUN
ijassa-1406	330	5	2	2	NUM
ijassa-1406	330	6	]	]	SYM
ijassa-1406	330	7	19	19	NUM
ijassa-1406	330	8	1	1	NUM
ijassa-1406	330	9	1	1	NUM
ijassa-1406	330	10	1	1	NUM
ijassa-1406	330	11	table	table	NOUN
ijassa-1406	330	12	3.2	3.2	NUM
ijassa-1406	330	13	.	.	PUNCT
ijassa-1406	331	1	single	single	ADJ
ijassa-1406	331	2	runs	run	NOUN
ijassa-1406	331	3	from	from	ADP
ijassa-1406	331	4	“	"	PUNCT
ijassa-1406	331	5	standard	standard	NOUN
ijassa-1406	331	6	”	"	PUNCT
ijassa-1406	331	7	starting	start	VERB
ijassa-1406	331	8	points	point	NOUN
ijassa-1406	331	9	.	.	PUNCT
ijassa-1406	332	1	copyright	copyright	NOUN
ijassa-1406	332	2	©	©	PROPN
ijassa-1406	332	3	2023	2023	NUM
ijassa-1406	332	4	assa	assa	NOUN
ijassa-1406	332	5	.	.	PUNCT
ijassa-1406	333	1	adv	adv	PROPN
ijassa-1406	333	2	syst	syst	PROPN
ijassa-1406	333	3	sci	sci	PROPN
ijassa-1406	333	4	appl	appl	PROPN
ijassa-1406	333	5	(	(	PUNCT
ijassa-1406	333	6	2023	2023	NUM
ijassa-1406	333	7	)	)	PUNCT
ijassa-1406	333	8	newton	newton	PROPN
ijassa-1406	333	9	method	method	NOUN
ijassa-1406	333	10	vs.	vs.	ADP
ijassa-1406	333	11	semismooth	semismooth	NOUN
ijassa-1406	333	12	newton	newton	PROPN
ijassa-1406	333	13	method	method	VERB
ijassa-1406	333	14	29	29	NUM
ijassa-1406	333	15	test	test	NOUN
ijassa-1406	333	16	problems	problem	NOUN
ijassa-1406	333	17	nm	nm	ADP
ijassa-1406	333	18	nm	nm	NOUN
ijassa-1406	333	19	-	-	ADJ
ijassa-1406	333	20	ep	ep	ADJ
ijassa-1406	333	21	snm	snm	PROPN
ijassa-1406	333	22	snm	snm	PROPN
ijassa-1406	333	23	-	-	PUNCT
ijassa-1406	333	24	ep	ep	PROPN
ijassa-1406	333	25	quarp	quarp	NOUN
ijassa-1406	333	26	100/18/5.1e-04	100/18/5.1e-04	NUM
ijassa-1406	333	27	100/16/6.7e-04	100/16/6.7e-04	NUM
ijassa-1406	333	28	100/16/4.9e-04	100/16/4.9e-04	NUM
ijassa-1406	333	29	100/15/6.9e-04	100/15/6.9e-04	NUM
ijassa-1406	334	1	dis61	dis61	NOUN
ijassa-1406	334	2	100/17/1.7e-06	100/17/1.7e-06	NUM
ijassa-1406	334	3	100/9/1.2e-06	100/9/1.2e-06	PROPN
ijassa-1406	334	4	100/15/2.4e-06	100/15/2.4e-06	NUM
ijassa-1406	334	5	100/11/5.9e-09	100/11/5.9e-09	NUM
ijassa-1406	334	6	quarquad	quarquad	NOUN
ijassa-1406	334	7	,	,	PUNCT
ijassa-1406	334	8	1	1	NUM
ijassa-1406	334	9	100/20/6.7e-07	100/20/6.7e-07	NUM
ijassa-1406	334	10	100/13/4.0e-07	100/13/4.0e-07	NUM
ijassa-1406	334	11	100/10/1.7e-13	100/10/1.7e-13	NUM
ijassa-1406	334	12	100/10/1.2e-13	100/10/1.2e-13	NUM
