id	sid	tid	token	lemma	pos
ijassa-1639	1	1	adv	adv	PROPN
ijassa-1639	1	2	syst	syst	PROPN
ijassa-1639	1	3	sci	sci	PROPN
ijassa-1639	1	4	appl	appl	PROPN
ijassa-1639	1	5	2024	2024	NUM
ijassa-1639	1	6	;	;	PUNCT
ijassa-1639	1	7	02:19–31	02:19–31	NUM
ijassa-1639	1	8	published	publish	VERB
ijassa-1639	1	9	online	online	ADV
ijassa-1639	1	10	at	at	ADP
ijassa-1639	1	11	https://ijassa.ipu.ru	https://ijassa.ipu.ru	ADV
ijassa-1639	1	12	.	.	PUNCT
ijassa-1639	2	1	piecewise	piecewise	PROPN
ijassa-1639	2	2	levenberg	levenberg	PROPN
ijassa-1639	2	3	–	–	PUNCT
ijassa-1639	2	4	marquardt	marquardt	PROPN
ijassa-1639	2	5	method	method	NOUN
ijassa-1639	2	6	for	for	ADP
ijassa-1639	2	7	generalized	generalized	ADJ
ijassa-1639	2	8	nash	nash	PROPN
ijassa-1639	2	9	equilibrium	equilibrium	NOUN
ijassa-1639	2	10	problems	problem	NOUN
ijassa-1639	2	11	alexey	alexey	PROPN
ijassa-1639	2	12	izmailov1	izmailov1	PROPN
ijassa-1639	2	13	*	*	PROPN
ijassa-1639	2	14	,	,	PUNCT
ijassa-1639	2	15	evgeniy	evgeniy	ADJ
ijassa-1639	2	16	uskov2	uskov2	PROPN
ijassa-1639	2	17	,	,	PUNCT
ijassa-1639	2	18	yan	yan	PROPN
ijassa-1639	2	19	zhibai1	zhibai1	PROPN
ijassa-1639	3	1	1lomonosov	1lomonosov	NUM
ijassa-1639	3	2	moscow	moscow	PROPN
ijassa-1639	3	3	state	state	PROPN
ijassa-1639	3	4	university	university	PROPN
ijassa-1639	3	5	,	,	PUNCT
ijassa-1639	3	6	moscow	moscow	PROPN
ijassa-1639	3	7	,	,	PUNCT
ijassa-1639	3	8	russia	russia	PROPN
ijassa-1639	3	9	2	2	NUM
ijassa-1639	3	10	derzhavin	derzhavin	PROPN
ijassa-1639	3	11	tambov	tambov	PROPN
ijassa-1639	3	12	state	state	PROPN
ijassa-1639	3	13	university	university	PROPN
ijassa-1639	3	14	,	,	PUNCT
ijassa-1639	3	15	tambov	tambov	PROPN
ijassa-1639	3	16	,	,	PUNCT
ijassa-1639	3	17	russia	russia	PROPN
ijassa-1639	3	18	abstract	abstract	NOUN
ijassa-1639	3	19	:	:	PUNCT
ijassa-1639	3	20	we	we	PRON
ijassa-1639	3	21	consider	consider	VERB
ijassa-1639	3	22	the	the	DET
ijassa-1639	3	23	constrained	constrain	VERB
ijassa-1639	3	24	piecewise	piecewise	NOUN
ijassa-1639	3	25	levenberg	levenberg	PROPN
ijassa-1639	3	26	–	–	PUNCT
ijassa-1639	3	27	marquardt	marquardt	PROPN
ijassa-1639	3	28	method	method	NOUN
ijassa-1639	3	29	globalized	globalize	VERB
ijassa-1639	3	30	by	by	ADP
ijassa-1639	3	31	linesearch	linesearch	NOUN
ijassa-1639	3	32	,	,	PUNCT
ijassa-1639	3	33	and	and	CCONJ
ijassa-1639	3	34	apply	apply	VERB
ijassa-1639	3	35	it	it	PRON
ijassa-1639	3	36	to	to	ADP
ijassa-1639	3	37	“	"	PUNCT
ijassa-1639	3	38	min	min	ADJ
ijassa-1639	3	39	”	"	PUNCT
ijassa-1639	3	40	reformulations	reformulation	NOUN
ijassa-1639	3	41	of	of	ADP
ijassa-1639	3	42	the	the	DET
ijassa-1639	3	43	optimality	optimality	NOUN
ijassa-1639	3	44	systems	system	NOUN
ijassa-1639	3	45	for	for	ADP
ijassa-1639	3	46	generalized	generalized	ADJ
ijassa-1639	3	47	nash	nash	PROPN
ijassa-1639	3	48	equilibrium	equilibrium	NOUN
ijassa-1639	3	49	problems	problem	NOUN
ijassa-1639	3	50	.	.	PUNCT
ijassa-1639	4	1	numerical	numerical	ADJ
ijassa-1639	4	2	comparison	comparison	NOUN
ijassa-1639	4	3	of	of	ADP
ijassa-1639	4	4	the	the	DET
ijassa-1639	4	5	performance	performance	NOUN
ijassa-1639	4	6	of	of	ADP
ijassa-1639	4	7	this	this	DET
ijassa-1639	4	8	method	method	NOUN
ijassa-1639	4	9	with	with	ADP
ijassa-1639	4	10	some	some	DET
ijassa-1639	4	11	relevant	relevant	ADJ
ijassa-1639	4	12	existing	exist	VERB
ijassa-1639	4	13	alternatives	alternative	NOUN
ijassa-1639	4	14	is	be	AUX
ijassa-1639	4	15	provided	provide	VERB
ijassa-1639	4	16	.	.	PUNCT
ijassa-1639	5	1	keywords	keyword	NOUN
ijassa-1639	5	2	:	:	PUNCT
ijassa-1639	5	3	generalized	generalize	VERB
ijassa-1639	5	4	nash	nash	PROPN
ijassa-1639	5	5	equilibrium	equilibrium	PROPN
ijassa-1639	5	6	problem	problem	NOUN
ijassa-1639	5	7	,	,	PUNCT
ijassa-1639	5	8	piecewise	piecewise	NOUN
ijassa-1639	5	9	smooth	smooth	ADJ
ijassa-1639	5	10	equation	equation	NOUN
ijassa-1639	5	11	,	,	PUNCT
ijassa-1639	5	12	constrained	constrain	VERB
ijassa-1639	5	13	equation	equation	NOUN
ijassa-1639	5	14	,	,	PUNCT
ijassa-1639	5	15	levenberg	levenberg	PROPN
ijassa-1639	5	16	–	–	PUNCT
ijassa-1639	5	17	marquardt	marquardt	PROPN
ijassa-1639	5	18	method	method	NOUN
ijassa-1639	5	19	,	,	PUNCT
ijassa-1639	5	20	lp	lp	PROPN
ijassa-1639	5	21	-	-	PUNCT
ijassa-1639	5	22	newton	newton	PROPN
ijassa-1639	5	23	method	method	NOUN
ijassa-1639	5	24	,	,	PUNCT
ijassa-1639	5	25	globalization	globalization	NOUN
ijassa-1639	5	26	of	of	ADP
ijassa-1639	5	27	convergence	convergence	NOUN
ijassa-1639	5	28	1	1	NUM
ijassa-1639	5	29	.	.	PUNCT
ijassa-1639	6	1	introduction	introduction	NOUN
ijassa-1639	6	2	this	this	DET
ijassa-1639	6	3	paper	paper	NOUN
ijassa-1639	6	4	aims	aim	VERB
ijassa-1639	6	5	at	at	ADP
ijassa-1639	6	6	application	application	NOUN
ijassa-1639	6	7	of	of	ADP
ijassa-1639	6	8	the	the	DET
ijassa-1639	6	9	globalized	globalize	VERB
ijassa-1639	6	10	constrained	constrain	VERB
ijassa-1639	6	11	piecewise	piecewise	NOUN
ijassa-1639	6	12	levenberg	levenberg	PROPN
ijassa-1639	6	13	–	–	PUNCT
ijassa-1639	6	14	marquardt	marquardt	PROPN
ijassa-1639	6	15	method	method	NOUN
ijassa-1639	6	16	developed	develop	VERB
ijassa-1639	6	17	in	in	ADP
ijassa-1639	6	18	[	[	X
ijassa-1639	6	19	24	24	NUM
ijassa-1639	6	20	]	]	PUNCT
ijassa-1639	6	21	to	to	ADP
ijassa-1639	6	22	“	"	PUNCT
ijassa-1639	6	23	min	min	NOUN
ijassa-1639	6	24	”	"	PUNCT
ijassa-1639	6	25	reformulations	reformulation	NOUN
ijassa-1639	6	26	of	of	ADP
ijassa-1639	6	27	the	the	DET
ijassa-1639	6	28	optimality	optimality	NOUN
ijassa-1639	6	29	systems	system	NOUN
ijassa-1639	6	30	for	for	ADP
ijassa-1639	6	31	generalized	generalized	ADJ
ijassa-1639	6	32	nash	nash	PROPN
ijassa-1639	6	33	equilibrium	equilibrium	NOUN
ijassa-1639	6	34	problems	problem	NOUN
ijassa-1639	6	35	(	(	PUNCT
ijassa-1639	6	36	gnep	gnep	NOUN
ijassa-1639	6	37	)	)	PUNCT
ijassa-1639	6	38	,	,	PUNCT
ijassa-1639	6	39	and	and	CCONJ
ijassa-1639	6	40	comparison	comparison	NOUN
ijassa-1639	6	41	with	with	ADP
ijassa-1639	6	42	the	the	DET
ijassa-1639	6	43	existing	exist	VERB
ijassa-1639	6	44	alternatives	alternative	NOUN
ijassa-1639	6	45	.	.	PUNCT
ijassa-1639	7	1	in	in	ADP
ijassa-1639	7	2	section	section	NOUN
ijassa-1639	7	3	2	2	NUM
ijassa-1639	7	4	,	,	PUNCT
ijassa-1639	7	5	we	we	PRON
ijassa-1639	7	6	recall	recall	VERB
ijassa-1639	7	7	the	the	DET
ijassa-1639	7	8	statement	statement	NOUN
ijassa-1639	7	9	of	of	ADP
ijassa-1639	7	10	a	a	DET
ijassa-1639	7	11	gnep	gnep	NOUN
ijassa-1639	7	12	and	and	CCONJ
ijassa-1639	7	13	the	the	DET
ijassa-1639	7	14	related	related	ADJ
ijassa-1639	7	15	first	first	ADJ
ijassa-1639	7	16	-	-	PUNCT
ijassa-1639	7	17	order	order	NOUN
ijassa-1639	7	18	optimality	optimality	NOUN
ijassa-1639	7	19	system	system	NOUN
ijassa-1639	7	20	,	,	PUNCT
ijassa-1639	7	21	and	and	CCONJ
ijassa-1639	7	22	we	we	PRON
ijassa-1639	7	23	discuss	discuss	VERB
ijassa-1639	7	24	some	some	DET
ijassa-1639	7	25	possible	possible	ADJ
ijassa-1639	7	26	equivalent	equivalent	ADJ
ijassa-1639	7	27	reformulations	reformulation	NOUN
ijassa-1639	7	28	of	of	ADP
ijassa-1639	7	29	the	the	DET
ijassa-1639	7	30	latter	latter	ADJ
ijassa-1639	7	31	as	as	ADP
ijassa-1639	7	32	constrained	constrain	VERB
ijassa-1639	7	33	systems	system	NOUN
ijassa-1639	7	34	of	of	ADP
ijassa-1639	7	35	equations	equation	NOUN
ijassa-1639	7	36	.	.	PUNCT
ijassa-1639	8	1	section	section	NOUN
ijassa-1639	8	2	3	3	NUM
ijassa-1639	8	3	discusses	discuss	VERB
ijassa-1639	8	4	the	the	DET
ijassa-1639	8	5	levenberg	levenberg	PROPN
ijassa-1639	8	6	–	–	PUNCT
ijassa-1639	8	7	marquardt	marquardt	PROPN
ijassa-1639	8	8	method	method	NOUN
ijassa-1639	8	9	for	for	ADP
ijassa-1639	8	10	piecewise	piecewise	NOUN
ijassa-1639	8	11	smooth	smooth	ADJ
ijassa-1639	8	12	equations	equation	NOUN
ijassa-1639	8	13	,	,	PUNCT
ijassa-1639	8	14	its	its	PRON
ijassa-1639	8	15	linesearch	linesearch	NOUN
ijassa-1639	8	16	-	-	PUNCT
ijassa-1639	8	17	based	base	VERB
ijassa-1639	8	18	globalization	globalization	NOUN
ijassa-1639	8	19	,	,	PUNCT
ijassa-1639	8	20	and	and	CCONJ
ijassa-1639	8	21	the	the	DET
ijassa-1639	8	22	related	relate	VERB
ijassa-1639	8	23	global	global	ADJ
ijassa-1639	8	24	convergence	convergence	NOUN
ijassa-1639	8	25	and	and	CCONJ
ijassa-1639	8	26	superlinear	superlinear	NOUN
ijassa-1639	8	27	rate	rate	NOUN
ijassa-1639	8	28	of	of	ADP
ijassa-1639	8	29	convergence	convergence	NOUN
ijassa-1639	8	30	theory	theory	NOUN
ijassa-1639	8	31	.	.	PUNCT
ijassa-1639	9	1	finally	finally	ADV
ijassa-1639	9	2	,	,	PUNCT
ijassa-1639	9	3	in	in	ADP
ijassa-1639	9	4	section	section	NOUN
ijassa-1639	9	5	4	4	NUM
ijassa-1639	9	6	,	,	PUNCT
ijassa-1639	9	7	we	we	PRON
ijassa-1639	9	8	apply	apply	VERB
ijassa-1639	9	9	this	this	DET
ijassa-1639	9	10	method	method	NOUN
ijassa-1639	9	11	to	to	ADP
ijassa-1639	9	12	the	the	DET
ijassa-1639	9	13	piecewise	piecewise	NOUN
ijassa-1639	9	14	smooth	smooth	ADJ
ijassa-1639	9	15	reformulation	reformulation	NOUN
ijassa-1639	9	16	of	of	ADP
ijassa-1639	9	17	the	the	DET
ijassa-1639	9	18	first	first	ADJ
ijassa-1639	9	19	-	-	PUNCT
ijassa-1639	9	20	order	order	NOUN
ijassa-1639	9	21	optimality	optimality	NOUN
ijassa-1639	9	22	system	system	NOUN
ijassa-1639	9	23	for	for	ADP
ijassa-1639	9	24	gnep	gnep	NOUN
ijassa-1639	9	25	,	,	PUNCT
ijassa-1639	9	26	and	and	CCONJ
ijassa-1639	9	27	compare	compare	VERB
ijassa-1639	9	28	this	this	DET
ijassa-1639	9	29	algorithm	algorithm	NOUN
ijassa-1639	9	30	with	with	ADP
ijassa-1639	9	31	the	the	DET
ijassa-1639	9	32	usual	usual	ADJ
ijassa-1639	9	33	levenberg	levenberg	PROPN
ijassa-1639	9	34	–	–	PUNCT
ijassa-1639	9	35	marquardt	marquardt	PROPN
ijassa-1639	9	36	method	method	NOUN
ijassa-1639	9	37	for	for	ADP
ijassa-1639	9	38	a	a	DET
ijassa-1639	9	39	smooth	smooth	ADJ
ijassa-1639	9	40	constrained	constrain	VERB
ijassa-1639	9	41	reformulation	reformulation	NOUN
ijassa-1639	9	42	,	,	PUNCT
ijassa-1639	9	43	and	and	CCONJ
ijassa-1639	9	44	with	with	ADP
ijassa-1639	9	45	the	the	DET
ijassa-1639	9	46	corresponding	correspond	VERB
ijassa-1639	9	47	two	two	NUM
ijassa-1639	9	48	versions	version	NOUN
ijassa-1639	9	49	of	of	ADP
ijassa-1639	9	50	the	the	DET
ijassa-1639	9	51	lp	lp	PROPN
ijassa-1639	9	52	-	-	PUNCT
ijassa-1639	9	53	newton	newton	PROPN
ijassa-1639	9	54	method	method	NOUN
ijassa-1639	9	55	[	[	X
ijassa-1639	9	56	7	7	X
ijassa-1639	9	57	]	]	PUNCT
ijassa-1639	9	58	globalized	globalize	VERB
ijassa-1639	9	59	according	accord	VERB
ijassa-1639	9	60	to	to	ADP
ijassa-1639	9	61	[	[	X
ijassa-1639	9	62	13	13	NUM
ijassa-1639	9	63	]	]	PUNCT
ijassa-1639	9	64	.	.	PUNCT
ijassa-1639	10	1	some	some	DET
ijassa-1639	10	2	words	word	NOUN
ijassa-1639	10	3	about	about	ADP
ijassa-1639	10	4	our	our	PRON
ijassa-1639	10	5	notation	notation	NOUN
ijassa-1639	10	6	and	and	CCONJ
ijassa-1639	10	7	blanket	blanket	NOUN
ijassa-1639	10	8	arrangements	arrangement	NOUN
ijassa-1639	10	9	are	be	AUX
ijassa-1639	10	10	in	in	ADP
ijassa-1639	10	11	order	order	NOUN
ijassa-1639	10	12	.	.	PUNCT
ijassa-1639	11	1	let	let	VERB
ijassa-1639	11	2	all	all	DET
ijassa-1639	11	3	the	the	DET
ijassa-1639	11	4	norms	norm	NOUN
ijassa-1639	11	5	be	be	VERB
ijassa-1639	11	6	euclidian	euclidian	ADJ
ijassa-1639	11	7	,	,	PUNCT
ijassa-1639	11	8	unless	unless	SCONJ
ijassa-1639	11	9	something	something	PRON
ijassa-1639	11	10	different	different	ADJ
ijassa-1639	11	11	is	be	AUX
ijassa-1639	11	12	explicitly	explicitly	ADV
ijassa-1639	11	13	specified	specify	VERB
ijassa-1639	11	14	.	.	PUNCT
ijassa-1639	12	1	for	for	ADP
ijassa-1639	12	2	a	a	DET
ijassa-1639	12	3	given	give	VERB
ijassa-1639	12	4	y	y	PROPN
ijassa-1639	12	5	∈	∈	PROPN
ijassa-1639	12	6	rm	rm	NOUN
ijassa-1639	12	7	and	and	CCONJ
ijassa-1639	12	8	an	an	DET
ijassa-1639	12	9	index	index	NOUN
ijassa-1639	12	10	set	set	VERB
ijassa-1639	12	11	i	i	PRON
ijassa-1639	12	12	⊂	⊂	X
ijassa-1639	12	13	{	{	PUNCT
ijassa-1639	12	14	1	1	NUM
ijassa-1639	12	15	,	,	PUNCT
ijassa-1639	12	16	.	.	PUNCT
ijassa-1639	12	17	.	.	PUNCT
ijassa-1639	12	18	.	.	PUNCT
ijassa-1639	13	1	,	,	PUNCT
ijassa-1639	13	2	m	m	VERB
ijassa-1639	13	3	}	}	PUNCT
ijassa-1639	13	4	,	,	PUNCT
ijassa-1639	13	5	we	we	PRON
ijassa-1639	13	6	denote	denote	VERB
ijassa-1639	13	7	by	by	ADP
ijassa-1639	13	8	yi	yi	PROPN
ijassa-1639	13	9	the	the	DET
ijassa-1639	13	10	subvector	subvector	NOUN
ijassa-1639	13	11	of	of	ADP
ijassa-1639	13	12	y	y	PROPN
ijassa-1639	13	13	with	with	ADP
ijassa-1639	13	14	the	the	DET
ijassa-1639	13	15	components	component	NOUN
ijassa-1639	13	16	yi	yi	PROPN
ijassa-1639	13	17	,	,	PUNCT
ijassa-1639	13	18	i	i	PRON
ijassa-1639	13	19	∈	∈	VERB
ijassa-1639	14	1	i	i	PRON
ijassa-1639	14	2	.	.	PUNCT
ijassa-1639	15	1	for	for	ADP
ijassa-1639	15	2	a	a	DET
ijassa-1639	15	3	sequence	sequence	NOUN
ijassa-1639	15	4	{	{	PUNCT
ijassa-1639	15	5	uk	uk	PROPN
ijassa-1639	15	6	}	}	PUNCT
ijassa-1639	15	7	⊂	⊂	PROPN
ijassa-1639	15	8	rp	rp	NOUN
ijassa-1639	15	9	convergent	convergent	NOUN
ijassa-1639	15	10	to	to	ADP
ijassa-1639	15	11	some	some	DET
ijassa-1639	15	12	u∗	u∗	PROPN
ijassa-1639	15	13	∈	∈	PROPN
ijassa-1639	15	14	rp	rp	NOUN
ijassa-1639	15	15	,	,	PUNCT
ijassa-1639	15	16	the	the	DET
ijassa-1639	15	17	rate	rate	NOUN
ijassa-1639	15	18	of	of	ADP
ijassa-1639	15	19	convergence	convergence	NOUN
ijassa-1639	15	20	is	be	AUX
ijassa-1639	15	21	referred	refer	VERB
ijassa-1639	15	22	to	to	ADP
ijassa-1639	15	23	as	as	ADP
ijassa-1639	15	24	superlinear	superlinear	NOUN
ijassa-1639	15	25	with	with	ADP
ijassa-1639	15	26	q	q	NOUN
ijassa-1639	15	27	-	-	PUNCT
ijassa-1639	15	28	order	order	NOUN
ijassa-1639	15	29	ν	ν	X
ijassa-1639	15	30	>	>	X
ijassa-1639	15	31	1	1	NUM
ijassa-1639	15	32	if	if	SCONJ
ijassa-1639	15	33	there	there	PRON
ijassa-1639	15	34	exists	exist	VERB
ijassa-1639	15	35	c	c	NOUN
ijassa-1639	15	36	>	>	X
ijassa-1639	15	37	0	0	NUM
ijassa-1639	15	38	such	such	ADJ
ijassa-1639	15	39	that	that	PRON
ijassa-1639	15	40	∥uk+1	∥uk+1	VERB
ijassa-1639	15	41	−	−	PROPN
ijassa-1639	15	42	u∗∥	u∗∥	NOUN
ijassa-1639	15	43	≤	≤	NOUN
ijassa-1639	15	44	c∥uk	c∥uk	PROPN
ijassa-1639	15	45	−	−	PROPN
ijassa-1639	15	46	u∗∥ν	u∗∥ν	NOUN
ijassa-1639	15	47	for	for	ADP
ijassa-1639	15	48	all	all	DET
ijassa-1639	15	49	k	k	NOUN
ijassa-1639	15	50	large	large	ADJ
ijassa-1639	15	51	enough	enough	ADV
ijassa-1639	15	52	.	.	PUNCT
ijassa-1639	16	1	∗corresponding	∗corresponde	VERB
ijassa-1639	16	2	author	author	NOUN
ijassa-1639	16	3	:	:	PUNCT
ijassa-1639	16	4	izmaf@cs.msu.ru	izmaf@cs.msu.ru	ADJ
ijassa-1639	16	5	20	20	NUM
ijassa-1639	16	6	a.	a.	NOUN
ijassa-1639	16	7	f.	f.	PROPN
ijassa-1639	16	8	izmailov	izmailov	PROPN
ijassa-1639	16	9	,	,	PUNCT
ijassa-1639	16	10	e.	e.	PROPN
ijassa-1639	16	11	i.	i.	PROPN
ijassa-1639	16	12	uskov	uskov	PROPN
ijassa-1639	16	13	,	,	PUNCT
ijassa-1639	16	14	yan	yan	PROPN
ijassa-1639	16	15	zhibai	zhibai	PROPN
ijassa-1639	16	16	2	2	NUM
ijassa-1639	16	17	.	.	PUNCT
ijassa-1639	16	18	generalized	generalize	VERB
ijassa-1639	16	19	nash	nash	PROPN
ijassa-1639	16	20	equilibrium	equilibrium	PROPN
ijassa-1639	16	21	problem	problem	NOUN
ijassa-1639	16	22	and	and	CCONJ
ijassa-1639	16	23	related	relate	VERB
ijassa-1639	16	24	constrained	constrain	VERB
ijassa-1639	16	25	equations	equation	NOUN
ijassa-1639	16	26	in	in	ADP
ijassa-1639	16	27	a	a	DET
ijassa-1639	16	28	gnep	gnep	NOUN
ijassa-1639	16	29	,	,	PUNCT
ijassa-1639	16	30	n	n	PRON
ijassa-1639	16	31	players	player	NOUN
ijassa-1639	16	32	are	be	AUX
ijassa-1639	16	33	involved	involve	VERB
ijassa-1639	16	34	,	,	PUNCT
ijassa-1639	16	35	and	and	CCONJ
ijassa-1639	16	36	each	each	DET
ijassa-1639	16	37	player	player	NOUN
ijassa-1639	16	38	indexed	index	VERB
ijassa-1639	16	39	by	by	ADP
ijassa-1639	16	40	ν	ν	NOUN
ijassa-1639	16	41	∈	∈	PROPN
ijassa-1639	16	42	{	{	PUNCT
ijassa-1639	16	43	1	1	NUM
ijassa-1639	16	44	,	,	PUNCT
ijassa-1639	16	45	.	.	PUNCT
ijassa-1639	16	46	.	.	PUNCT
ijassa-1639	17	1	.	.	PUNCT
ijassa-1639	18	1	,	,	PUNCT
ijassa-1639	18	2	n	n	CCONJ
ijassa-1639	18	3	}	}	PUNCT
ijassa-1639	18	4	controls	control	VERB
ijassa-1639	18	5	the	the	DET
ijassa-1639	18	6	variable	variable	NOUN
ijassa-1639	18	7	xν	xν	PROPN
ijassa-1639	18	8	∈	∈	PROPN
ijassa-1639	18	9	rnν	rnν	NOUN
ijassa-1639	18	10	,	,	PUNCT
ijassa-1639	18	11	and	and	CCONJ
ijassa-1639	18	12	aims	aim	VERB
ijassa-1639	18	13	at	at	ADP
ijassa-1639	18	14	minimizing	minimize	VERB
ijassa-1639	18	15	a	a	DET
ijassa-1639	18	16	smooth	smooth	ADJ
ijassa-1639	18	17	objective	objective	ADJ
ijassa-1639	18	18	function	function	NOUN
ijassa-1639	18	19	fν	fν	NOUN
ijassa-1639	18	20	:	:	PUNCT
ijassa-1639	18	21	rn	rn	PROPN
ijassa-1639	18	22	→	→	SYM
ijassa-1639	18	23	r	r	NOUN
ijassa-1639	18	24	subject	subject	NOUN
ijassa-1639	18	25	to	to	ADP
ijassa-1639	18	26	constraints	constraint	NOUN
ijassa-1639	18	27	given	give	VERB
ijassa-1639	18	28	by	by	ADP
ijassa-1639	18	29	a	a	DET
ijassa-1639	18	30	smooth	smooth	ADJ
ijassa-1639	18	31	mapping	mapping	NOUN
ijassa-1639	18	32	gν	gν	VERB
ijassa-1639	18	33	:	:	PUNCT
ijassa-1639	18	34	rn	rn	PROPN
ijassa-1639	18	35	→	→	SYM
ijassa-1639	18	36	rmν	rmν	PROPN
ijassa-1639	18	37	,	,	PUNCT
ijassa-1639	19	1	where	where	SCONJ
ijassa-1639	19	2	n	n	ADP
ijassa-1639	19	3	=	=	SYM
ijassa-1639	19	4	∑n	∑n	PROPN
ijassa-1639	19	5	ν=1	ν=1	INTJ
ijassa-1639	19	6	nν	nν	INTJ
ijassa-1639	19	7	.	.	PUNCT
ijassa-1639	20	1	in	in	ADP
ijassa-1639	20	2	particular	particular	ADJ
ijassa-1639	20	3	,	,	PUNCT
ijassa-1639	20	4	both	both	DET
ijassa-1639	20	5	fν	fν	VERB
ijassa-1639	20	6	and	and	CCONJ
ijassa-1639	20	7	gν	gν	PROPN
ijassa-1639	20	8	may	may	AUX
ijassa-1639	20	9	depend	depend	VERB
ijassa-1639	20	10	not	not	PART
ijassa-1639	20	11	only	only	ADV
ijassa-1639	20	12	on	on	ADP
ijassa-1639	20	13	xν	xν	PROPN
ijassa-1639	20	14	,	,	PUNCT
ijassa-1639	20	15	but	but	CCONJ
ijassa-1639	20	16	also	also	ADV
ijassa-1639	20	17	on	on	ADP
ijassa-1639	20	18	the	the	DET
ijassa-1639	20	19	variables	variable	NOUN
ijassa-1639	20	20	of	of	ADP
ijassa-1639	20	21	rival	rival	ADJ
ijassa-1639	20	22	players	player	NOUN
ijassa-1639	20	23	,	,	PUNCT
ijassa-1639	20	24	denoted	denote	VERB
ijassa-1639	20	25	by	by	ADP
ijassa-1639	20	26	x−ν	x−ν	PROPN
ijassa-1639	20	27	∈	∈	PROPN
ijassa-1639	20	28	rn−nν	rn−nν	NOUN
ijassa-1639	20	29	,	,	PUNCT
ijassa-1639	20	30	thus	thus	ADV
ijassa-1639	20	31	forming	form	VERB
ijassa-1639	20	32	the	the	DET
ijassa-1639	20	33	entire	entire	ADJ
ijassa-1639	20	34	vector	vector	NOUN
ijassa-1639	20	35	of	of	ADP
ijassa-1639	20	36	variables	variable	NOUN
ijassa-1639	20	37	x	x	PUNCT
ijassa-1639	20	38	=	=	SYM
ijassa-1639	20	39	(	(	PUNCT
ijassa-1639	20	40	xν	xν	PROPN
ijassa-1639	20	41	,	,	PUNCT
ijassa-1639	20	42	x−ν	x−ν	PROPN
ijassa-1639	20	43	)	)	PUNCT
ijassa-1639	20	44	∈	∈	PROPN
ijassa-1639	20	45	rn	rn	PROPN
ijassa-1639	20	46	.	.	PROPN
ijassa-1639	20	47	with	with	ADP
ijassa-1639	20	48	this	this	DET
ijassa-1639	20	49	notation	notation	NOUN
ijassa-1639	20	50	,	,	PUNCT
ijassa-1639	20	51	the	the	DET
ijassa-1639	20	52	optimization	optimization	NOUN
ijassa-1639	20	53	problem	problem	NOUN
ijassa-1639	20	54	of	of	ADP
ijassa-1639	20	55	the	the	DET
ijassa-1639	20	56	ν	ν	PROPN
ijassa-1639	20	57	-	-	PUNCT
ijassa-1639	20	58	th	th	VERB
ijassa-1639	20	59	player	player	NOUN
ijassa-1639	20	60	is	be	AUX
ijassa-1639	20	61	written	write	VERB
ijassa-1639	20	62	as	as	SCONJ
ijassa-1639	20	63	follows	follow	VERB
ijassa-1639	20	64	:	:	PUNCT
ijassa-1639	20	65	minimize	minimize	VERB
ijassa-1639	20	66	xν	xν	PROPN
ijassa-1639	20	67	fν(x	fν(x	NUM
ijassa-1639	20	68	ν	ν	NOUN
ijassa-1639	20	69	,	,	PUNCT
ijassa-1639	20	70	x−ν	x−ν	PROPN
ijassa-1639	20	71	)	)	PUNCT
ijassa-1639	20	72	subject	subject	NOUN
ijassa-1639	20	73	to	to	ADP
ijassa-1639	20	74	gν(xν	gν(xν	PROPN
ijassa-1639	20	75	,	,	PUNCT
ijassa-1639	20	76	x−ν	x−ν	PROPN
ijassa-1639	20	77	)	)	PUNCT
ijassa-1639	20	78	≤	≤	NOUN
ijassa-1639	20	79	0	0	NUM
ijassa-1639	20	80	.	.	PUNCT
ijassa-1639	21	1	(	(	PUNCT
ijassa-1639	21	2	2.1	2.1	NUM
ijassa-1639	21	3	)	)	PUNCT
ijassa-1639	21	4	the	the	DET
ijassa-1639	21	5	specified	specified	ADJ
ijassa-1639	21	6	problem	problem	NOUN
ijassa-1639	21	7	setting	setting	NOUN
ijassa-1639	21	8	goes	go	VERB
ijassa-1639	21	9	back	back	ADV
ijassa-1639	21	10	to	to	ADP
ijassa-1639	21	11	[	[	X
ijassa-1639	21	12	30	30	NUM
ijassa-1639	21	13	]	]	PUNCT
ijassa-1639	21	14	;	;	PUNCT
ijassa-1639	21	15	recent	recent	ADJ
ijassa-1639	21	16	surveys	survey	NOUN
ijassa-1639	21	17	can	can	AUX
ijassa-1639	21	18	be	be	AUX
ijassa-1639	21	19	found	find	VERB
ijassa-1639	21	20	in	in	ADP
ijassa-1639	21	21	[	[	X
ijassa-1639	21	22	10	10	NUM
ijassa-1639	21	23	,	,	PUNCT
ijassa-1639	21	24	15	15	NUM
ijassa-1639	21	25	]	]	PUNCT
ijassa-1639	21	26	,	,	PUNCT
ijassa-1639	21	27	including	include	VERB
ijassa-1639	21	28	various	various	ADJ
ijassa-1639	21	29	applications	application	NOUN
ijassa-1639	21	30	.	.	PUNCT
ijassa-1639	22	1	among	among	ADP
ijassa-1639	22	2	other	other	ADJ
ijassa-1639	22	3	relevant	relevant	ADJ
ijassa-1639	22	4	references	reference	NOUN
ijassa-1639	22	5	on	on	ADP
ijassa-1639	22	6	theory	theory	NOUN
ijassa-1639	22	7	and	and	CCONJ
ijassa-1639	22	8	numerical	numerical	ADJ
ijassa-1639	22	9	methods	method	NOUN
ijassa-1639	22	10	for	for	ADP
ijassa-1639	22	11	gnep	gnep	NOUN
ijassa-1639	22	12	are	be	AUX
ijassa-1639	22	13	[	[	X
ijassa-1639	22	14	5	5	NUM
ijassa-1639	22	15	,	,	PUNCT
ijassa-1639	22	16	8	8	NUM
ijassa-1639	22	17	,	,	PUNCT
ijassa-1639	22	18	9	9	NUM
ijassa-1639	22	19	,	,	PUNCT
ijassa-1639	22	20	11	11	NUM
ijassa-1639	22	21	,	,	PUNCT
ijassa-1639	22	22	19–22	19–22	NUM
ijassa-1639	22	23	,	,	PUNCT
ijassa-1639	22	24	27–29	27–29	NUM
ijassa-1639	22	25	]	]	PUNCT
ijassa-1639	22	26	.	.	PUNCT
ijassa-1639	23	1	gneps	gneps	PROPN
ijassa-1639	23	2	form	form	VERB
ijassa-1639	23	3	a	a	DET
ijassa-1639	23	4	difficult	difficult	ADJ
ijassa-1639	23	5	problem	problem	NOUN
ijassa-1639	23	6	class	class	NOUN
ijassa-1639	23	7	,	,	PUNCT
ijassa-1639	23	8	in	in	ADP
ijassa-1639	23	9	particular	particular	ADJ
ijassa-1639	23	10	,	,	PUNCT
ijassa-1639	23	11	because	because	SCONJ
ijassa-1639	23	12	their	their	PRON
ijassa-1639	23	13	solutions	solution	NOUN
ijassa-1639	23	14	are	be	AUX
ijassa-1639	23	15	naturally	naturally	ADV
ijassa-1639	23	16	nonisolated	nonisolate	VERB
ijassa-1639	23	17	.	.	PUNCT
ijassa-1639	24	1	considering	consider	VERB
ijassa-1639	24	2	x−ν	x−ν	PROPN
ijassa-1639	24	3	as	as	ADP
ijassa-1639	24	4	a	a	DET
ijassa-1639	24	5	parameter	parameter	NOUN
ijassa-1639	24	6	,	,	PUNCT
ijassa-1639	24	7	we	we	PRON