ijassa-1406	334	13	quarquad	quarquad	NOUN
ijassa-1406	334	14	,	,	PUNCT
ijassa-1406	334	15	2	2	NUM
ijassa-1406	334	16	97/20/5.6e-04	97/20/5.6e-04	NUM
ijassa-1406	334	17	97/17/6.2e-04	97/17/6.2e-04	NUM
ijassa-1406	334	18	100/17/5.6e-04	100/17/5.6e-04	NUM
ijassa-1406	334	19	100/16/7.1e-04	100/16/7.1e-04	NUM
ijassa-1406	334	20	affknot1	affknot1	PROPN
ijassa-1406	334	21	100/11/4.9e-06	100/11/4.9e-06	NUM
ijassa-1406	335	1	100/5/2.8e-07	100/5/2.8e-07	PROPN
ijassa-1406	335	2	94/5/5.1e-05	94/5/5.1e-05	NUM
ijassa-1406	335	3	94/5/5.2e-05	94/5/5.2e-05	NUM
ijassa-1406	335	4	affknot2	affknot2	NOUN
ijassa-1406	335	5	100/19/4.5e-06	100/19/4.5e-06	NUM
ijassa-1406	336	1	100/9/5.7e-13	100/9/5.7e-13	NUM
ijassa-1406	336	2	100/5/2.7e-13	100/5/2.7e-13	NUM
ijassa-1406	336	3	100/5/3.3e-13	100/5/3.3e-13	NUM
ijassa-1406	336	4	quadknot	quadknot	PROPN
ijassa-1406	336	5	100/19/2.1e-06	100/19/2.1e-06	NUM
ijassa-1406	336	6	100/9/1.3e-06	100/9/1.3e-06	NOUN
ijassa-1406	336	7	49/17/2.2e-06	49/17/2.2e-06	NUM
ijassa-1406	336	8	68/10/1.3e-07	68/10/1.3e-07	NUM
ijassa-1406	336	9	munson4	munson4	NOUN
ijassa-1406	336	10	100/19/1.7e-06	100/19/1.7e-06	NUM
ijassa-1406	336	11	100/9/1.5e-06	100/9/1.5e-06	NUM
ijassa-1406	336	12	100/18/2.5e-06	100/18/2.5e-06	NUM
ijassa-1406	336	13	100/7/1.4e-06	100/7/1.4e-06	PROPN
ijassa-1406	336	14	dis64	dis64	NOUN
ijassa-1406	336	15	100/19/1.7e-06	100/19/1.7e-06	NUM
ijassa-1406	336	16	100/1/5.8e-17	100/1/5.8e-17	NUM
ijassa-1406	336	17	100/1/2.5e-16	100/1/2.5e-16	NUM
ijassa-1406	336	18	100/1/2.9e-16	100/1/2.9e-16	NUM
ijassa-1406	336	19	ne	ne	PROPN
ijassa-1406	336	20	-	-	ADJ
ijassa-1406	336	21	hard	hard	ADJ
ijassa-1406	336	22	100/22/2.1e-06	100/22/2.1e-06	NUM
ijassa-1406	336	23	100/15/2.4e-07	100/15/2.4e-07	NUM
ijassa-1406	336	24	100/6/5.6e-06	100/6/5.6e-06	PROPN
ijassa-1406	336	25	100/6/7.7e-06	100/6/7.7e-06	NUM
ijassa-1406	336	26	doubleknot	doubleknot	NOUN
ijassa-1406	336	27	88/19/2.6e-06	88/19/2.6e-06	NUM
ijassa-1406	336	28	88/10/6.6e-13	88/10/6.6e-13	NUM
ijassa-1406	336	29	70/5/4.4e-13	70/5/4.4e-13	NUM
ijassa-1406	336	30	71/5/4.3e-13	71/5/4.3e-13	NUM
ijassa-1406	336	31	quad1	quad1	NOUN
ijassa-1406	336	32	100/19/7.2e-05	100/19/7.2e-05	NUM
ijassa-1406	336	33	100/13/7.0e-05	100/13/7.0e-05	NUM
ijassa-1406	336	34	100/16/2.3e-06	100/16/2.3e-06	NUM