ijassa-1639	24	8	introduce	introduce	VERB
ijassa-1639	24	9	the	the	DET
ijassa-1639	24	10	lagrangian	lagrangian	ADJ
ijassa-1639	24	11	lν	lν	NOUN
ijassa-1639	24	12	:	:	PUNCT
ijassa-1639	24	13	rnν	rnν	NOUN
ijassa-1639	24	14	×	×	NOUN
ijassa-1639	24	15	rn−nν	rn−nν	NOUN
ijassa-1639	24	16	×	×	ADJ
ijassa-1639	24	17	rmν	rmν	NOUN
ijassa-1639	24	18	→	→	PUNCT
ijassa-1639	24	19	r	r	NOUN
ijassa-1639	24	20	of	of	ADP
ijassa-1639	24	21	(	(	PUNCT
ijassa-1639	24	22	2.1	2.1	NUM
ijassa-1639	24	23	)	)	PUNCT
ijassa-1639	24	24	as	as	ADP
ijassa-1639	24	25	lν(x	lν(x	PUNCT
ijassa-1639	24	26	ν	ν	NOUN
ijassa-1639	24	27	,	,	PUNCT
ijassa-1639	24	28	x−ν	x−ν	PROPN
ijassa-1639	24	29	,	,	PUNCT
ijassa-1639	24	30	λν	λν	PROPN
ijassa-1639	24	31	)	)	PUNCT
ijassa-1639	24	32	=	=	PRON
ijassa-1639	24	33	fν(x	fν(x	NUM
ijassa-1639	24	34	ν	ν	NOUN
ijassa-1639	24	35	,	,	PUNCT
ijassa-1639	24	36	x−ν	x−ν	PROPN
ijassa-1639	24	37	)	)	PUNCT
ijassa-1639	25	1	+	+	CCONJ
ijassa-1639	25	2	⟨λν	⟨λν	NUM
ijassa-1639	25	3	,	,	PUNCT
ijassa-1639	25	4	gν(xν	gν(xν	PROPN
ijassa-1639	25	5	,	,	PUNCT
ijassa-1639	26	1	x−ν)⟩.	x−ν)⟩.	ADP
ijassa-1639	26	2	then	then	ADV
ijassa-1639	26	3	the	the	DET
ijassa-1639	26	4	karush	karush	NOUN
ijassa-1639	26	5	–	–	PUNCT
ijassa-1639	26	6	kuhn	kuhn	PROPN
ijassa-1639	26	7	–	–	PUNCT
ijassa-1639	26	8	tucker	tucker	PROPN
ijassa-1639	26	9	(	(	PUNCT
ijassa-1639	26	10	kkt	kkt	PROPN
ijassa-1639	26	11	)	)	PUNCT
ijassa-1639	26	12	system	system	NOUN
ijassa-1639	26	13	characterizing	characterize	VERB
ijassa-1639	26	14	stationary	stationary	ADJ
ijassa-1639	26	15	points	point	NOUN
ijassa-1639	26	16	and	and	CCONJ
ijassa-1639	26	17	lagrange	lagrange	NOUN
ijassa-1639	26	18	multipliers	multiplier	NOUN
ijassa-1639	26	19	of	of	ADP
ijassa-1639	26	20	the	the	DET
ijassa-1639	26	21	ν	ν	PROPN
ijassa-1639	26	22	-	-	PUNCT
ijassa-1639	26	23	th	th	X
ijassa-1639	26	24	player	player	NOUN
ijassa-1639	26	25	’s	’s	PART
ijassa-1639	26	26	optimization	optimization	NOUN
ijassa-1639	26	27	problem	problem	NOUN
ijassa-1639	26	28	(	(	PUNCT
ijassa-1639	26	29	2.1	2.1	NUM
ijassa-1639	26	30	)	)	PUNCT
ijassa-1639	26	31	has	have	VERB
ijassa-1639	26	32	the	the	DET
ijassa-1639	26	33	form	form	NOUN
ijassa-1639	26	34	:	:	PUNCT
ijassa-1639	26	35	∂lν	∂lν	PROPN
ijassa-1639	26	36	∂xν	∂xν	PROPN
ijassa-1639	26	37	(	(	PUNCT
ijassa-1639	26	38	xν	xν	PROPN
ijassa-1639	26	39	,	,	PUNCT
ijassa-1639	26	40	x−ν	x−ν	PROPN
ijassa-1639	26	41	,	,	PUNCT
ijassa-1639	26	42	λν	λν	PROPN
ijassa-1639	26	43	)	)	PUNCT
ijassa-1639	26	44	=	=	SYM
ijassa-1639	26	45	0	0	NUM
ijassa-1639	26	46	,	,	PUNCT
ijassa-1639	26	47	λν	λν	ADP
ijassa-1639	26	48	≥	≥	NOUN
ijassa-1639	26	49	0	0	NUM
ijassa-1639	26	50	,	,	PUNCT
ijassa-1639	26	51	gν(xν	gν(xν	X
ijassa-1639	26	52	,	,	PUNCT
ijassa-1639	26	53	x−ν	x−ν	PROPN
ijassa-1639	26	54	)	)	PUNCT
ijassa-1639	26	55	≤	≤	NOUN
ijassa-1639	26	56	0	0	NUM
ijassa-1639	26	57	,	,	PUNCT
ijassa-1639	26	58	⟨λν	⟨λν	NUM
ijassa-1639	26	59	,	,	PUNCT
ijassa-1639	26	60	gν(xν	gν(xν	PROPN
ijassa-1639	26	61	,	,	PUNCT
ijassa-1639	26	62	x−ν)⟩	x−ν)⟩	X
ijassa-1639	27	1	=	=	SYM
ijassa-1639	27	2	0	0	X
ijassa-1639	27	3	.	.	PUNCT
ijassa-1639	28	1	concatenating	concatenate	VERB
ijassa-1639	28	2	these	these	DET
ijassa-1639	28	3	systems	system	NOUN
ijassa-1639	28	4	over	over	ADP
ijassa-1639	28	5	all	all	DET
ijassa-1639	28	6	players	player	NOUN
ijassa-1639	28	7	yields	yield	VERB
ijassa-1639	28	8	the	the	DET
ijassa-1639	28	9	kkt	kkt	PROPN
ijassa-1639	28	10	-	-	PUNCT
ijassa-1639	28	11	type	type	NOUN
ijassa-1639	28	12	system	system	NOUN
ijassa-1639	28	13	of	of	ADP
ijassa-1639	28	14	the	the	DET
ijassa-1639	28	15	gnep	gnep	NOUN
ijassa-1639	28	16	:	:	PUNCT
ijassa-1639	28	17	l(x	l(x	PROPN
ijassa-1639	28	18	,	,	PUNCT
ijassa-1639	28	19	λ	λ	NOUN
ijassa-1639	28	20	)	)	PUNCT
ijassa-1639	28	21	=	=	SYM
ijassa-1639	29	1	0	0	NUM
ijassa-1639	29	2	,	,	PUNCT
ijassa-1639	29	3	λ	λ	X
ijassa-1639	29	4	≥	≥	NOUN
ijassa-1639	29	5	0	0	NUM
ijassa-1639	29	6	,	,	PUNCT
ijassa-1639	29	7	g(x	g(x	NOUN
ijassa-1639	29	8	)	)	PUNCT
ijassa-1639	29	9	≤	≤	NOUN
ijassa-1639	29	10	0	0	NUM
ijassa-1639	29	11	,	,	PUNCT
ijassa-1639	29	12	⟨λν	⟨λν	NUM
ijassa-1639	29	13	,	,	PUNCT
ijassa-1639	29	14	gν(x)⟩	gν(x)⟩	PROPN
ijassa-1639	29	15	=	=	SYM
ijassa-1639	29	16	0	0	NUM
ijassa-1639	29	17	,	,	PUNCT
ijassa-1639	29	18	ν	ν	X
ijassa-1639	29	19	=	=	SYM
ijassa-1639	29	20	1	1	NUM
ijassa-1639	29	21	,	,	PUNCT
ijassa-1639	29	22	.	.	PUNCT
ijassa-1639	29	23	.	.	PUNCT
ijassa-1639	30	1	.	.	PUNCT
ijassa-1639	31	1	,	,	PUNCT
ijassa-1639	31	2	n	n	CCONJ
ijassa-1639	31	3	,	,	PUNCT
ijassa-1639	31	4	(	(	PUNCT
ijassa-1639	31	5	2.2	2.2	NUM
ijassa-1639	31	6	)	)	PUNCT
ijassa-1639	31	7	where	where	SCONJ
ijassa-1639	31	8	we	we	PRON
ijassa-1639	31	9	define	define	VERB
ijassa-1639	31	10	λ	λ	X
ijassa-1639	31	11	=	=	SYM
ijassa-1639	31	12	(	(	PUNCT
ijassa-1639	31	13	λ1	λ1	ADJ
ijassa-1639	31	14	,	,	PUNCT
ijassa-1639	31	15	.	.	PUNCT
ijassa-1639	31	16	.	.	PUNCT
ijassa-1639	32	1	.	.	PUNCT
ijassa-1639	33	1	,	,	PUNCT
ijassa-1639	33	2	λn	λn	NOUN
ijassa-1639	33	3	)	)	PUNCT
ijassa-1639	33	4	∈	∈	PROPN
ijassa-1639	33	5	rm	rm	PROPN
ijassa-1639	33	6	,	,	PUNCT
ijassa-1639	33	7	g	g	PROPN
ijassa-1639	33	8	:	:	PUNCT
ijassa-1639	33	9	rn	rn	PROPN
ijassa-1639	33	10	→	→	SYM
ijassa-1639	33	11	rm	rm	PROPN
ijassa-1639	33	12	,	,	PUNCT
ijassa-1639	33	13	g(x	g(x	NOUN
ijassa-1639	33	14	)	)	PUNCT
ijassa-1639	33	15	=	=	SYM
ijassa-1639	33	16	(	(	PUNCT
ijassa-1639	33	17	g1(x	g1(x	NOUN
ijassa-1639	33	18	)	)	PUNCT
ijassa-1639	33	19	,	,	PUNCT
ijassa-1639	33	20	.	.	PUNCT
ijassa-1639	33	21	.	.	PUNCT
ijassa-1639	33	22	.	.	PUNCT
ijassa-1639	34	1	,	,	PUNCT
ijassa-1639	34	2	gn(x	gn(x	X
ijassa-1639	34	3	)	)	PUNCT
ijassa-1639	34	4	)	)	PUNCT
ijassa-1639	34	5	,	,	PUNCT
ijassa-1639	34	6	with	with	ADP
ijassa-1639	34	7	m	m	PROPN
ijassa-1639	34	8	=	=	SYM
ijassa-1639	34	9	∑n	∑n	PROPN
ijassa-1639	34	10	ν=1mν	ν=1mν	NUM
ijassa-1639	34	11	,	,	PUNCT
ijassa-1639	34	12	and	and	CCONJ
ijassa-1639	34	13	l(x	l(x	PROPN
ijassa-1639	34	14	,	,	PUNCT
ijassa-1639	34	15	λ	λ	NOUN
ijassa-1639	34	16	)	)	PUNCT
ijassa-1639	34	17	=	=	SYM
ijassa-1639	34	18	(	(	PUNCT
ijassa-1639	34	19	∂l1	∂l1	NOUN
ijassa-1639	34	20	∂x1	∂x1	NOUN
ijassa-1639	34	21	(	(	PUNCT
ijassa-1639	34	22	x1	x1	PROPN
ijassa-1639	34	23	,	,	PUNCT
ijassa-1639	34	24	x−1	x−1	PROPN
ijassa-1639	34	25	,	,	PUNCT
ijassa-1639	34	26	λ1	λ1	ADJ
ijassa-1639	34	27	)	)	PUNCT
ijassa-1639	34	28	,	,	PUNCT
ijassa-1639	34	29	.	.	PUNCT
ijassa-1639	34	30	.	.	PUNCT
ijassa-1639	35	1	.	.	PUNCT
ijassa-1639	36	1	,	,	PUNCT
ijassa-1639	36	2	∂ln	∂ln	PROPN
ijassa-1639	36	3	∂xn	∂xn	PROPN
ijassa-1639	36	4	(	(	PUNCT
ijassa-1639	36	5	xn	xn	PROPN
ijassa-1639	36	6	,	,	PUNCT
ijassa-1639	36	7	x−n	x−n	PROPN
ijassa-1639	36	8	,	,	PUNCT
ijassa-1639	36	9	λn	λn	NOUN
ijassa-1639	36	10	)	)	PUNCT
ijassa-1639	36	11	)	)	PUNCT
ijassa-1639	36	12	.	.	PUNCT
ijassa-1639	37	1	furthermore	furthermore	ADV
ijassa-1639	37	2	,	,	PUNCT
ijassa-1639	37	3	the	the	DET
ijassa-1639	37	4	system	system	NOUN
ijassa-1639	37	5	(	(	PUNCT
ijassa-1639	37	6	2.2	2.2	NUM
ijassa-1639	37	7	)	)	PUNCT
ijassa-1639	37	8	can	can	AUX
ijassa-1639	37	9	be	be	AUX
ijassa-1639	37	10	equivalently	equivalently	ADV
ijassa-1639	37	11	reformulated	reformulate	VERB
ijassa-1639	37	12	as	as	ADP
ijassa-1639	37	13	a	a	DET
ijassa-1639	37	14	constrained	constrained	ADJ
ijassa-1639	37	15	equation	equation	NOUN
ijassa-1639	37	16	φ(u	φ(u	NOUN
ijassa-1639	37	17	)	)	PUNCT
ijassa-1639	37	18	=	=	SYM
ijassa-1639	37	19	0	0	NUM
ijassa-1639	37	20	,	,	PUNCT
ijassa-1639	37	21	u	u	NOUN
ijassa-1639	37	22	∈	∈	PROPN
ijassa-1639	37	23	p	p	X
ijassa-1639	37	24	,	,	PUNCT
ijassa-1639	37	25	(	(	PUNCT
ijassa-1639	37	26	2.3	2.3	NUM
ijassa-1639	37	27	)	)	PUNCT
ijassa-1639	37	28	with	with	ADP
ijassa-1639	37	29	some	some	DET
ijassa-1639	37	30	mapping	mapping	NOUN
ijassa-1639	37	31	φ	φ	NOUN
ijassa-1639	37	32	:	:	PUNCT
ijassa-1639	37	33	rp	rp	NOUN
ijassa-1639	37	34	→	→	SYM
ijassa-1639	37	35	rq	rq	NOUN
ijassa-1639	37	36	and	and	CCONJ
ijassa-1639	37	37	a	a	DET
ijassa-1639	37	38	nonempty	nonempty	ADV
ijassa-1639	37	39	closed	close	VERB
ijassa-1639	37	40	convex	convex	NOUN
ijassa-1639	37	41	set	set	VERB
ijassa-1639	37	42	p	p	PROPN
ijassa-1639	37	43	⊂	⊂	PROPN
ijassa-1639	37	44	rp	rp	PROPN
ijassa-1639	37	45	.	.	PUNCT
ijassa-1639	38	1	this	this	PRON
ijassa-1639	38	2	can	can	AUX
ijassa-1639	38	3	be	be	AUX
ijassa-1639	38	4	done	do	VERB
ijassa-1639	38	5	in	in	ADP
ijassa-1639	38	6	many	many	ADJ
ijassa-1639	38	7	different	different	ADJ
ijassa-1639	38	8	ways	way	NOUN
ijassa-1639	38	9	,	,	PUNCT
ijassa-1639	38	10	and	and	CCONJ
ijassa-1639	38	11	we	we	PRON
ijassa-1639	38	12	restrict	restrict	VERB
ijassa-1639	38	13	ourselves	ourselves	PRON
ijassa-1639	38	14	to	to	ADP
ijassa-1639	38	15	the	the	DET
ijassa-1639	38	16	following	follow	VERB
ijassa-1639	38	17	two	two	NUM
ijassa-1639	38	18	adopted	adopt	VERB
ijassa-1639	38	19	,	,	PUNCT
ijassa-1639	38	20	for	for	ADP
ijassa-1639	38	21	example	example	NOUN
ijassa-1639	38	22	,	,	PUNCT
ijassa-1639	38	23	in	in	ADP
ijassa-1639	38	24	[	[	X
ijassa-1639	38	25	13	13	NUM
ijassa-1639	38	26	]	]	PUNCT
ijassa-1639	38	27	.	.	PUNCT
ijassa-1639	39	1	in	in	ADP
ijassa-1639	39	2	both	both	PRON
ijassa-1639	39	3	,	,	PUNCT
ijassa-1639	39	4	p	p	NOUN
ijassa-1639	39	5	=	=	NOUN
ijassa-1639	39	6	q	q	NOUN
ijassa-1639	39	7	=	=	PUNCT
ijassa-1639	39	8	n+	n+	PROPN
ijassa-1639	39	9	2	2	NUM
ijassa-1639	39	10	m	m	NOUN
ijassa-1639	39	11	,	,	PUNCT
ijassa-1639	39	12	u	u	NOUN
ijassa-1639	39	13	=	=	PUNCT
ijassa-1639	39	14	(	(	PUNCT
ijassa-1639	39	15	x	x	X
ijassa-1639	39	16	,	,	PUNCT
ijassa-1639	39	17	λ	λ	PROPN
ijassa-1639	39	18	,	,	PUNCT
ijassa-1639	39	19	y	y	PROPN
ijassa-1639	39	20	)	)	PUNCT
ijassa-1639	39	21	,	,	PUNCT
ijassa-1639	39	22	with	with	ADP
ijassa-1639	39	23	y	y	PROPN
ijassa-1639	39	24	=	=	SYM
ijassa-1639	39	25	(	(	PUNCT
ijassa-1639	39	26	y1	y1	PROPN
ijassa-1639	39	27	,	,	PUNCT
ijassa-1639	39	28	.	.	PUNCT
ijassa-1639	39	29	.	.	PUNCT
ijassa-1639	39	30	.	.	PUNCT
ijassa-1639	40	1	,	,	PUNCT
ijassa-1639	40	2	yn	yn	X
ijassa-1639	40	3	)	)	PUNCT
ijassa-1639	40	4	∈	∈	PROPN
ijassa-1639	40	5	rm	rm	NOUN
ijassa-1639	40	6	being	be	AUX
ijassa-1639	40	7	a	a	DET
ijassa-1639	40	8	slack	slack	NOUN
ijassa-1639	40	9	variable	variable	NOUN
ijassa-1639	40	10	,	,	PUNCT
ijassa-1639	40	11	and	and	CCONJ
ijassa-1639	40	12	the	the	DET
ijassa-1639	40	13	constraint	constraint	NOUN
ijassa-1639	40	14	set	set	NOUN
ijassa-1639	40	15	is	be	AUX
ijassa-1639	40	16	p	p	X
ijassa-1639	40	17	=	=	PUNCT
ijassa-1639	40	18	rn	rn	PROPN
ijassa-1639	40	19	×	×	PROPN
ijassa-1639	40	20	rm	rm	PROPN
ijassa-1639	40	21	+	+	CCONJ
ijassa-1639	40	22	×	×	PROPN
ijassa-1639	40	23	rm	rm	NOUN
ijassa-1639	40	24	+	+	X
ijassa-1639	40	25	.	.	PUNCT
ijassa-1639	41	1	(	(	PUNCT
ijassa-1639	41	2	2.4	2.4	NUM
ijassa-1639	41	3	)	)	PUNCT
ijassa-1639	41	4	the	the	DET
ijassa-1639	41	5	difference	difference	NOUN
ijassa-1639	41	6	is	be	AUX
ijassa-1639	41	7	in	in	ADP
ijassa-1639	41	8	how	how	SCONJ
ijassa-1639	41	9	φ	φ	PROPN
ijassa-1639	41	10	is	be	AUX
ijassa-1639	41	11	defined	define	VERB
ijassa-1639	41	12	.	.	PUNCT
ijassa-1639	42	1	one	one	NUM
ijassa-1639	42	2	possibility	possibility	NOUN
ijassa-1639	42	3	is	be	AUX
ijassa-1639	42	4	to	to	PART
ijassa-1639	42	5	adopt	adopt	VERB
ijassa-1639	42	6	a	a	DET
ijassa-1639	42	7	piecewise	piecewise	NOUN
ijassa-1639	42	8	smooth	smooth	ADJ
ijassa-1639	42	9	“	"	PUNCT
ijassa-1639	42	10	min	min	NOUN
ijassa-1639	42	11	”	"	PUNCT
ijassa-1639	42	12	reformulation	reformulation	NOUN
ijassa-1639	42	13	with	with	ADP
ijassa-1639	42	14	φ(u	φ(u	NOUN
ijassa-1639	42	15	)	)	PUNCT
ijassa-1639	42	16	=	=	SYM
ijassa-1639	42	17	(	(	PUNCT
ijassa-1639	42	18	l(x	l(x	PROPN
ijassa-1639	42	19	,	,	PUNCT
ijassa-1639	42	20	λ	λ	NOUN
ijassa-1639	42	21	)	)	PUNCT
ijassa-1639	42	22	,	,	PUNCT
ijassa-1639	42	23	g(x	g(x	NOUN
ijassa-1639	42	24	)	)	PUNCT
ijassa-1639	43	1	+	+	CCONJ
ijassa-1639	43	2	y	y	PROPN
ijassa-1639	43	3	,	,	PUNCT
ijassa-1639	43	4	min{λ	min{λ	PROPN
ijassa-1639	43	5	,	,	PUNCT
ijassa-1639	43	6	y	y	PROPN
ijassa-1639	43	7	}	}	PUNCT
ijassa-1639	43	8	)	)	PUNCT
ijassa-1639	43	9	,	,	PUNCT
ijassa-1639	43	10	(	(	PUNCT
ijassa-1639	43	11	2.5	2.5	NUM
ijassa-1639	43	12	)	)	PUNCT
ijassa-1639	43	13	where	where	SCONJ
ijassa-1639	43	14	min	min	NOUN
ijassa-1639	43	15	is	be	AUX
ijassa-1639	43	16	taken	take	VERB
ijassa-1639	43	17	componentwise	componentwise	NOUN
ijassa-1639	43	18	,	,	PUNCT
ijassa-1639	43	19	while	while	SCONJ
ijassa-1639	43	20	another	another	DET
ijassa-1639	43	21	reformulation	reformulation	NOUN
ijassa-1639	43	22	is	be	AUX
ijassa-1639	43	23	smooth	smooth	ADJ
ijassa-1639	43	24	,	,	PUNCT
ijassa-1639	43	25	with	with	ADP
ijassa-1639	43	26	φ(u	φ(u	NOUN
ijassa-1639	43	27	)	)	PUNCT
ijassa-1639	43	28	=	=	SYM
ijassa-1639	43	29	(	(	PUNCT
ijassa-1639	43	30	l(x	l(x	PROPN
ijassa-1639	43	31	,	,	PUNCT
ijassa-1639	43	32	λ	λ	NOUN
ijassa-1639	43	33	)	)	PUNCT
ijassa-1639	43	34	,	,	PUNCT
ijassa-1639	43	35	g(x	g(x	NOUN
ijassa-1639	43	36	)	)	PUNCT
ijassa-1639	44	1	+	+	CCONJ
ijassa-1639	44	2	y	y	PROPN
ijassa-1639	44	3	,	,	PUNCT
ijassa-1639	44	4	λ	λ	X
ijassa-1639	44	5	◦	◦	NOUN
ijassa-1639	44	6	y	y	NOUN
ijassa-1639	44	7	)	)	PUNCT
ijassa-1639	44	8	,	,	PUNCT
ijassa-1639	44	9	(	(	PUNCT
ijassa-1639	44	10	2.6	2.6	NUM
ijassa-1639	44	11	)	)	PUNCT
ijassa-1639	44	12	copyright	copyright	NOUN
ijassa-1639	44	13	©	©	PROPN
ijassa-1639	44	14	2024	2024	NUM
ijassa-1639	44	15	assa	assa	NOUN
ijassa-1639	44	16	.	.	PUNCT
ijassa-1639	45	1	adv	adv	PROPN
ijassa-1639	45	2	syst	syst	PROPN
ijassa-1639	45	3	sci	sci	PROPN
ijassa-1639	45	4	appl	appl	PROPN
ijassa-1639	45	5	(	(	PUNCT
ijassa-1639	45	6	2024	2024	NUM
ijassa-1639	45	7	)	)	PUNCT
ijassa-1639	45	8	piecewise	piecewise	NOUN
ijassa-1639	45	9	levenberg	levenberg	PROPN
ijassa-1639	45	10	–	–	PUNCT
ijassa-1639	45	11	marquardt	marquardt	PROPN
ijassa-1639	45	12	method	method	NOUN
ijassa-1639	45	13	for	for	ADP
ijassa-1639	45	14	gneps	gneps	NOUN
ijassa-1639	45	15	21	21	NUM
ijassa-1639	45	16	employing	employ	VERB
ijassa-1639	45	17	the	the	DET
ijassa-1639	45	18	hadamard	hadamard	ADJ
ijassa-1639	45	19	product	product	NOUN
ijassa-1639	45	20	λ	λ	NOUN
ijassa-1639	45	21	◦	◦	NOUN
ijassa-1639	45	22	y	y	NOUN
ijassa-1639	45	23	=	=	SYM
ijassa-1639	45	24	(	(	PUNCT
ijassa-1639	45	25	λ1y1	λ1y1	PROPN
ijassa-1639	45	26	,	,	PUNCT
ijassa-1639	45	27	.	.	PUNCT
ijassa-1639	45	28	.	.	PUNCT
ijassa-1639	45	29	.	.	PUNCT
ijassa-1639	46	1	,	,	PUNCT
ijassa-1639	46	2	λmym	λmym	NOUN
ijassa-1639	46	3	)	)	PUNCT
ijassa-1639	46	4	.	.	PUNCT
ijassa-1639	47	1	observe	observe	VERB
ijassa-1639	47	2	that	that	SCONJ
ijassa-1639	47	3	the	the	DET
ijassa-1639	47	4	set	set	NOUN
ijassa-1639	47	5	p	p	NOUN
ijassa-1639	47	6	in	in	ADP
ijassa-1639	47	7	(	(	PUNCT
ijassa-1639	47	8	2.4	2.4	NUM
ijassa-1639	47	9	)	)	PUNCT
ijassa-1639	47	10	is	be	AUX
ijassa-1639	47	11	polyhedral	polyhedral	ADJ
ijassa-1639	47	12	,	,	PUNCT
ijassa-1639	47	13	and	and	CCONJ
ijassa-1639	47	14	moreover	moreover	ADV
ijassa-1639	47	15	,	,	PUNCT
ijassa-1639	47	16	given	give	VERB
ijassa-1639	47	17	by	by	ADP
ijassa-1639	47	18	simple	simple	ADJ
ijassa-1639	47	19	bounds	bound	NOUN
ijassa-1639	47	20	,	,	PUNCT
ijassa-1639	47	21	and	and	CCONJ
ijassa-1639	47	22	this	this	PRON
ijassa-1639	47	23	is	be	AUX
ijassa-1639	47	24	the	the	DET
ijassa-1639	47	25	main	main	ADJ
ijassa-1639	47	26	reason	reason	NOUN
ijassa-1639	47	27	to	to	PART
ijassa-1639	47	28	use	use	VERB
ijassa-1639	47	29	slack	slack	NOUN
ijassa-1639	47	30	variables	variable	NOUN
ijassa-1639	47	31	in	in	ADP
ijassa-1639	47	32	these	these	DET
ijassa-1639	47	33	reformulations	reformulation	NOUN
ijassa-1639	47	34	.	.	PUNCT
ijassa-1639	48	1	note	note	VERB
ijassa-1639	48	2	also	also	ADV
ijassa-1639	48	3	that	that	SCONJ
ijassa-1639	48	4	for	for	ADP
ijassa-1639	48	5	φ	φ	PROPN
ijassa-1639	48	6	defined	define	VERB
ijassa-1639	48	7	in	in	ADP
ijassa-1639	48	8	(	(	PUNCT
ijassa-1639	48	9	2.5	2.5	NUM
ijassa-1639	48	10	)	)	PUNCT
ijassa-1639	48	11	,	,	PUNCT
ijassa-1639	48	12	one	one	PRON
ijassa-1639	48	13	could	could	AUX
ijassa-1639	48	14	actually	actually	ADV
ijassa-1639	48	15	take	take	VERB
ijassa-1639	48	16	p	p	NOUN
ijassa-1639	48	17	=	=	X
ijassa-1639	48	18	rn	rn	PROPN
ijassa-1639	48	19	×	×	PROPN
ijassa-1639	48	20	rm	rm	PROPN
ijassa-1639	48	21	×	×	PROPN
ijassa-1639	48	22	rm	rm	PROPN
ijassa-1639	48	23	,	,	PUNCT
ijassa-1639	48	24	and	and	CCONJ
ijassa-1639	48	25	(	(	PUNCT
ijassa-1639	48	26	2.3	2.3	NUM
ijassa-1639	48	27	)	)	PUNCT
ijassa-1639	48	28	would	would	AUX
ijassa-1639	48	29	still	still	ADV
ijassa-1639	48	30	be	be	AUX
ijassa-1639	48	31	equivalent	equivalent	ADJ
ijassa-1639	48	32	to	to	ADP
ijassa-1639	48	33	(	(	PUNCT
ijassa-1639	48	34	2.2	2.2	NUM
ijassa-1639	48	35	)	)	PUNCT
ijassa-1639	48	36	.	.	PUNCT
ijassa-1639	49	1	however	however	ADV
ijassa-1639	49	2	,	,	PUNCT
ijassa-1639	49	3	the	the	DET
ijassa-1639	49	4	nonnegativity	nonnegativity	NOUN
ijassa-1639	49	5	constraints	constraint	VERB
ijassa-1639	49	6	on	on	ADP
ijassa-1639	49	7	λ	λ	PROPN
ijassa-1639	49	8	and	and	CCONJ
ijassa-1639	49	9	y	y	PROPN
ijassa-1639	49	10	are	be	AUX
ijassa-1639	49	11	needed	need	VERB
ijassa-1639	49	12	to	to	PART
ijassa-1639	49	13	ensure	ensure	VERB
ijassa-1639	49	14	the	the	DET
ijassa-1639	49	15	so	so	ADV
ijassa-1639	49	16	-	-	PUNCT
ijassa-1639	49	17	called	call	VERB
ijassa-1639	49	18	p	p	NOUN
ijassa-1639	49	19	-property	-property	NOUN
ijassa-1639	49	20	and	and	CCONJ
ijassa-1639	49	21	condition	condition	NOUN
ijassa-1639	49	22	(	(	PUNCT
ijassa-1639	49	23	3.13	3.13	NUM
ijassa-1639	49	24	)	)	PUNCT
ijassa-1639	49	25	that	that	PRON
ijassa-1639	49	26	will	will	AUX
ijassa-1639	49	27	be	be	AUX
ijassa-1639	49	28	essential	essential	ADJ
ijassa-1639	49	29	for	for	ADP
ijassa-1639	49	30	the	the	DET
ijassa-1639	49	31	results	result	NOUN
ijassa-1639	49	32	presented	present	VERB
ijassa-1639	49	33	in	in	ADP
ijassa-1639	49	34	section	section	NOUN
ijassa-1639	49	35	3	3	NUM
ijassa-1639	49	36	below	below	ADV
ijassa-1639	49	37	.	.	PUNCT
ijassa-1639	50	1	reformulation	reformulation	ADJ
ijassa-1639	50	2	employing	employing	NOUN
ijassa-1639	50	3	(	(	PUNCT
ijassa-1639	50	4	2.5	2.5	NUM
ijassa-1639	50	5	)	)	PUNCT
ijassa-1639	50	6	will	will	AUX
ijassa-1639	50	7	be	be	AUX
ijassa-1639	50	8	of	of	ADP
ijassa-1639	50	9	primary	primary	ADJ
ijassa-1639	50	10	interest	interest	NOUN
ijassa-1639	50	11	for	for	ADP
ijassa-1639	50	12	us	we	PRON
ijassa-1639	50	13	,	,	PUNCT
ijassa-1639	50	14	and	and	CCONJ
ijassa-1639	50	15	to	to	ADP
ijassa-1639	50	16	that	that	DET
ijassa-1639	50	17	end	end	NOUN
ijassa-1639	50	18	,	,	PUNCT
ijassa-1639	50	19	we	we	PRON
ijassa-1639	50	20	next	next	ADV
ijassa-1639	50	21	recall	recall	VERB
ijassa-1639	50	22	some	some	DET
ijassa-1639	50	23	terminology	terminology	NOUN
ijassa-1639	50	24	related	relate	VERB
ijassa-1639	50	25	to	to	AUX
ijassa-1639	50	26	piecewise	piecewise	VERB
ijassa-1639	50	27	smoothness	smoothness	PROPN
ijassa-1639	50	28	.	.	PUNCT
ijassa-1639	51	1	a	a	DET
ijassa-1639	51	2	mapping	mapping	NOUN
ijassa-1639	51	3	φ	φ	PROPN
ijassa-1639	51	4	is	be	AUX
ijassa-1639	51	5	refereed	refereed	ADJ
ijassa-1639	51	6	to	to	ADP
ijassa-1639	51	7	as	as	SCONJ
ijassa-1639	51	8	piecewise	piecewise	NOUN
ijassa-1639	51	9	smooth	smooth	VERB
ijassa-1639	51	10	if	if	SCONJ
ijassa-1639	51	11	it	it	PRON
ijassa-1639	51	12	is	be	AUX
ijassa-1639	51	13	continuous	continuous	ADJ
ijassa-1639	51	14	,	,	PUNCT
ijassa-1639	51	15	and	and	CCONJ
ijassa-1639	51	16	there	there	PRON
ijassa-1639	51	17	exists	exist	VERB
ijassa-1639	51	18	a	a	DET
ijassa-1639	51	19	finite	finite	ADJ
ijassa-1639	51	20	collection	collection	NOUN
ijassa-1639	51	21	of	of	ADP
ijassa-1639	51	22	smooth	smooth	ADJ
ijassa-1639	51	23	selection	selection	NOUN
ijassa-1639	51	24	mappings	mapping	NOUN
ijassa-1639	51	25	φ1	φ1	NOUN
ijassa-1639	51	26	,	,	PUNCT
ijassa-1639	51	27	.	.	PUNCT
ijassa-1639	51	28	.	.	PUNCT
ijassa-1639	51	29	.	.	PUNCT
ijassa-1639	52	1	,	,	PUNCT
ijassa-1639	52	2	φs	φs	PROPN
ijassa-1639	52	3	:	:	PUNCT
ijassa-1639	52	4	rp	rp	NOUN
ijassa-1639	52	5	→	→	PUNCT
ijassa-1639	52	6	rq	rq	NOUN
ijassa-1639	52	7	such	such	ADJ
ijassa-1639	52	8	that	that	SCONJ
ijassa-1639	52	9	φ(u	φ(u	NOUN
ijassa-1639	52	10	)	)	PUNCT
ijassa-1639	52	11	∈	∈	PROPN
ijassa-1639	52	12	{	{	PUNCT
ijassa-1639	52	13	φ1(u	φ1(u	NUM
ijassa-1639	52	14	)	)	PUNCT
ijassa-1639	52	15	,	,	PUNCT
ijassa-1639	52	16	.	.	PUNCT
ijassa-1639	52	17	.	.	PUNCT
ijassa-1639	53	1	.	.	PUNCT
ijassa-1639	54	1	,	,	PUNCT
ijassa-1639	54	2	φs(u	φs(u	NUM
ijassa-1639	54	3	)	)	PUNCT
ijassa-1639	54	4	}	}	PUNCT
ijassa-1639	54	5	∀u	∀u	PROPN
ijassa-1639	54	6	∈	∈	NOUN
ijassa-1639	54	7	rp	rp	NOUN
ijassa-1639	54	8	.	.	PUNCT
ijassa-1639	55	1	considering	consider	VERB
ijassa-1639	55	2	s	s	X
ijassa-1639	55	3	=	=	SYM
ijassa-1639	55	4	1	1	NUM
ijassa-1639	55	5	recovers	recover	VERB
ijassa-1639	55	6	the	the	DET
ijassa-1639	55	7	case	case	NOUN
ijassa-1639	55	8	of	of	ADP
ijassa-1639	55	9	a	a	DET
ijassa-1639	55	10	smooth	smooth	ADJ
ijassa-1639	55	11	mapping	mapping	NOUN
ijassa-1639	55	12	φ	φ	NOUN
ijassa-1639	55	13	.	.	PUNCT
ijassa-1639	56	1	needless	needless	ADJ
ijassa-1639	56	2	to	to	PART
ijassa-1639	56	3	say	say	VERB
ijassa-1639	56	4	,	,	PUNCT
ijassa-1639	56	5	a	a	DET
ijassa-1639	56	6	collection	collection	NOUN
ijassa-1639	56	7	of	of	ADP
ijassa-1639	56	8	smooth	smooth	ADJ
ijassa-1639	56	9	selection	selection	NOUN
ijassa-1639	56	10	mappings	mapping	NOUN
ijassa-1639	56	11	corresponding	correspond	VERB
ijassa-1639	56	12	to	to	ADP
ijassa-1639	56	13	a	a	DET
ijassa-1639	56	14	given	give	VERB
ijassa-1639	56	15	piecewise	piecewise	NOUN
ijassa-1639	56	16	smooth	smooth	ADJ
ijassa-1639	56	17	mapping	mapping	NOUN
ijassa-1639	56	18	is	be	AUX
ijassa-1639	56	19	not	not	PART
ijassa-1639	56	20	uniquely	uniquely	ADV
ijassa-1639	56	21	defined	define	VERB
ijassa-1639	56	22	,	,	PUNCT
ijassa-1639	56	23	and	and	CCONJ
ijassa-1639	56	24	we	we	PRON
ijassa-1639	56	25	will	will	AUX
ijassa-1639	56	26	assume	assume	VERB
ijassa-1639	56	27	that	that	SCONJ
ijassa-1639	56	28	some	some	DET
ijassa-1639	56	29	such	such	ADJ
ijassa-1639	56	30	collection	collection	NOUN
ijassa-1639	56	31	is	be	AUX
ijassa-1639	56	32	fixed	fix	VERB
ijassa-1639	56	33	,	,	PUNCT
ijassa-1639	56	34	i.e.	i.e.	X
ijassa-1639	56	35	,	,	PUNCT
ijassa-1639	56	36	φ	φ	PROPN
ijassa-1639	56	37	is	be	AUX