ijassa-1406	336	35	100/16/2.2e-06	100/16/2.2e-06	NUM
ijassa-1406	336	36	quad2	quad2	NOUN
ijassa-1406	336	37	100/19/6.3e-05	100/19/6.3e-05	NUM
ijassa-1406	336	38	100/12/7.0e-05	100/12/7.0e-05	NUM
ijassa-1406	336	39	100/16/2.3e-06	100/16/2.3e-06	NUM
ijassa-1406	336	40	100/16/2.2e-06	100/16/2.2e-06	NUM
ijassa-1406	336	41	quarn	quarn	PROPN
ijassa-1406	336	42	100/19/1.0e-04	100/19/1.0e-04	NUM
ijassa-1406	336	43	100/18/7.3e-04	100/18/7.3e-04	NUM
ijassa-1406	336	44	100/19/6.2e-04	100/19/6.2e-04	NOUN
ijassa-1406	336	45	100/18/5.3e-04	100/18/5.3e-04	ADP
ijassa-1406	337	1	[	[	X
ijassa-1406	337	2	1	1	NUM
ijassa-1406	337	3	,	,	PUNCT
ijassa-1406	337	4	example	example	NOUN
ijassa-1406	337	5	3.1	3.1	NUM
ijassa-1406	337	6	]	]	PUNCT
ijassa-1406	337	7	–	–	PUNCT
ijassa-1406	337	8	–	–	PUNCT
ijassa-1406	337	9	–	–	PUNCT
ijassa-1406	337	10	–	–	PUNCT
ijassa-1406	337	11	[	[	X
ijassa-1406	337	12	1	1	NUM
ijassa-1406	337	13	,	,	PUNCT
ijassa-1406	337	14	example	example	NOUN
ijassa-1406	337	15	3.2	3.2	NUM
ijassa-1406	337	16	]	]	PUNCT
ijassa-1406	338	1	50/18/2.3e-06	50/18/2.3e-06	NUM
ijassa-1406	338	2	51/8/8.4e-13	51/8/8.4e-13	NUM
ijassa-1406	338	3	53/4/5.7e-13	53/4/5.7e-13	NUM
ijassa-1406	338	4	50/4/5.5e-13	50/4/5.5e-13	NUM
ijassa-1406	338	5	[	[	X
ijassa-1406	338	6	1	1	NUM
ijassa-1406	338	7	,	,	PUNCT
ijassa-1406	338	8	example	example	NOUN
ijassa-1406	338	9	3.3	3.3	NUM
ijassa-1406	338	10	]	]	PUNCT
ijassa-1406	338	11	,	,	PUNCT
ijassa-1406	338	12	1	1	NUM
ijassa-1406	338	13	100/10/2.8e-06	100/10/2.8e-06	NUM
ijassa-1406	338	14	100/4/3.4e-7	100/4/3.4e-7	NUM
ijassa-1406	338	15	100/7/1.0e-10	100/7/1.0e-10	PRON
ijassa-1406	338	16	100/5/8.9e-07	100/5/8.9e-07	NOUN
ijassa-1406	338	17	[	[	X
ijassa-1406	338	18	1	1	NUM
ijassa-1406	338	19	,	,	PUNCT
ijassa-1406	338	20	example	example	NOUN
ijassa-1406	338	21	3.3	3.3	NUM
ijassa-1406	338	22	]	]	PUNCT
ijassa-1406	338	23	,	,	PUNCT
ijassa-1406	338	24	2	2	NUM
ijassa-1406	338	25	100/5/2.3e-06	100/5/2.3e-06	NOUN
ijassa-1406	338	26	100/2/3.0e-05	100/2/3.0e-05	NUM
ijassa-1406	338	27	100/10/7.3e-06	100/10/7.3e-06	NUM
ijassa-1406	338	28	100/6/8.2e-06	100/6/8.2e-06	NOUN
ijassa-1406	338	29	[	[	X
ijassa-1406	338	30	1	1	NUM
ijassa-1406	338	31	,	,	PUNCT
ijassa-1406	338	32	example	example	NOUN
ijassa-1406	338	33	3.4	3.4	NUM
ijassa-1406	338	34	]	]	SYM
ijassa-1406	338	35	100/17/7.0e-05	100/17/7.0e-05	NUM
ijassa-1406	338	36	100/11/6.0e-05	100/11/6.0e-05	NUM
ijassa-1406	338	37	100/15/3.3e-06	100/15/3.3e-06	NUM
ijassa-1406	338	38	100/7/3.9e-06	100/7/3.9e-06	NUM
ijassa-1406	338	39	[	[	X
ijassa-1406	338	40	3	3	NUM
ijassa-1406	338	41	,	,	PUNCT
ijassa-1406	338	42	example	example	NOUN
ijassa-1406	338	43	6	6	NUM
ijassa-1406	338	44	]	]	SYM
ijassa-1406	338	45	100/19/1.9e-06	100/19/1.9e-06	NUM
ijassa-1406	338	46	100/1/2.2e-16	100/1/2.2e-16	NUM
ijassa-1406	338	47	100/1/1.8e-16	100/1/1.8e-16	NUM
ijassa-1406	338	48	100/1/1.7e-16	100/1/1.7e-16	NUM
ijassa-1406	338	49	[	[	X
ijassa-1406	338	50	3	3	NUM
ijassa-1406	338	51	,	,	PUNCT
ijassa-1406	338	52	example	example	NOUN
ijassa-1406	338	53	7	7	NUM
ijassa-1406	338	54	]	]	SYM
ijassa-1406	338	55	100/18/2.8e-06	100/18/2.8e-06	NUM
ijassa-1406	338	56	100/1/2.7e-16	100/1/2.7e-16	NUM
ijassa-1406	338	57	100/1/2.1e-16	100/1/2.1e-16	PROPN
ijassa-1406	338	58	100/1/2.0e-16	100/1/2.0e-16	PROPN
ijassa-1406	338	59	[	[	X
ijassa-1406	338	60	3	3	NUM
ijassa-1406	338	61	,	,	PUNCT
ijassa-1406	338	62	example	example	NOUN
ijassa-1406	338	63	8	8	NUM
ijassa-1406	338	64	]	]	SYM
ijassa-1406	338	65	100/17/1.9e-06	100/17/1.9e-06	NUM
ijassa-1406	338	66	100/8/1.3e-06	100/8/1.3e-06	NUM
ijassa-1406	338	67	100/15/2.5e-06	100/15/2.5e-06	NUM
ijassa-1406	338	68	100/11/2.2e-12	100/11/2.2e-12	NOUN
ijassa-1406	338	69	[	[	X
ijassa-1406	338	70	3	3	NUM
ijassa-1406	338	71	,	,	PUNCT
ijassa-1406	338	72	example	example	NOUN
ijassa-1406	338	73	9	9	NUM
ijassa-1406	338	74	]	]	PUNCT
ijassa-1406	338	75	100/19/2.2e-06	100/19/2.2e-06	NUM
ijassa-1406	338	76	100/1/6.0e-16	100/1/6.0e-16	NUM
ijassa-1406	338	77	100/1/1.7e-16	100/1/1.7e-16	NUM
ijassa-1406	338	78	100/1/1.7e-16	100/1/1.7e-16	NUM
ijassa-1406	338	79	[	[	X
ijassa-1406	338	80	5	5	NUM
ijassa-1406	338	81	,	,	PUNCT
ijassa-1406	338	82	example	example	NOUN
ijassa-1406	338	83	1	1	NUM
ijassa-1406	338	84	]	]	PUNCT
ijassa-1406	338	85	100/19/7.2e-05	100/19/7.2e-05	NUM
ijassa-1406	338	86	100/12/7.0e-05	100/12/7.0e-05	NUM
ijassa-1406	338	87	100/16/2.3e-06	100/16/2.3e-06	NUM
ijassa-1406	338	88	100/16/2.2e-06	100/16/2.2e-06	NUM
ijassa-1406	338	89	[	[	X
ijassa-1406	338	90	5	5	NUM
ijassa-1406	338	91	,	,	PUNCT
ijassa-1406	338	92	example	example	NOUN
ijassa-1406	338	93	3	3	NUM