ijassa-1639	56	38	defined	define	VERB
ijassa-1639	56	39	by	by	ADP
ijassa-1639	56	40	a	a	DET
ijassa-1639	56	41	given	give	VERB
ijassa-1639	56	42	collection	collection	NOUN
ijassa-1639	56	43	of	of	ADP
ijassa-1639	56	44	smooth	smooth	ADJ
ijassa-1639	56	45	selection	selection	NOUN
ijassa-1639	56	46	mappings	mapping	NOUN
ijassa-1639	56	47	.	.	PUNCT
ijassa-1639	57	1	obviously	obviously	ADV
ijassa-1639	57	2	,	,	PUNCT
ijassa-1639	57	3	the	the	DET
ijassa-1639	57	4	mapping	mapping	NOUN
ijassa-1639	57	5	φ	φ	PROPN
ijassa-1639	57	6	defined	define	VERB
ijassa-1639	57	7	according	accord	VERB
ijassa-1639	57	8	to	to	ADP
ijassa-1639	57	9	(	(	PUNCT
ijassa-1639	57	10	2.5	2.5	NUM
ijassa-1639	57	11	)	)	PUNCT
ijassa-1639	57	12	is	be	AUX
ijassa-1639	57	13	piecewise	piecewise	NOUN
ijassa-1639	57	14	smooth	smooth	ADJ
ijassa-1639	57	15	,	,	PUNCT
ijassa-1639	57	16	with	with	ADP
ijassa-1639	57	17	a	a	DET
ijassa-1639	57	18	natural	natural	ADJ
ijassa-1639	57	19	collection	collection	NOUN
ijassa-1639	57	20	of	of	ADP
ijassa-1639	57	21	smooth	smooth	ADJ
ijassa-1639	57	22	selection	selection	NOUN
ijassa-1639	57	23	mappings	mapping	NOUN
ijassa-1639	57	24	φj(u	φj(u	NOUN
ijassa-1639	57	25	)	)	PUNCT
ijassa-1639	57	26	=	=	NOUN
ijassa-1639	58	1	(	(	PUNCT
ijassa-1639	58	2	l(x	l(x	PROPN
ijassa-1639	58	3	,	,	PUNCT
ijassa-1639	58	4	λ	λ	NOUN
ijassa-1639	58	5	)	)	PUNCT
ijassa-1639	58	6	,	,	PUNCT
ijassa-1639	58	7	g(x	g(x	NOUN
ijassa-1639	58	8	)	)	PUNCT
ijassa-1639	59	1	+	+	CCONJ
ijassa-1639	59	2	y	y	NOUN
ijassa-1639	59	3	,	,	PUNCT
ijassa-1639	59	4	λi(j	λi(j	NUM
ijassa-1639	59	5	)	)	PUNCT
ijassa-1639	59	6	,	,	PUNCT
ijassa-1639	59	7	y{1	y{1	PROPN
ijassa-1639	59	8	,	,	PUNCT
ijassa-1639	59	9	...	...	PUNCT
ijassa-1639	59	10	,	,	PUNCT
ijassa-1639	59	11	m}\i(j	m}\i(j	NOUN
ijassa-1639	59	12	)	)	PUNCT
ijassa-1639	59	13	)	)	PUNCT
ijassa-1639	59	14	,	,	PUNCT
ijassa-1639	59	15	(	(	PUNCT
ijassa-1639	59	16	2.7	2.7	NUM
ijassa-1639	59	17	)	)	PUNCT
ijassa-1639	59	18	where	where	SCONJ
ijassa-1639	59	19	a	a	DET
ijassa-1639	59	20	one	one	NUM
ijassa-1639	59	21	-	-	PUNCT
ijassa-1639	59	22	to	to	ADP
ijassa-1639	59	23	-	-	PUNCT
ijassa-1639	59	24	one	one	NUM
ijassa-1639	59	25	mapping	mapping	NOUN
ijassa-1639	59	26	j	j	PROPN
ijassa-1639	59	27	7→	7→	NUM
ijassa-1639	59	28	i(j	i(j	ADJ
ijassa-1639	59	29	)	)	PUNCT
ijassa-1639	59	30	from	from	ADP
ijassa-1639	59	31	{	{	PUNCT
ijassa-1639	59	32	1	1	NUM
ijassa-1639	59	33	,	,	PUNCT
ijassa-1639	59	34	.	.	PUNCT
ijassa-1639	59	35	.	.	PUNCT
ijassa-1639	59	36	.	.	PUNCT
ijassa-1639	60	1	,	,	PUNCT
ijassa-1639	60	2	2	2	NUM
ijassa-1639	60	3	m	m	NOUN
ijassa-1639	60	4	}	}	PUNCT
ijassa-1639	60	5	to	to	ADP
ijassa-1639	60	6	the	the	DET
ijassa-1639	60	7	set	set	NOUN
ijassa-1639	60	8	of	of	ADP
ijassa-1639	60	9	all	all	DET
ijassa-1639	60	10	different	different	ADJ
ijassa-1639	60	11	subsets	subset	NOUN
ijassa-1639	60	12	of	of	ADP
ijassa-1639	60	13	{	{	PUNCT
ijassa-1639	60	14	1	1	NUM
ijassa-1639	60	15	,	,	PUNCT
ijassa-1639	60	16	.	.	PUNCT
ijassa-1639	60	17	.	.	PUNCT
ijassa-1639	61	1	.	.	PUNCT
ijassa-1639	62	1	,	,	PUNCT
ijassa-1639	62	2	m	m	AUX
ijassa-1639	62	3	}	}	PUNCT
ijassa-1639	62	4	is	be	AUX
ijassa-1639	62	5	supposed	suppose	VERB
ijassa-1639	62	6	to	to	PART
ijassa-1639	62	7	be	be	AUX
ijassa-1639	62	8	fixed	fix	VERB
ijassa-1639	62	9	.	.	PUNCT
ijassa-1639	63	1	3	3	X
ijassa-1639	63	2	.	.	X
ijassa-1639	63	3	piecewise	piecewise	PROPN
ijassa-1639	63	4	levenberg	levenberg	PROPN
ijassa-1639	63	5	–	–	PUNCT
ijassa-1639	63	6	marquardt	marquardt	PROPN
ijassa-1639	63	7	method	method	NOUN
ijassa-1639	63	8	getting	get	VERB
ijassa-1639	63	9	back	back	ADV
ijassa-1639	63	10	to	to	ADP
ijassa-1639	63	11	a	a	DET
ijassa-1639	63	12	general	general	ADJ
ijassa-1639	63	13	piecewise	piecewise	NOUN
ijassa-1639	63	14	smooth	smooth	ADJ
ijassa-1639	63	15	mapping	mapping	NOUN
ijassa-1639	63	16	φ	φ	NOUN
ijassa-1639	63	17	,	,	PUNCT
ijassa-1639	63	18	for	for	ADP
ijassa-1639	63	19	each	each	DET
ijassa-1639	63	20	u	u	PROPN
ijassa-1639	63	21	∈	∈	PROPN
ijassa-1639	63	22	rp	rp	NOUN
ijassa-1639	63	23	we	we	PRON
ijassa-1639	63	24	define	define	VERB
ijassa-1639	63	25	the	the	DET
ijassa-1639	63	26	set	set	NOUN
ijassa-1639	63	27	a(u	a(u	PROPN
ijassa-1639	63	28	)	)	PUNCT
ijassa-1639	63	29	=	=	PRON
ijassa-1639	64	1	{	{	PUNCT
ijassa-1639	64	2	j	j	PROPN
ijassa-1639	64	3	∈	∈	PROPN
ijassa-1639	64	4	{	{	PUNCT
ijassa-1639	64	5	1	1	NUM
ijassa-1639	64	6	,	,	PUNCT
ijassa-1639	64	7	.	.	PUNCT
ijassa-1639	64	8	.	.	PUNCT
ijassa-1639	64	9	.	.	PUNCT
ijassa-1639	65	1	,	,	PUNCT
ijassa-1639	65	2	s	s	X
ijassa-1639	65	3	}	}	PUNCT
ijassa-1639	65	4	|	|	ADV
ijassa-1639	65	5	φ(u	φ(u	NOUN
ijassa-1639	65	6	)	)	PUNCT
ijassa-1639	65	7	=	=	SYM
ijassa-1639	65	8	φj(u	φj(u	NOUN
ijassa-1639	65	9	)	)	PUNCT
ijassa-1639	65	10	}	}	PUNCT
ijassa-1639	65	11	(	(	PUNCT
ijassa-1639	65	12	3.8	3.8	NUM
ijassa-1639	65	13	)	)	PUNCT
ijassa-1639	65	14	of	of	ADP
ijassa-1639	65	15	indices	index	NOUN
ijassa-1639	65	16	of	of	ADP
ijassa-1639	65	17	smooth	smooth	ADJ
ijassa-1639	65	18	selection	selection	NOUN
ijassa-1639	65	19	mappings	mapping	NOUN
ijassa-1639	65	20	active	active	ADJ
ijassa-1639	65	21	at	at	ADP
ijassa-1639	65	22	u.	u.	NOUN
ijassa-1639	65	23	let	let	VERB
ijassa-1639	65	24	g	g	NOUN
ijassa-1639	65	25	:	:	PUNCT
ijassa-1639	65	26	rp	rp	NOUN
ijassa-1639	65	27	→	→	PUNCT
ijassa-1639	65	28	rq×p	rq×p	NOUN
ijassa-1639	65	29	be	be	AUX
ijassa-1639	65	30	any	any	DET
ijassa-1639	65	31	mapping	mapping	NOUN
ijassa-1639	65	32	satisfying	satisfy	VERB
ijassa-1639	65	33	g(u	g(u	PROPN
ijassa-1639	65	34	)	)	PUNCT
ijassa-1639	65	35	∈	∈	PROPN
ijassa-1639	65	36	{	{	PUNCT
ijassa-1639	65	37	(	(	PUNCT
ijassa-1639	65	38	φj)′(u	φj)′(u	NOUN
ijassa-1639	65	39	)	)	PUNCT
ijassa-1639	66	1	|	|	ADV
ijassa-1639	66	2	j	j	PROPN
ijassa-1639	66	3	∈	∈	PROPN
ijassa-1639	66	4	a(u	a(u	PROPN
ijassa-1639	66	5	)	)	PUNCT
ijassa-1639	66	6	}	}	PUNCT
ijassa-1639	66	7	∀u	∀u	PROPN
ijassa-1639	66	8	∈	∈	PROPN
ijassa-1639	66	9	rp	rp	NOUN
ijassa-1639	66	10	.	.	PUNCT
ijassa-1639	66	11	(	(	PUNCT
ijassa-1639	66	12	3.9	3.9	NUM
ijassa-1639	66	13	)	)	PUNCT
ijassa-1639	66	14	for	for	ADP
ijassa-1639	66	15	a	a	DET
ijassa-1639	66	16	current	current	ADJ
ijassa-1639	66	17	iterate	iterate	NOUN
ijassa-1639	66	18	uk	uk	PROPN
ijassa-1639	66	19	∈	∈	PROPN
ijassa-1639	66	20	p	p	PROPN
ijassa-1639	66	21	,	,	PUNCT
ijassa-1639	66	22	the	the	DET
ijassa-1639	66	23	(	(	PUNCT
ijassa-1639	66	24	constrained	constrained	ADJ
ijassa-1639	66	25	)	)	PUNCT
ijassa-1639	66	26	piecewise	piecewise	NOUN
ijassa-1639	66	27	levenberg	levenberg	PROPN
ijassa-1639	66	28	–	–	PUNCT
ijassa-1639	66	29	marquardt	marquardt	PROPN
ijassa-1639	66	30	(	(	PUNCT
ijassa-1639	66	31	lm	lm	INTJ
ijassa-1639	66	32	)	)	PUNCT
ijassa-1639	66	33	method	method	NOUN
ijassa-1639	66	34	generates	generate	VERB
ijassa-1639	66	35	the	the	DET
ijassa-1639	66	36	next	next	ADJ
ijassa-1639	66	37	iterate	iterate	NOUN
ijassa-1639	66	38	as	as	ADP
ijassa-1639	66	39	uk	uk	PROPN
ijassa-1639	66	40	+	+	CCONJ
ijassa-1639	66	41	vk	vk	PROPN
ijassa-1639	66	42	,	,	PUNCT
ijassa-1639	66	43	where	where	SCONJ
ijassa-1639	66	44	vk	vk	NOUN
ijassa-1639	66	45	is	be	AUX
ijassa-1639	66	46	a	a	DET
ijassa-1639	66	47	solution	solution	NOUN
ijassa-1639	66	48	of	of	ADP
ijassa-1639	66	49	the	the	DET
ijassa-1639	66	50	problem	problem	NOUN
ijassa-1639	66	51	minimize	minimize	VERB
ijassa-1639	66	52	1	1	NUM
ijassa-1639	66	53	2	2	NUM
ijassa-1639	66	54	∥φ(uk	∥φ(uk	NOUN
ijassa-1639	66	55	)	)	PUNCT
ijassa-1639	67	1	+	+	NOUN
ijassa-1639	67	2	g(uk)v∥2	g(uk)v∥2	PUNCT
ijassa-1639	67	3	+	+	CCONJ
ijassa-1639	67	4	1	1	NUM
ijassa-1639	67	5	2	2	NUM
ijassa-1639	67	6	σ(uk)∥v∥2	σ(uk)∥v∥2	NOUN
ijassa-1639	67	7	subject	subject	ADJ
ijassa-1639	67	8	to	to	ADP
ijassa-1639	67	9	uk	uk	PROPN
ijassa-1639	67	10	+	+	CCONJ
ijassa-1639	67	11	v	v	NOUN
ijassa-1639	67	12	∈	∈	NOUN
ijassa-1639	67	13	p.	p.	NOUN
ijassa-1639	67	14	(	(	PUNCT
ijassa-1639	67	15	3.10	3.10	NUM
ijassa-1639	67	16	)	)	PUNCT
ijassa-1639	68	1	where	where	SCONJ
ijassa-1639	68	2	σ	σ	NOUN
ijassa-1639	68	3	:	:	PUNCT
ijassa-1639	68	4	p	p	X
ijassa-1639	68	5	→	→	PUNCT
ijassa-1639	68	6	r+	r+	NOUN
ijassa-1639	68	7	defines	define	VERB
ijassa-1639	68	8	the	the	DET
ijassa-1639	68	9	values	value	NOUN
ijassa-1639	68	10	of	of	ADP
ijassa-1639	68	11	the	the	DET
ijassa-1639	68	12	regularization	regularization	NOUN
ijassa-1639	68	13	parameter	parameter	NOUN
ijassa-1639	68	14	.	.	PUNCT
ijassa-1639	69	1	if	if	SCONJ
ijassa-1639	69	2	σ(uk	σ(uk	NOUN
ijassa-1639	69	3	)	)	PUNCT
ijassa-1639	69	4	>	>	X
ijassa-1639	69	5	0	0	NUM
ijassa-1639	69	6	,	,	PUNCT
ijassa-1639	69	7	and	and	CCONJ
ijassa-1639	69	8	if	if	SCONJ
ijassa-1639	69	9	p	p	NOUN
ijassa-1639	69	10	is	be	AUX
ijassa-1639	69	11	polyhedral	polyhedral	ADJ
ijassa-1639	69	12	,	,	PUNCT
ijassa-1639	69	13	then	then	ADV
ijassa-1639	69	14	(	(	PUNCT
ijassa-1639	69	15	3.10	3.10	NUM
ijassa-1639	69	16	)	)	PUNCT
ijassa-1639	69	17	is	be	AUX
ijassa-1639	69	18	a	a	DET
ijassa-1639	69	19	quadratic	quadratic	ADJ
ijassa-1639	69	20	programming	programming	NOUN
ijassa-1639	69	21	problem	problem	NOUN
ijassa-1639	69	22	with	with	ADP
ijassa-1639	69	23	a	a	DET
ijassa-1639	69	24	strongly	strongly	ADV
ijassa-1639	69	25	convex	convex	ADJ
ijassa-1639	69	26	objective	objective	ADJ
ijassa-1639	69	27	function	function	NOUN
ijassa-1639	69	28	,	,	PUNCT
ijassa-1639	69	29	and	and	CCONJ
ijassa-1639	69	30	in	in	ADP
ijassa-1639	69	31	particular	particular	ADJ
ijassa-1639	69	32	this	this	DET
ijassa-1639	69	33	subproblem	subproblem	NOUN
ijassa-1639	69	34	is	be	AUX
ijassa-1639	69	35	uniquely	uniquely	ADV
ijassa-1639	69	36	solvable	solvable	ADJ
ijassa-1639	69	37	.	.	PUNCT
ijassa-1639	70	1	it	it	PRON
ijassa-1639	70	2	follows	follow	VERB
ijassa-1639	70	3	from	from	ADP
ijassa-1639	70	4	(	(	PUNCT
ijassa-1639	70	5	3.8	3.8	NUM
ijassa-1639	70	6	)	)	PUNCT
ijassa-1639	70	7	and	and	CCONJ
ijassa-1639	70	8	(	(	PUNCT
ijassa-1639	70	9	3.9	3.9	NUM
ijassa-1639	70	10	)	)	PUNCT
ijassa-1639	70	11	that	that	SCONJ
ijassa-1639	70	12	the	the	DET
ijassa-1639	70	13	subproblem	subproblem	NOUN
ijassa-1639	70	14	(	(	PUNCT
ijassa-1639	70	15	3.10	3.10	NUM
ijassa-1639	70	16	)	)	PUNCT
ijassa-1639	70	17	can	can	AUX
ijassa-1639	70	18	be	be	AUX
ijassa-1639	70	19	written	write	VERB
ijassa-1639	70	20	in	in	ADP
ijassa-1639	70	21	the	the	DET
ijassa-1639	70	22	form	form	NOUN
ijassa-1639	70	23	minimize	minimize	VERB
ijassa-1639	70	24	1	1	NUM
ijassa-1639	70	25	2	2	NUM
ijassa-1639	70	26	∥φj(uk	∥φj(uk	NUM
ijassa-1639	70	27	)	)	PUNCT
ijassa-1639	71	1	+	+	CCONJ
ijassa-1639	71	2	(	(	PUNCT
ijassa-1639	71	3	φj)′(uk)v∥2	φj)′(uk)v∥2	NUM
ijassa-1639	71	4	+	+	NUM
ijassa-1639	71	5	1	1	NUM
ijassa-1639	71	6	2	2	NUM
ijassa-1639	71	7	σ(uk)∥v∥2	σ(uk)∥v∥2	NOUN
ijassa-1639	71	8	subject	subject	ADJ
ijassa-1639	71	9	to	to	ADP
ijassa-1639	71	10	uk	uk	PROPN
ijassa-1639	71	11	+	+	CCONJ
ijassa-1639	71	12	v	v	NOUN
ijassa-1639	71	13	∈	∈	NOUN
ijassa-1639	71	14	p	p	NOUN
ijassa-1639	71	15	,	,	PUNCT
ijassa-1639	71	16	with	with	ADP
ijassa-1639	71	17	some	some	DET
ijassa-1639	71	18	j	j	PROPN
ijassa-1639	71	19	∈	∈	PROPN
ijassa-1639	71	20	a(uk	a(uk	PROPN
ijassa-1639	71	21	)	)	PUNCT