ijassa-1406	338	94	]	]	PUNCT
ijassa-1406	338	95	,	,	PUNCT
ijassa-1406	338	96	1	1	NUM
ijassa-1406	338	97	100/19/6.9e-05	100/19/6.9e-05	NUM
ijassa-1406	338	98	100/13/3.8e-09	100/13/3.8e-09	NUM
ijassa-1406	338	99	100/10/4.3e-13	100/10/4.3e-13	NUM
ijassa-1406	338	100	100/10/5.4e-13	100/10/5.4e-13	NUM
ijassa-1406	339	1	[	[	X
ijassa-1406	339	2	5	5	NUM
ijassa-1406	339	3	,	,	PUNCT
ijassa-1406	339	4	example	example	NOUN
ijassa-1406	339	5	3	3	NUM
ijassa-1406	339	6	]	]	PUNCT
ijassa-1406	339	7	,	,	PUNCT
ijassa-1406	339	8	2	2	NUM
ijassa-1406	339	9	100/19/6.9e-05	100/19/6.9e-05	NUM
ijassa-1406	339	10	100/13/6.2e-05	100/13/6.2e-05	NUM
ijassa-1406	339	11	100/15/2.2e-06	100/15/2.2e-06	NUM
ijassa-1406	339	12	100/15/2.2e-06	100/15/2.2e-06	NUM
ijassa-1406	340	1	[	[	X
ijassa-1406	340	2	6	6	NUM
ijassa-1406	340	3	,	,	PUNCT
ijassa-1406	340	4	example	example	NOUN
ijassa-1406	340	5	4.2	4.2	NUM
ijassa-1406	340	6	]	]	PUNCT
ijassa-1406	340	7	100/18/2.1e-06	100/18/2.1e-06	NUM
ijassa-1406	340	8	100/1/1.4e-16	100/1/1.4e-16	NUM
ijassa-1406	340	9	100/1/6.5e-15	100/1/6.5e-15	NUM
ijassa-1406	340	10	100/1/7.4e-15	100/1/7.4e-15	NUM
ijassa-1406	341	1	[	[	X
ijassa-1406	341	2	6	6	NUM
ijassa-1406	341	3	,	,	PUNCT
ijassa-1406	341	4	example	example	NOUN
ijassa-1406	341	5	4.3	4.3	NUM
ijassa-1406	341	6	]	]	PUNCT
ijassa-1406	341	7	100/19/1.6e-06	100/19/1.6e-06	NUM
ijassa-1406	342	1	100/8/1.3e-10	100/8/1.3e-10	NUM
ijassa-1406	342	2	100/5/5.3e-13	100/5/5.3e-13	NUM
ijassa-1406	342	3	100/5/4.7e-13	100/5/4.7e-13	NUM
ijassa-1406	342	4	[	[	X
ijassa-1406	342	5	12	12	NUM
ijassa-1406	342	6	,	,	PUNCT
ijassa-1406	342	7	example	example	NOUN
ijassa-1406	342	8	3.4	3.4	NUM
ijassa-1406	342	9	]	]	PUNCT
ijassa-1406	342	10	100/18/1.6e-06	100/18/1.6e-06	NUM
ijassa-1406	342	11	100/1/6.3e-18	100/1/6.3e-18	NUM
ijassa-1406	342	12	100/1/6.6e-17	100/1/6.6e-17	NUM
ijassa-1406	342	13	100/1/6.6e-17	100/1/6.6e-17	NUM
ijassa-1406	343	1	[	[	X
ijassa-1406	343	2	12	12	NUM
ijassa-1406	343	3	,	,	PUNCT
ijassa-1406	343	4	example	example	NOUN
ijassa-1406	343	5	3.5	3.5	NUM
ijassa-1406	343	6	]	]	PUNCT
ijassa-1406	343	7	100/19/1.6e-06	100/19/1.6e-06	NUM
ijassa-1406	344	1	100/1/8.4e-16	100/1/8.4e-16	NUM
ijassa-1406	344	2	100/1/3.5e-15	100/1/3.5e-15	NUM
ijassa-1406	344	3	100/1/3.6e-15	100/1/3.6e-15	PROPN
ijassa-1406	344	4	[	[	X