ijassa-1639	71	22	(	(	PUNCT
ijassa-1639	71	23	that	that	PRON
ijassa-1639	71	24	may	may	AUX
ijassa-1639	71	25	be	be	AUX
ijassa-1639	71	26	different	different	ADJ
ijassa-1639	71	27	for	for	ADP
ijassa-1639	71	28	different	different	ADJ
ijassa-1639	71	29	k	k	NOUN
ijassa-1639	71	30	,	,	PUNCT
ijassa-1639	71	31	of	of	ADP
ijassa-1639	71	32	course	course	NOUN
ijassa-1639	71	33	)	)	PUNCT
ijassa-1639	71	34	.	.	PUNCT
ijassa-1639	72	1	this	this	PRON
ijassa-1639	72	2	means	mean	VERB
ijassa-1639	72	3	that	that	SCONJ
ijassa-1639	72	4	the	the	DET
ijassa-1639	72	5	iteration	iteration	NOUN
ijassa-1639	72	6	of	of	ADP
ijassa-1639	72	7	this	this	DET
ijassa-1639	72	8	method	method	NOUN
ijassa-1639	72	9	coincides	coincide	VERB
ijassa-1639	72	10	with	with	ADP
ijassa-1639	72	11	the	the	DET
ijassa-1639	72	12	iteration	iteration	NOUN
ijassa-1639	72	13	of	of	ADP
ijassa-1639	72	14	the	the	DET
ijassa-1639	72	15	constrained	constrain	VERB
ijassa-1639	72	16	lm	lm	NOUN
ijassa-1639	72	17	method	method	NOUN
ijassa-1639	72	18	applied	apply	VERB
ijassa-1639	72	19	to	to	ADP
ijassa-1639	72	20	the	the	DET
ijassa-1639	72	21	smooth	smooth	ADJ
ijassa-1639	72	22	constrained	constrain	VERB
ijassa-1639	72	23	equation	equation	NOUN
ijassa-1639	72	24	φj(u	φj(u	NOUN
ijassa-1639	72	25	)	)	PUNCT
ijassa-1639	72	26	=	=	SYM
ijassa-1639	72	27	0	0	NUM
ijassa-1639	72	28	,	,	PUNCT
ijassa-1639	72	29	u	u	PROPN
ijassa-1639	72	30	∈	∈	PROPN
ijassa-1639	72	31	p.	p.	NOUN
ijassa-1639	72	32	(	(	PUNCT
ijassa-1639	72	33	3.11	3.11	NUM
ijassa-1639	72	34	)	)	PUNCT
ijassa-1639	72	35	copyright	copyright	NOUN
ijassa-1639	72	36	©	©	PROPN
ijassa-1639	72	37	2024	2024	NUM
ijassa-1639	72	38	assa	assa	NOUN
ijassa-1639	72	39	.	.	PUNCT
ijassa-1639	73	1	adv	adv	PROPN
ijassa-1639	73	2	syst	syst	PROPN
ijassa-1639	73	3	sci	sci	PROPN
ijassa-1639	73	4	appl	appl	PROPN
ijassa-1639	73	5	(	(	PUNCT
ijassa-1639	73	6	2024	2024	NUM
ijassa-1639	73	7	)	)	PUNCT
ijassa-1639	73	8	22	22	NUM
ijassa-1639	73	9	a.	a.	PROPN
ijassa-1639	73	10	f.	f.	PROPN
ijassa-1639	73	11	izmailov	izmailov	PROPN
ijassa-1639	73	12	,	,	PUNCT
ijassa-1639	73	13	e.	e.	PROPN
ijassa-1639	73	14	i.	i.	PROPN
ijassa-1639	73	15	uskov	uskov	PROPN
ijassa-1639	73	16	,	,	PUNCT
ijassa-1639	73	17	yan	yan	PROPN
ijassa-1639	73	18	zhibai	zhibai	PROPN
ijassa-1639	73	19	in	in	ADP
ijassa-1639	73	20	the	the	DET
ijassa-1639	73	21	smooth	smooth	ADJ
ijassa-1639	73	22	case	case	NOUN
ijassa-1639	73	23	,	,	PUNCT
ijassa-1639	73	24	the	the	DET
ijassa-1639	73	25	constrained	constrain	VERB
ijassa-1639	73	26	lm	lm	NOUN
ijassa-1639	73	27	method	method	NOUN
ijassa-1639	73	28	was	be	AUX
ijassa-1639	73	29	proposed	propose	VERB
ijassa-1639	73	30	in	in	ADP
ijassa-1639	73	31	[	[	X
ijassa-1639	73	32	26	26	NUM
ijassa-1639	73	33	]	]	PUNCT
ijassa-1639	73	34	,	,	PUNCT
ijassa-1639	73	35	and	and	CCONJ
ijassa-1639	73	36	sharp	sharp	ADJ
ijassa-1639	73	37	results	result	NOUN
ijassa-1639	73	38	on	on	ADP
ijassa-1639	73	39	its	its	PRON
ijassa-1639	73	40	local	local	ADJ
ijassa-1639	73	41	superlinear	superlinear	NOUN
ijassa-1639	73	42	convergence	convergence	NOUN
ijassa-1639	73	43	were	be	AUX
ijassa-1639	73	44	obtained	obtain	VERB
ijassa-1639	73	45	in	in	ADP
ijassa-1639	73	46	[	[	X
ijassa-1639	73	47	1	1	NUM
ijassa-1639	73	48	]	]	PUNCT
ijassa-1639	73	49	.	.	PUNCT
ijassa-1639	74	1	the	the	DET
ijassa-1639	74	2	piecewise	piecewise	NOUN
ijassa-1639	74	3	smooth	smooth	ADJ
ijassa-1639	74	4	case	case	NOUN
ijassa-1639	74	5	was	be	AUX
ijassa-1639	74	6	studied	study	VERB
ijassa-1639	74	7	in	in	ADP
ijassa-1639	74	8	[	[	X
ijassa-1639	74	9	6	6	NUM
ijassa-1639	74	10	,	,	PUNCT
ijassa-1639	74	11	14	14	NUM
ijassa-1639	74	12	]	]	PUNCT
ijassa-1639	74	13	,	,	PUNCT
ijassa-1639	74	14	and	and	CCONJ
ijassa-1639	74	15	an	an	DET
ijassa-1639	74	16	overview	overview	NOUN
ijassa-1639	74	17	of	of	ADP
ijassa-1639	74	18	these	these	DET
ijassa-1639	74	19	developments	development	NOUN
ijassa-1639	74	20	can	can	AUX
ijassa-1639	74	21	be	be	AUX
ijassa-1639	74	22	found	find	VERB
ijassa-1639	74	23	in	in	ADP
ijassa-1639	74	24	[	[	X
ijassa-1639	74	25	17	17	NUM
ijassa-1639	74	26	]	]	PUNCT
ijassa-1639	74	27	.	.	PUNCT
ijassa-1639	75	1	see	see	VERB
ijassa-1639	75	2	also	also	ADV
ijassa-1639	75	3	the	the	DET
ijassa-1639	75	4	very	very	ADV
ijassa-1639	75	5	recent	recent	ADJ
ijassa-1639	75	6	improvements	improvement	NOUN
ijassa-1639	75	7	of	of	ADP
ijassa-1639	75	8	the	the	DET
ijassa-1639	75	9	local	local	ADJ
ijassa-1639	75	10	convergence	convergence	NOUN
ijassa-1639	75	11	analysis	analysis	NOUN
ijassa-1639	75	12	of	of	ADP
ijassa-1639	75	13	the	the	DET
ijassa-1639	75	14	piecewise	piecewise	NOUN
ijassa-1639	75	15	lm	lm	INTJ
ijassa-1639	75	16	method	method	NOUN
ijassa-1639	75	17	in	in	ADP
ijassa-1639	75	18	[	[	X
ijassa-1639	75	19	25	25	NUM
ijassa-1639	75	20	]	]	PUNCT
ijassa-1639	75	21	.	.	PUNCT
ijassa-1639	76	1	we	we	PRON
ijassa-1639	76	2	proceed	proceed	VERB
ijassa-1639	76	3	with	with	ADP
ijassa-1639	76	4	an	an	DET
ijassa-1639	76	5	exposition	exposition	NOUN
ijassa-1639	76	6	of	of	ADP
ijassa-1639	76	7	the	the	DET
ijassa-1639	76	8	globalized	globalized	ADJ
ijassa-1639	76	9	piecewise	piecewise	NOUN
ijassa-1639	76	10	lm	lm	X
ijassa-1639	76	11	method	method	NOUN
ijassa-1639	76	12	and	and	CCONJ
ijassa-1639	76	13	the	the	DET
ijassa-1639	76	14	related	related	ADJ
ijassa-1639	76	15	convergence	convergence	NOUN
ijassa-1639	76	16	theory	theory	NOUN
ijassa-1639	76	17	developed	develop	VERB
ijassa-1639	76	18	in	in	ADP
ijassa-1639	76	19	[	[	X
ijassa-1639	76	20	24	24	NUM
ijassa-1639	76	21	]	]	PUNCT
ijassa-1639	76	22	.	.	PUNCT
ijassa-1639	77	1	the	the	DET
ijassa-1639	77	2	algorithm	algorithm	NOUN
ijassa-1639	77	3	below	below	ADV
ijassa-1639	77	4	can	can	AUX
ijassa-1639	77	5	be	be	AUX
ijassa-1639	77	6	regarded	regard	VERB
ijassa-1639	77	7	as	as	ADP
ijassa-1639	77	8	a	a	DET
ijassa-1639	77	9	generalization	generalization	NOUN
ijassa-1639	77	10	of	of	ADP
ijassa-1639	77	11	the	the	DET
ijassa-1639	77	12	proposal	proposal	NOUN
ijassa-1639	77	13	in	in	ADP
ijassa-1639	77	14	[	[	X
ijassa-1639	77	15	18	18	NUM
ijassa-1639	77	16	]	]	PUNCT
ijassa-1639	77	17	,	,	PUNCT
ijassa-1639	77	18	where	where	SCONJ
ijassa-1639	77	19	the	the	DET
ijassa-1639	77	20	smooth	smooth	ADJ
ijassa-1639	77	21	case	case	NOUN
ijassa-1639	77	22	was	be	AUX
ijassa-1639	77	23	considered	consider	VERB
ijassa-1639	77	24	,	,	PUNCT
ijassa-1639	77	25	and	and	CCONJ
ijassa-1639	77	26	θ	θ	X
ijassa-1639	77	27	=	=	SYM
ijassa-1639	77	28	2	2	NUM
ijassa-1639	77	29	was	be	AUX
ijassa-1639	77	30	taken	take	VERB
ijassa-1639	77	31	in	in	ADP
ijassa-1639	77	32	the	the	DET
ijassa-1639	77	33	algorithm	algorithm	NOUN
ijassa-1639	77	34	.	.	PUNCT
ijassa-1639	78	1	algorithm	algorithm	PROPN
ijassa-1639	78	2	3.1	3.1	NUM
ijassa-1639	78	3	:	:	PUNCT
ijassa-1639	78	4	choose	choose	VERB
ijassa-1639	78	5	the	the	DET
ijassa-1639	78	6	parameters	parameter	NOUN
ijassa-1639	78	7	θ	θ	X
ijassa-1639	78	8	>	>	X
ijassa-1639	78	9	0	0	PROPN
ijassa-1639	78	10	,	,	PUNCT
ijassa-1639	78	11	ε	ε	PROPN
ijassa-1639	78	12	∈	∈	PROPN
ijassa-1639	78	13	(	(	PUNCT
ijassa-1639	78	14	0	0	NUM
ijassa-1639	78	15	,	,	PUNCT
ijassa-1639	78	16	1	1	NUM
ijassa-1639	78	17	)	)	PUNCT
ijassa-1639	78	18	and	and	CCONJ
ijassa-1639	78	19	κ	κ	PROPN
ijassa-1639	78	20	∈	∈	PROPN
ijassa-1639	78	21	(	(	PUNCT
ijassa-1639	78	22	0	0	NUM
ijassa-1639	78	23	,	,	PUNCT
ijassa-1639	78	24	1	1	NUM
ijassa-1639	78	25	)	)	PUNCT
ijassa-1639	78	26	.	.	PUNCT
ijassa-1639	79	1	choose	choose	VERB
ijassa-1639	79	2	u0	u0	PROPN
ijassa-1639	79	3	∈	∈	PROPN
ijassa-1639	79	4	p	p	NOUN
ijassa-1639	79	5	,	,	PUNCT
ijassa-1639	79	6	and	and	CCONJ
ijassa-1639	79	7	set	set	VERB
ijassa-1639	79	8	k	k	PROPN
ijassa-1639	79	9	=	=	PUNCT
ijassa-1639	79	10	0	0	NUM
ijassa-1639	79	11	.	.	NOUN
ijassa-1639	80	1	1	1	NUM
ijassa-1639	80	2	.	.	X
ijassa-1639	81	1	if	if	SCONJ
ijassa-1639	81	2	φ(uk	φ(uk	NOUN
ijassa-1639	81	3	)	)	PUNCT
ijassa-1639	81	4	=	=	SYM
ijassa-1639	81	5	0	0	NUM
ijassa-1639	81	6	,	,	PUNCT
ijassa-1639	81	7	stop	stop	VERB
ijassa-1639	81	8	.	.	PUNCT
ijassa-1639	82	1	2	2	X
ijassa-1639	82	2	.	.	X
ijassa-1639	82	3	set	set	VERB
ijassa-1639	82	4	σ(uk	σ(uk	NOUN
ijassa-1639	82	5	)	)	PUNCT
ijassa-1639	82	6	=	=	PUNCT
ijassa-1639	82	7	∥φ(uk)∥θ	∥φ(uk)∥θ	NOUN
ijassa-1639	82	8	,	,	PUNCT
ijassa-1639	82	9	and	and	CCONJ
ijassa-1639	82	10	compute	compute	NOUN
ijassa-1639	82	11	vk	vk	NOUN
ijassa-1639	82	12	as	as	ADP
ijassa-1639	82	13	the	the	DET
ijassa-1639	82	14	solution	solution	NOUN
ijassa-1639	82	15	of	of	ADP
ijassa-1639	82	16	(	(	PUNCT
ijassa-1639	82	17	3.10	3.10	NUM
ijassa-1639	82	18	)	)	PUNCT
ijassa-1639	82	19	.	.	PUNCT
ijassa-1639	83	1	if	if	SCONJ
ijassa-1639	83	2	vk	vk	VERB
ijassa-1639	83	3	=	=	SYM
ijassa-1639	83	4	0	0	NUM
ijassa-1639	83	5	,	,	PUNCT
ijassa-1639	83	6	stop	stop	VERB
ijassa-1639	83	7	.	.	PUNCT
ijassa-1639	84	1	3	3	X
ijassa-1639	84	2	.	.	X
ijassa-1639	84	3	set	set	VERB
ijassa-1639	84	4	α	α	NOUN
ijassa-1639	84	5	=	=	SYM
ijassa-1639	84	6	1	1	X
ijassa-1639	84	7	.	.	PUNCT
ijassa-1639	85	1	if	if	SCONJ
ijassa-1639	85	2	for	for	ADP
ijassa-1639	85	3	j	j	PROPN
ijassa-1639	85	4	∈	∈	PROPN
ijassa-1639	85	5	a(uk	a(uk	PROPN
ijassa-1639	85	6	)	)	PUNCT
ijassa-1639	85	7	such	such	ADJ
ijassa-1639	85	8	that	that	SCONJ
ijassa-1639	85	9	g(uk	g(uk	PROPN
ijassa-1639	85	10	)	)	PUNCT
ijassa-1639	85	11	=	=	SYM
ijassa-1639	85	12	(	(	PUNCT
ijassa-1639	85	13	φj)′(uk	φj)′(uk	PROPN
ijassa-1639	85	14	)	)	PUNCT
ijassa-1639	85	15	(	(	PUNCT
ijassa-1639	85	16	see	see	VERB
ijassa-1639	85	17	(	(	PUNCT
ijassa-1639	85	18	3.9	3.9	NUM
ijassa-1639	85	19	)	)	PUNCT
ijassa-1639	85	20	)	)	PUNCT
ijassa-1639	86	1	the	the	DET
ijassa-1639	86	2	inequality	inequality	NOUN
ijassa-1639	86	3	∥φ(uk	∥φ(uk	VERB
ijassa-1639	86	4	+	+	CCONJ
ijassa-1639	86	5	αvk)∥2	αvk)∥2	ADJ
ijassa-1639	86	6	≤	≤	ADJ
ijassa-1639	86	7	∥φ(uk)∥2	∥φ(uk)∥2	NOUN
ijassa-1639	86	8	−	−	PROPN
ijassa-1639	86	9	εσ(uk)α∥vk∥2	εσ(uk)α∥vk∥2	PROPN
ijassa-1639	86	10	(	(	PUNCT
ijassa-1639	86	11	3.12	3.12	NUM
ijassa-1639	86	12	)	)	PUNCT
ijassa-1639	86	13	holds	hold	NOUN
ijassa-1639	86	14	,	,	PUNCT
ijassa-1639	86	15	set	set	VERB
ijassa-1639	86	16	αk	αk	NOUN
ijassa-1639	86	17	=	=	NOUN
ijassa-1639	86	18	α	α	X
ijassa-1639	86	19	.	.	PUNCT
ijassa-1639	87	1	otherwise	otherwise	ADV
ijassa-1639	87	2	replace	replace	VERB
ijassa-1639	87	3	α	α	NOUN
ijassa-1639	87	4	by	by	ADP
ijassa-1639	87	5	κα	κα	NOUN
ijassa-1639	87	6	and	and	CCONJ
ijassa-1639	87	7	check	check	VERB
ijassa-1639	87	8	again	again	ADV
ijassa-1639	87	9	the	the	DET
ijassa-1639	87	10	inequality	inequality	NOUN
ijassa-1639	87	11	in	in	ADP
ijassa-1639	87	12	(	(	PUNCT
ijassa-1639	87	13	3.12	3.12	NUM
ijassa-1639	87	14	)	)	PUNCT
ijassa-1639	87	15	,	,	PUNCT
ijassa-1639	87	16	etc	etc	X
ijassa-1639	87	17	.	.	X
ijassa-1639	87	18	,	,	PUNCT
ijassa-1639	87	19	until	until	ADP
ijassa-1639	87	20	(	(	PUNCT
ijassa-1639	87	21	3.12	3.12	NUM
ijassa-1639	87	22	)	)	PUNCT
ijassa-1639	87	23	is	be	AUX
ijassa-1639	87	24	satisfied	satisfied	ADJ
ijassa-1639	87	25	,	,	PUNCT
ijassa-1639	87	26	and	and	CCONJ
ijassa-1639	87	27	then	then	ADV
ijassa-1639	87	28	set	set	VERB
ijassa-1639	87	29	αk	αk	NOUN
ijassa-1639	87	30	=	=	SYM