ijassa-1406	344	5	14	14	NUM
ijassa-1406	344	6	,	,	PUNCT
ijassa-1406	344	7	example	example	NOUN
ijassa-1406	344	8	1	1	NUM
ijassa-1406	344	9	]	]	SYM
ijassa-1406	344	10	100/19/1.7e-06	100/19/1.7e-06	NUM
ijassa-1406	344	11	100/9/1.2e-06	100/9/1.2e-06	NUM
ijassa-1406	344	12	100/18/2.3e-06	100/18/2.3e-06	NUM
ijassa-1406	344	13	100/6/1.3e-06	100/6/1.3e-06	NUM
ijassa-1406	344	14	[	[	X
ijassa-1406	344	15	14	14	NUM
ijassa-1406	344	16	,	,	PUNCT
ijassa-1406	344	17	example	example	NOUN
ijassa-1406	344	18	2	2	NUM
ijassa-1406	344	19	]	]	PUNCT
ijassa-1406	344	20	100/18/2.0e-06	100/18/2.0e-06	NUM
ijassa-1406	344	21	100/1/7.2e-16	100/1/7.2e-16	NUM
ijassa-1406	344	22	100/1/9.5e-16	100/1/9.5e-16	NUM
ijassa-1406	344	23	100/1/5.3e-16	100/1/5.3e-16	PROPN
ijassa-1406	344	24	table	table	NOUN
ijassa-1406	344	25	3.3	3.3	NUM
ijassa-1406	344	26	.	.	PUNCT
ijassa-1406	345	1	multiple	multiple	ADJ
ijassa-1406	345	2	runs	run	NOUN
ijassa-1406	345	3	from	from	ADP
ijassa-1406	345	4	random	random	ADJ
ijassa-1406	345	5	starting	starting	NOUN
ijassa-1406	345	6	points	point	NOUN
ijassa-1406	345	7	.	.	PUNCT
ijassa-1406	346	1	copyright	copyright	NOUN
ijassa-1406	346	2	©	©	PROPN
ijassa-1406	346	3	2023	2023	NUM
ijassa-1406	346	4	assa	assa	NOUN
ijassa-1406	346	5	.	.	PUNCT
ijassa-1406	347	1	adv	adv	PROPN
ijassa-1406	347	2	syst	syst	PROPN
ijassa-1406	347	3	sci	sci	PROPN
ijassa-1406	347	4	appl	appl	PROPN
ijassa-1406	347	5	(	(	PUNCT
ijassa-1406	347	6	2023	2023	NUM
ijassa-1406	347	7	)	)	PUNCT
ijassa-1406	347	8	introduction	introduction	NOUN
ijassa-1406	347	9	smooth	smooth	ADJ
ijassa-1406	347	10	complementarity	complementarity	NOUN
ijassa-1406	347	11	function	function	NOUN
ijassa-1406	347	12	and	and	CCONJ
ijassa-1406	347	13	newton	newton	PROPN
ijassa-1406	347	14	method	method	PROPN
ijassa-1406	347	15	fischer	fischer	PROPN
ijassa-1406	347	16	–	–	PUNCT
ijassa-1406	347	17	burmeister	burmeister	NOUN
ijassa-1406	347	18	complementarity	complementarity	NOUN
ijassa-1406	347	19	function	function	NOUN
ijassa-1406	347	20	and	and	CCONJ
ijassa-1406	347	21	semismooth	semismooth	NOUN
ijassa-1406	347	22	newton	newton	PROPN
ijassa-1406	347	23	method	method	PROPN
ijassa-1406	347	24	numerical	numerical	PROPN
ijassa-1406	347	25	results	result	NOUN
ijassa-1406	347	26	concluding	conclude	VERB
ijassa-1406	347	27	remarks	remark	NOUN