ijassa-1639	87	31	α	α	NOUN
ijassa-1639	87	32	.	.	PROPN
ijassa-1639	87	33	4	4	X
ijassa-1639	87	34	.	.	X
ijassa-1639	87	35	set	set	VERB
ijassa-1639	87	36	uk+1	uk+1	NOUN
ijassa-1639	87	37	=	=	SYM
ijassa-1639	87	38	uk	uk	PROPN
ijassa-1639	87	39	+	+	CCONJ
ijassa-1639	87	40	αkv	αkv	PROPN
ijassa-1639	87	41	k	k	NOUN
ijassa-1639	87	42	,	,	PUNCT
ijassa-1639	87	43	increase	increase	VERB
ijassa-1639	87	44	k	k	NOUN
ijassa-1639	87	45	by	by	ADP
ijassa-1639	87	46	1	1	NUM
ijassa-1639	87	47	and	and	CCONJ
ijassa-1639	87	48	go	go	VERB
ijassa-1639	87	49	to	to	PART
ijassa-1639	87	50	step	step	VERB
ijassa-1639	87	51	1	1	NUM
ijassa-1639	87	52	.	.	PUNCT
ijassa-1639	88	1	the	the	DET
ijassa-1639	88	2	key	key	ADJ
ijassa-1639	88	3	ingredient	ingredient	NOUN
ijassa-1639	88	4	of	of	ADP
ijassa-1639	88	5	the	the	DET
ijassa-1639	88	6	global	global	ADJ
ijassa-1639	88	7	convergence	convergence	NOUN
ijassa-1639	88	8	analysis	analysis	NOUN
ijassa-1639	88	9	is	be	AUX
ijassa-1639	88	10	the	the	DET
ijassa-1639	88	11	following	follow	VERB
ijassa-1639	88	12	assumption	assumption	NOUN
ijassa-1639	88	13	[	[	X
ijassa-1639	88	14	24	24	NUM
ijassa-1639	88	15	,	,	PUNCT
ijassa-1639	88	16	(	(	PUNCT
ijassa-1639	88	17	1.5	1.5	NUM
ijassa-1639	88	18	)	)	PUNCT
ijassa-1639	88	19	]	]	PUNCT
ijassa-1639	88	20	that	that	PRON
ijassa-1639	88	21	appeared	appear	VERB
ijassa-1639	88	22	before	before	ADV
ijassa-1639	88	23	in	in	ADP
ijassa-1639	88	24	[	[	X
ijassa-1639	88	25	13	13	NUM
ijassa-1639	88	26	,	,	PUNCT
ijassa-1639	88	27	(	(	PUNCT
ijassa-1639	88	28	4.8	4.8	NUM
ijassa-1639	88	29	)	)	PUNCT
ijassa-1639	88	30	]	]	PUNCT
ijassa-1639	88	31	,	,	PUNCT
ijassa-1639	88	32	[	[	X
ijassa-1639	88	33	16	16	NUM
ijassa-1639	88	34	,	,	PUNCT
ijassa-1639	88	35	(	(	PUNCT
ijassa-1639	88	36	32	32	NUM
ijassa-1639	88	37	)	)	PUNCT
ijassa-1639	88	38	]	]	PUNCT
ijassa-1639	88	39	,	,	PUNCT
ijassa-1639	88	40	and	and	CCONJ
ijassa-1639	88	41	in	in	ADP
ijassa-1639	88	42	[	[	X
ijassa-1639	88	43	3	3	NUM
ijassa-1639	88	44	,	,	PUNCT
ijassa-1639	88	45	(	(	PUNCT
ijassa-1639	88	46	0.6	0.6	NUM
ijassa-1639	88	47	)	)	PUNCT
ijassa-1639	88	48	]	]	PUNCT
ijassa-1639	88	49	:	:	PUNCT
ijassa-1639	88	50	∥φ(u)∥	∥φ(u)∥	PROPN
ijassa-1639	88	51	≤	≤	NUM
ijassa-1639	88	52	∥φj(u)∥	∥φj(u)∥	X
ijassa-1639	88	53	∀	∀	X
ijassa-1639	88	54	j	j	PROPN
ijassa-1639	88	55	∈	∈	PROPN
ijassa-1639	88	56	{	{	PUNCT
ijassa-1639	88	57	1	1	NUM
ijassa-1639	88	58	,	,	PUNCT
ijassa-1639	88	59	.	.	PUNCT
ijassa-1639	88	60	.	.	PUNCT
ijassa-1639	89	1	.	.	PUNCT
ijassa-1639	90	1	,	,	PUNCT
ijassa-1639	90	2	s	s	X
ijassa-1639	90	3	}	}	PUNCT
ijassa-1639	90	4	,	,	PUNCT
ijassa-1639	90	5	∀u	∀u	PROPN
ijassa-1639	90	6	∈	∈	PROPN
ijassa-1639	90	7	p.	p.	NOUN
ijassa-1639	90	8	(	(	PUNCT
ijassa-1639	90	9	3.13	3.13	NUM
ijassa-1639	90	10	)	)	PUNCT
ijassa-1639	90	11	theorem	theorem	VERB
ijassa-1639	90	12	3.1	3.1	NUM
ijassa-1639	90	13	:	:	PUNCT
ijassa-1639	90	14	let	let	VERB
ijassa-1639	90	15	φ	φ	PROPN
ijassa-1639	90	16	:	:	PUNCT
ijassa-1639	90	17	rp	rp	NOUN
ijassa-1639	90	18	→	→	PUNCT
ijassa-1639	90	19	rq	rq	AUX
ijassa-1639	90	20	be	be	AUX
ijassa-1639	90	21	a	a	DET
ijassa-1639	90	22	piecewise	piecewise	NOUN
ijassa-1639	90	23	smooth	smooth	ADJ
ijassa-1639	90	24	mapping	mapping	NOUN
ijassa-1639	90	25	with	with	ADP
ijassa-1639	90	26	continuously	continuously	ADV
ijassa-1639	90	27	differentiable	differentiable	VERB
ijassa-1639	90	28	smooth	smooth	ADJ
ijassa-1639	90	29	selection	selection	NOUN
ijassa-1639	90	30	mappings	mapping	NOUN
ijassa-1639	90	31	φ1	φ1	NOUN
ijassa-1639	90	32	,	,	PUNCT
ijassa-1639	90	33	.	.	PUNCT
ijassa-1639	90	34	.	.	PUNCT
ijassa-1639	91	1	.	.	PUNCT
ijassa-1639	92	1	,	,	PUNCT
ijassa-1639	92	2	φs	φs	PROPN
ijassa-1639	92	3	:	:	PUNCT
ijassa-1639	92	4	rp	rp	NOUN
ijassa-1639	92	5	→	→	SYM
ijassa-1639	92	6	rq	rq	X
ijassa-1639	92	7	.	.	PUNCT
ijassa-1639	93	1	let	let	VERB
ijassa-1639	93	2	p	p	PROPN
ijassa-1639	93	3	⊂	⊂	PRON
ijassa-1639	93	4	rp	rp	NOUN
ijassa-1639	93	5	be	be	AUX
ijassa-1639	93	6	a	a	DET
ijassa-1639	93	7	nonempty	nonempty	ADV
ijassa-1639	93	8	closed	close	VERB
ijassa-1639	93	9	convex	convex	NOUN
ijassa-1639	93	10	set	set	NOUN
ijassa-1639	93	11	,	,	PUNCT
ijassa-1639	93	12	and	and	CCONJ
ijassa-1639	93	13	assume	assume	VERB
ijassa-1639	93	14	that	that	SCONJ
ijassa-1639	93	15	(	(	PUNCT
ijassa-1639	93	16	3.13	3.13	NUM
ijassa-1639	93	17	)	)	PUNCT
ijassa-1639	93	18	holds	hold	VERB
ijassa-1639	93	19	.	.	PUNCT
ijassa-1639	94	1	let	let	VERB
ijassa-1639	94	2	g	g	NOUN
ijassa-1639	94	3	:	:	PUNCT
ijassa-1639	94	4	rp	rp	NOUN
ijassa-1639	94	5	→	→	PUNCT
ijassa-1639	94	6	rq×p	rq×p	NOUN
ijassa-1639	94	7	be	be	AUX
ijassa-1639	94	8	a	a	DET
ijassa-1639	94	9	fixed	fix	VERB
ijassa-1639	94	10	mapping	mapping	NOUN
ijassa-1639	94	11	satisfying	satisfying	ADJ
ijassa-1639	94	12	(	(	PUNCT
ijassa-1639	94	13	3.9	3.9	NUM
ijassa-1639	94	14	)	)	PUNCT
ijassa-1639	94	15	.	.	PUNCT
ijassa-1639	95	1	then	then	ADV
ijassa-1639	95	2	algorithm	algorithm	NOUN
ijassa-1639	95	3	3.1	3.1	NUM
ijassa-1639	95	4	uniquely	uniquely	ADV
ijassa-1639	95	5	defines	define	VERB
ijassa-1639	95	6	the	the	DET
ijassa-1639	95	7	iterates	iterate	NOUN
ijassa-1639	95	8	u0	u0	ADJ
ijassa-1639	95	9	,	,	PUNCT
ijassa-1639	95	10	u1	u1	NOUN
ijassa-1639	95	11	,	,	PUNCT
ijassa-1639	95	12	.	.	PUNCT
ijassa-1639	95	13	.	.	PUNCT
ijassa-1639	96	1	.	.	PUNCT
ijassa-1639	97	1	,	,	PUNCT
ijassa-1639	97	2	and	and	CCONJ
ijassa-1639	97	3	either	either	CCONJ
ijassa-1639	97	4	terminates	terminate	VERB
ijassa-1639	97	5	at	at	ADP
ijassa-1639	97	6	a	a	DET
ijassa-1639	97	7	point	point	NOUN
ijassa-1639	97	8	uk	uk	PROPN
ijassa-1639	97	9	∈	∈	PROPN
ijassa-1639	97	10	p	p	NOUN
ijassa-1639	97	11	satisfying	satisfy	VERB
ijassa-1639	97	12	⟨((φj)′(uk))⊤φ(uk	⟨((φj)′(uk))⊤φ(uk	PROPN
ijassa-1639	97	13	)	)	PUNCT
ijassa-1639	97	14	,	,	PUNCT
ijassa-1639	97	15	u−	u−	PROPN
ijassa-1639	97	16	uk⟩	uk⟩	NUM
ijassa-1639	97	17	≥	≥	NOUN
ijassa-1639	97	18	0	0	NUM
ijassa-1639	97	19	∀u	∀u	NOUN
ijassa-1639	97	20	∈	∈	NOUN
ijassa-1639	97	21	p	p	X
ijassa-1639	97	22	,	,	PUNCT
ijassa-1639	97	23	(	(	PUNCT
ijassa-1639	97	24	3.14	3.14	NUM
ijassa-1639	97	25	)	)	PUNCT
ijassa-1639	97	26	for	for	ADP
ijassa-1639	97	27	at	at	ADV
ijassa-1639	97	28	least	least	ADV
ijassa-1639	97	29	one	one	NUM
ijassa-1639	97	30	j	j	PROPN
ijassa-1639	97	31	∈	∈	PROPN
ijassa-1639	97	32	a(uk	a(uk	PROPN
ijassa-1639	97	33	)	)	PUNCT
ijassa-1639	97	34	,	,	PUNCT
ijassa-1639	97	35	or	or	CCONJ
ijassa-1639	97	36	generates	generate	VERB
ijassa-1639	97	37	an	an	DET
ijassa-1639	97	38	infinite	infinite	ADJ
ijassa-1639	97	39	sequence	sequence	NOUN
ijassa-1639	97	40	{	{	PUNCT
ijassa-1639	97	41	uk	uk	PROPN
ijassa-1639	97	42	}	}	PUNCT
ijassa-1639	97	43	,	,	PUNCT
ijassa-1639	97	44	and	and	CCONJ
ijassa-1639	97	45	any	any	DET
ijassa-1639	97	46	accumulation	accumulation	NOUN
ijassa-1639	97	47	point	point	NOUN
ijassa-1639	97	48	ū	ū	NOUN
ijassa-1639	97	49	of	of	ADP
ijassa-1639	97	50	this	this	DET
ijassa-1639	97	51	sequence	sequence	NOUN
ijassa-1639	97	52	belongs	belong	VERB
ijassa-1639	97	53	to	to	ADP
ijassa-1639	97	54	p	p	NOUN
ijassa-1639	97	55	and	and	CCONJ
ijassa-1639	97	56	satisfies	satisfie	NOUN
ijassa-1639	97	57	⟨((φj)′(ū))⊤φ(ū	⟨((φj)′(ū))⊤φ(ū	PROPN
ijassa-1639	97	58	)	)	PUNCT
ijassa-1639	97	59	,	,	PUNCT
ijassa-1639	97	60	u−	u−	PROPN
ijassa-1639	97	61	ū⟩	ū⟩	ADJ
ijassa-1639	97	62	≥	≥	NOUN
ijassa-1639	97	63	0	0	NUM
ijassa-1639	97	64	∀u	∀u	NOUN
ijassa-1639	97	65	∈	∈	NOUN
ijassa-1639	97	66	p	p	X
ijassa-1639	97	67	,	,	PUNCT
ijassa-1639	97	68	(	(	PUNCT
ijassa-1639	97	69	3.15	3.15	NUM
ijassa-1639	97	70	)	)	PUNCT
ijassa-1639	97	71	for	for	ADP
ijassa-1639	97	72	at	at	ADV
ijassa-1639	97	73	least	least	ADV
ijassa-1639	97	74	one	one	NUM
ijassa-1639	97	75	j	j	PROPN
ijassa-1639	97	76	∈	∈	PROPN
ijassa-1639	97	77	a(ū	a(ū	PROPN
ijassa-1639	97	78	)	)	PUNCT
ijassa-1639	97	79	.	.	PUNCT
ijassa-1639	98	1	we	we	PRON
ijassa-1639	98	2	complete	complete	VERB
ijassa-1639	98	3	this	this	DET
ijassa-1639	98	4	section	section	NOUN
ijassa-1639	98	5	with	with	ADP
ijassa-1639	98	6	a	a	DET
ijassa-1639	98	7	result	result	NOUN
ijassa-1639	98	8	on	on	ADP
ijassa-1639	98	9	asymptotic	asymptotic	ADJ
ijassa-1639	98	10	superlinear	superlinear	ADJ
ijassa-1639	98	11	convergence	convergence	NOUN
ijassa-1639	98	12	rate	rate	NOUN
ijassa-1639	98	13	,	,	PUNCT
ijassa-1639	98	14	and	and	CCONJ
ijassa-1639	98	15	in	in	ADP
ijassa-1639	98	16	order	order	NOUN
ijassa-1639	98	17	to	to	PART
ijassa-1639	98	18	do	do	AUX
ijassa-1639	98	19	this	this	PRON
ijassa-1639	98	20	,	,	PUNCT
ijassa-1639	98	21	we	we	PRON
ijassa-1639	98	22	need	need	VERB
ijassa-1639	98	23	the	the	DET
ijassa-1639	98	24	following	follow	VERB
ijassa-1639	98	25	two	two	NUM
ijassa-1639	98	26	assumptions	assumption	NOUN
ijassa-1639	98	27	.	.	PUNCT
ijassa-1639	99	1	the	the	DET
ijassa-1639	99	2	p	p	PROPN
ijassa-1639	99	3	-property	-property	NOUN
ijassa-1639	99	4	at	at	ADP
ijassa-1639	99	5	ū	ū	NOUN
ijassa-1639	99	6	,	,	PUNCT
ijassa-1639	99	7	introduced	introduce	VERB
ijassa-1639	99	8	in	in	ADP
ijassa-1639	99	9	[	[	X
ijassa-1639	99	10	14	14	NUM
ijassa-1639	99	11	,	,	PUNCT
ijassa-1639	99	12	p.	p.	NOUN
ijassa-1639	99	13	434	434	NUM
ijassa-1639	99	14	]	]	PUNCT
ijassa-1639	99	15	,	,	PUNCT
ijassa-1639	99	16	consists	consist	VERB
ijassa-1639	99	17	of	of	ADP
ijassa-1639	99	18	saying	say	VERB
ijassa-1639	99	19	that	that	SCONJ
ijassa-1639	99	20	uj	uj	PROPN
ijassa-1639	99	21	⊂	⊂	PROPN
ijassa-1639	99	22	u	u	PROPN
ijassa-1639	99	23	near	near	ADP
ijassa-1639	99	24	ū	ū	NOUN
ijassa-1639	99	25	for	for	ADP
ijassa-1639	99	26	all	all	DET
ijassa-1639	99	27	j	j	PROPN
ijassa-1639	99	28	∈	∈	PROPN
ijassa-1639	99	29	a(ū	a(ū	PROPN
ijassa-1639	99	30	)	)	PUNCT
ijassa-1639	99	31	,	,	PUNCT
ijassa-1639	99	32	where	where	SCONJ
ijassa-1639	99	33	u	u	PRON
ijassa-1639	99	34	stands	stand	VERB
ijassa-1639	99	35	for	for	ADP
ijassa-1639	99	36	the	the	DET
ijassa-1639	99	37	solution	solution	NOUN
ijassa-1639	99	38	set	set	VERB
ijassa-1639	99	39	of	of	ADP
ijassa-1639	99	40	(	(	PUNCT
ijassa-1639	99	41	2.3	2.3	NUM
ijassa-1639	99	42	)	)	PUNCT
ijassa-1639	99	43	,	,	PUNCT
ijassa-1639	99	44	while	while	SCONJ
ijassa-1639	99	45	uj	uj	PROPN
ijassa-1639	99	46	stands	stand	VERB
ijassa-1639	99	47	for	for	ADP
ijassa-1639	99	48	the	the	DET
ijassa-1639	99	49	solution	solution	NOUN
ijassa-1639	99	50	set	set	VERB
ijassa-1639	99	51	of	of	ADP
ijassa-1639	99	52	(	(	PUNCT
ijassa-1639	99	53	3.11	3.11	NUM
ijassa-1639	99	54	)	)	PUNCT
ijassa-1639	99	55	.	.	PUNCT
ijassa-1639	100	1	evidently	evidently	ADV
ijassa-1639	100	2	,	,	PUNCT
ijassa-1639	100	3	(	(	PUNCT
ijassa-1639	100	4	3.13	3.13	NUM
ijassa-1639	100	5	)	)	PUNCT
ijassa-1639	100	6	implies	imply	VERB
ijassa-1639	100	7	the	the	DET
ijassa-1639	100	8	p	p	ADJ
ijassa-1639	100	9	-property	-property	NOUN
ijassa-1639	100	10	at	at	ADP
ijassa-1639	100	11	any	any	DET
ijassa-1639	100	12	solution	solution	NOUN
ijassa-1639	100	13	.	.	PUNCT
ijassa-1639	101	1	another	another	DET
ijassa-1639	101	2	assumption	assumption	NOUN
ijassa-1639	101	3	we	we	PRON
ijassa-1639	101	4	need	need	VERB
ijassa-1639	101	5	is	be	AUX
ijassa-1639	101	6	the	the	DET
ijassa-1639	101	7	constrained	constrain	VERB
ijassa-1639	101	8	local	local	ADJ
ijassa-1639	101	9	lipschitzian	lipschitzian	ADJ
ijassa-1639	101	10	error	error	NOUN
ijassa-1639	101	11	bound	bind	VERB
ijassa-1639	101	12	for	for	ADP
ijassa-1639	101	13	each	each	DET
ijassa-1639	101	14	active	active	ADJ
ijassa-1639	101	15	selection	selection	NOUN
ijassa-1639	101	16	,	,	PUNCT
ijassa-1639	101	17	that	that	ADV
ijassa-1639	101	18	is	is	ADV
ijassa-1639	101	19	,	,	PUNCT
ijassa-1639	101	20	∀	∀	PUNCT
ijassa-1639	101	21	j	j	PROPN
ijassa-1639	101	22	∈	∈	PROPN
ijassa-1639	101	23	a(ū	a(ū	PROPN
ijassa-1639	101	24	)	)	PUNCT
ijassa-1639	101	25	dist(u	dist(u	PROPN
ijassa-1639	101	26	,	,	PUNCT
ijassa-1639	101	27	uj	uj	PROPN
ijassa-1639	101	28	)	)	PUNCT
ijassa-1639	101	29	=	=	SYM
ijassa-1639	101	30	o(∥φj(u)∥	o(∥φj(u)∥	NOUN
ijassa-1639	101	31	)	)	PUNCT
ijassa-1639	101	32	as	as	SCONJ
ijassa-1639	101	33	u	u	PROPN
ijassa-1639	101	34	∈	∈	PROPN
ijassa-1639	101	35	p	p	NOUN
ijassa-1639	101	36	tends	tend	VERB
ijassa-1639	101	37	to	to	ADP
ijassa-1639	101	38	ū.	ū.	PUNCT
ijassa-1639	101	39	(	(	PUNCT
ijassa-1639	101	40	3.16	3.16	NUM
ijassa-1639	101	41	)	)	PUNCT
ijassa-1639	101	42	theorem	theorem	NOUN
ijassa-1639	101	43	3.2	3.2	NUM
ijassa-1639	101	44	:	:	PUNCT
ijassa-1639	101	45	let	let	VERB
ijassa-1639	101	46	φ	φ	PROPN
ijassa-1639	101	47	:	:	PUNCT
ijassa-1639	101	48	rp	rp	NOUN
ijassa-1639	101	49	→	→	PUNCT
ijassa-1639	101	50	rq	rq	AUX
ijassa-1639	101	51	be	be	AUX
ijassa-1639	101	52	a	a	DET
ijassa-1639	101	53	given	give	VERB
ijassa-1639	101	54	mapping	mapping	NOUN
ijassa-1639	101	55	,	,	PUNCT
ijassa-1639	101	56	p	p	PROPN
ijassa-1639	101	57	⊂	⊂	PROPN
ijassa-1639	101	58	rp	rp	ADP
ijassa-1639	101	59	a	a	DET
ijassa-1639	101	60	closed	closed	ADJ
ijassa-1639	101	61	convex	convex	NOUN
ijassa-1639	101	62	set	set	NOUN
ijassa-1639	101	63	,	,	PUNCT
ijassa-1639	101	64	and	and	CCONJ
ijassa-1639	101	65	ū	ū	NOUN
ijassa-1639	101	66	∈	∈	PROPN
ijassa-1639	101	67	u	u	PROPN
ijassa-1639	101	68	.	.	PUNCT
ijassa-1639	102	1	assume	assume	VERB
ijassa-1639	102	2	that	that	SCONJ
ijassa-1639	102	3	φ	φ	PROPN
ijassa-1639	102	4	copyright	copyright	NOUN
ijassa-1639	102	5	©	©	PROPN
ijassa-1639	102	6	2024	2024	NUM
ijassa-1639	102	7	assa	assa	NOUN
ijassa-1639	102	8	.	.	PUNCT
ijassa-1639	103	1	adv	adv	PROPN
ijassa-1639	103	2	syst	syst	PROPN
ijassa-1639	103	3	sci	sci	PROPN
ijassa-1639	103	4	appl	appl	PROPN
ijassa-1639	103	5	(	(	PUNCT
ijassa-1639	103	6	2024	2024	NUM
ijassa-1639	103	7	)	)	PUNCT
ijassa-1639	103	8	piecewise	piecewise	NOUN
ijassa-1639	103	9	levenberg	levenberg	PROPN
ijassa-1639	103	10	–	–	PUNCT
ijassa-1639	103	11	marquardt	marquardt	PROPN
ijassa-1639	103	12	method	method	NOUN
ijassa-1639	103	13	for	for	ADP
ijassa-1639	103	14	gneps	gneps	NOUN
ijassa-1639	103	15	23	23	NUM
ijassa-1639	103	16	is	be	AUX
ijassa-1639	103	17	piecewise	piecewise	NOUN
ijassa-1639	103	18	smooth	smooth	ADJ
ijassa-1639	103	19	and	and	CCONJ
ijassa-1639	103	20	the	the	DET
ijassa-1639	103	21	derivatives	derivative	NOUN
ijassa-1639	103	22	of	of	ADP
ijassa-1639	103	23	its	its	PRON
ijassa-1639	103	24	smooth	smooth	ADJ
ijassa-1639	103	25	selection	selection	NOUN
ijassa-1639	103	26	mappings	mapping	NOUN
ijassa-1639	103	27	φ1	φ1	NOUN
ijassa-1639	103	28	,	,	PUNCT
ijassa-1639	103	29	.	.	PUNCT
ijassa-1639	103	30	.	.	PUNCT
ijassa-1639	104	1	.	.	PUNCT
ijassa-1639	105	1	,	,	PUNCT
ijassa-1639	105	2	φs	φs	PROPN
ijassa-1639	105	3	:	:	PUNCT
ijassa-1639	105	4	rp	rp	NOUN
ijassa-1639	105	5	→	→	NOUN
ijassa-1639	105	6	rq	rq	X
ijassa-1639	105	7	are	be	AUX
ijassa-1639	105	8	lipschitz	lipschitz	ADJ
ijassa-1639	105	9	-	-	PUNCT
ijassa-1639	105	10	continuous	continuous	ADJ
ijassa-1639	105	11	near	near	ADV
ijassa-1639	105	12	ū.	ū.	PUNCT
ijassa-1639	105	13	let	let	VERB
ijassa-1639	105	14	the	the	DET
ijassa-1639	105	15	p	p	NOUN
ijassa-1639	105	16	-property	-property	NOUN
ijassa-1639	105	17	at	at	ADP
ijassa-1639	105	18	ū	ū	NOUN
ijassa-1639	105	19	and	and	CCONJ
ijassa-1639	105	20	condition	condition	NOUN
ijassa-1639	105	21	(	(	PUNCT
ijassa-1639	105	22	3.16	3.16	NUM
ijassa-1639	105	23	)	)	PUNCT
ijassa-1639	105	24	as	as	SCONJ
ijassa-1639	105	25	u	u	PROPN
ijassa-1639	105	26	∈	∈	PROPN
ijassa-1639	105	27	p	p	NOUN
ijassa-1639	105	28	tends	tend	VERB
ijassa-1639	105	29	to	to	ADP
ijassa-1639	105	30	ū	ū	NOUN
ijassa-1639	105	31	be	be	AUX
ijassa-1639	105	32	satisfied	satisfied	ADJ
ijassa-1639	105	33	.	.	PUNCT
ijassa-1639	106	1	let	let	VERB
ijassa-1639	106	2	g	g	NOUN
ijassa-1639	106	3	:	:	PUNCT
ijassa-1639	106	4	rp	rp	NOUN
ijassa-1639	106	5	→	→	PUNCT
ijassa-1639	106	6	rq×p	rq×p	NOUN
ijassa-1639	106	7	be	be	AUX
ijassa-1639	106	8	a	a	DET
ijassa-1639	106	9	fixed	fix	VERB
ijassa-1639	106	10	mapping	mapping	NOUN
ijassa-1639	106	11	satisfying	satisfying	ADJ
ijassa-1639	106	12	(	(	PUNCT
ijassa-1639	106	13	3.9	3.9	NUM
ijassa-1639	106	14	)	)	PUNCT
ijassa-1639	106	15	.	.	PUNCT
ijassa-1639	107	1	then	then	ADV
ijassa-1639	107	2	,	,	PUNCT
ijassa-1639	107	3	if	if	SCONJ
ijassa-1639	107	4	algorithm	algorithm	PROPN
ijassa-1639	107	5	3.1	3.1	NUM
ijassa-1639	107	6	run	run	NOUN
ijassa-1639	107	7	with	with	ADP
ijassa-1639	107	8	θ	θ	PROPN
ijassa-1639	107	9	∈	∈	PROPN
ijassa-1639	107	10	(	(	PUNCT
ijassa-1639	107	11	0	0	NUM
ijassa-1639	107	12	,	,	PUNCT
ijassa-1639	107	13	2	2	NUM
ijassa-1639	107	14	]	]	PUNCT
ijassa-1639	107	15	generates	generate	VERB
ijassa-1639	107	16	an	an	DET
ijassa-1639	107	17	iterate	iterate	NOUN
ijassa-1639	107	18	close	close	ADJ
ijassa-1639	107	19	enough	enough	ADV
ijassa-1639	107	20	to	to	ADP
ijassa-1639	107	21	ū	ū	VERB
ijassa-1639	107	22	,	,	PUNCT
ijassa-1639	107	23	it	it	PRON
ijassa-1639	107	24	either	either	CCONJ
ijassa-1639	107	25	terminates	terminate	VERB
ijassa-1639	107	26	with	with	ADP
ijassa-1639	107	27	uk	uk	PROPN
ijassa-1639	107	28	∈	∈	PROPN
ijassa-1639	107	29	u	u	NOUN
ijassa-1639	107	30	,	,	PUNCT
ijassa-1639	107	31	or	or	CCONJ
ijassa-1639	107	32	generated	generate	VERB
ijassa-1639	107	33	an	an	DET
ijassa-1639	107	34	infinite	infinite	ADJ
ijassa-1639	107	35	sequence	sequence	NOUN
ijassa-1639	107	36	{	{	PUNCT
ijassa-1639	107	37	uk	uk	PROPN
ijassa-1639	107	38	}	}	PUNCT
ijassa-1639	107	39	convergent	convergent	NOUN
ijassa-1639	107	40	to	to	ADP
ijassa-1639	107	41	some	some	DET
ijassa-1639	107	42	u∗	u∗	NOUN
ijassa-1639	107	43	∈	∈	PROPN
ijassa-1639	107	44	u	u	NOUN
ijassa-1639	107	45	,	,	PUNCT
ijassa-1639	107	46	and	and	CCONJ
ijassa-1639	107	47	the	the	DET
ijassa-1639	107	48	rate	rate	NOUN
ijassa-1639	107	49	of	of	ADP
ijassa-1639	107	50	convergence	convergence	NOUN
ijassa-1639	107	51	is	be	AUX
ijassa-1639	107	52	superlinear	superlinear	ADJ
ijassa-1639	107	53	with	with	ADP
ijassa-1639	107	54	q	q	NOUN
ijassa-1639	107	55	-	-	PUNCT
ijassa-1639	107	56	order	order	NOUN
ijassa-1639	107	57	min{θ	min{θ	NOUN
ijassa-1639	108	1	+	+	CCONJ
ijassa-1639	108	2	1	1	NUM
ijassa-1639	108	3	,	,	PUNCT
ijassa-1639	108	4	2	2	NUM
ijassa-1639	108	5	}	}	PUNCT
ijassa-1639	108	6	.	.	PUNCT
ijassa-1639	109	1	one	one	PRON
ijassa-1639	109	2	can	can	AUX
ijassa-1639	109	3	easily	easily	ADV
ijassa-1639	109	4	see	see	VERB
ijassa-1639	109	5	that	that	SCONJ
ijassa-1639	109	6	the	the	DET
ijassa-1639	109	7	assumption	assumption	NOUN
ijassa-1639	109	8	(	(	PUNCT
ijassa-1639	109	9	3.13	3.13	NUM
ijassa-1639	109	10	)	)	PUNCT
ijassa-1639	109	11	,	,	PUNCT
ijassa-1639	109	12	and	and	CCONJ
ijassa-1639	109	13	hence	hence	ADV
ijassa-1639	109	14	,	,	PUNCT
ijassa-1639	109	15	the	the	DET
ijassa-1639	109	16	p	p	NOUN
ijassa-1639	109	17	-property	-property	NOUN
ijassa-1639	109	18	at	at	ADP
ijassa-1639	109	19	any	any	DET
ijassa-1639	109	20	solution	solution	NOUN
ijassa-1639	109	21	always	always	ADV
ijassa-1639	109	22	hold	hold	VERB
ijassa-1639	109	23	for	for	ADP
ijassa-1639	109	24	the	the	DET
ijassa-1639	109	25	gnep	gnep	PROPN
ijassa-1639	109	26	kkt	kkt	PROPN
ijassa-1639	109	27	-	-	PUNCT
ijassa-1639	109	28	type	type	NOUN
ijassa-1639	109	29	system	system	NOUN
ijassa-1639	109	30	reformulation	reformulation	NOUN
ijassa-1639	109	31	using	use	VERB
ijassa-1639	109	32	(	(	PUNCT
ijassa-1639	109	33	2.4	2.4	NUM
ijassa-1639	109	34	)	)	PUNCT
ijassa-1639	109	35	and	and	CCONJ
ijassa-1639	109	36	(	(	PUNCT
ijassa-1639	109	37	2.5	2.5	NUM
ijassa-1639	109	38	)	)	PUNCT
ijassa-1639	109	39	.	.	PUNCT
ijassa-1639	110	1	as	as	ADP
ijassa-1639	110	2	for	for	ADP
ijassa-1639	110	3	the	the	DET
ijassa-1639	110	4	assumption	assumption	NOUN
ijassa-1639	110	5	(	(	PUNCT
ijassa-1639	110	6	3.16	3.16	NUM
ijassa-1639	110	7	)	)	PUNCT
ijassa-1639	110	8	,	,	PUNCT
ijassa-1639	110	9	some	some	DET
ijassa-1639	110	10	natural	natural	ADJ
ijassa-1639	110	11	sufficient	sufficient	ADJ
ijassa-1639	110	12	conditions	condition	NOUN
ijassa-1639	110	13	for	for	ADP
ijassa-1639	110	14	it	it	PRON
ijassa-1639	110	15	were	be	AUX
ijassa-1639	110	16	derived	derive	VERB
ijassa-1639	110	17	in	in	ADP
ijassa-1639	110	18	[	[	X
ijassa-1639	110	19	14	14	NUM
ijassa-1639	110	20	,	,	PUNCT
ijassa-1639	110	21	theorems	theorem	NOUN
ijassa-1639	110	22	4	4	NUM
ijassa-1639	110	23	,	,	PUNCT
ijassa-1639	110	24	5	5	NUM
ijassa-1639	110	25	]	]	PUNCT
ijassa-1639	110	26	,	,	PUNCT
ijassa-1639	110	27	and	and	CCONJ
ijassa-1639	110	28	we	we	PRON
ijassa-1639	110	29	adapt	adapt	VERB
ijassa-1639	110	30	them	they	PRON
ijassa-1639	110	31	to	to	ADP
ijassa-1639	110	32	our	our	PRON
ijassa-1639	110	33	problem	problem	NOUN
ijassa-1639	110	34	setting	set	VERB
ijassa-1639	110	35	next	next	ADV
ijassa-1639	110	36	.	.	PUNCT
ijassa-1639	111	1	proposition	proposition	NOUN
ijassa-1639	111	2	3.1	3.1	NUM
ijassa-1639	111	3	:	:	PUNCT
ijassa-1639	111	4	let	let	VERB
ijassa-1639	111	5	fν	fν	VERB
ijassa-1639	111	6	:	:	PUNCT
ijassa-1639	111	7	rn	rn	PROPN
ijassa-1639	111	8	→	→	SYM
ijassa-1639	111	9	r	r	NOUN
ijassa-1639	111	10	and	and	CCONJ
ijassa-1639	111	11	gν	gν	INTJ
ijassa-1639	111	12	:	:	PUNCT
ijassa-1639	111	13	rn	rn	PROPN
ijassa-1639	111	14	→	→	PROPN
ijassa-1639	111	15	rmν	rmν	ADJ
ijassa-1639	111	16	,	,	PUNCT
ijassa-1639	111	17	ν	ν	PROPN
ijassa-1639	111	18	∈	∈	PROPN
ijassa-1639	111	19	{	{	PUNCT
ijassa-1639	111	20	1	1	NUM
ijassa-1639	111	21	,	,	PUNCT
ijassa-1639	111	22	.	.	PUNCT
ijassa-1639	111	23	.	.	PUNCT
ijassa-1639	112	1	.	.	PUNCT
ijassa-1639	113	1	,	,	PUNCT
ijassa-1639	113	2	n	n	CCONJ
ijassa-1639	113	3	}	}	PUNCT
ijassa-1639	113	4	,	,	PUNCT
ijassa-1639	113	5	be	be	AUX
ijassa-1639	113	6	twice	twice	ADV
ijassa-1639	113	7	differentiable	differentiable	ADJ
ijassa-1639	113	8	near	near	ADP
ijassa-1639	113	9	x̄	x̄	PROPN
ijassa-1639	113	10	∈	∈	PROPN
ijassa-1639	113	11	rn	rn	PROPN
ijassa-1639	113	12	,	,	PUNCT
ijassa-1639	113	13	with	with	ADP
ijassa-1639	113	14	their	their	PRON
ijassa-1639	113	15	second	second	ADJ
ijassa-1639	113	16	derivatives	derivative	NOUN
ijassa-1639	113	17	being	be	AUX
ijassa-1639	113	18	lipschitz	lipschitz	NOUN
ijassa-1639	113	19	-	-	PUNCT
ijassa-1639	113	20	continuous	continuous	ADJ
ijassa-1639	113	21	near	near	ADV
ijassa-1639	113	22	x̄.	x̄.	PUNCT
ijassa-1639	113	23	assume	assume	VERB
ijassa-1639	113	24	that	that	SCONJ
ijassa-1639	113	25	ū	ū	NOUN
ijassa-1639	113	26	=	=	SYM
ijassa-1639	113	27	(	(	PUNCT
ijassa-1639	113	28	x̄	x̄	NOUN
ijassa-1639	113	29	,	,	PUNCT
ijassa-1639	113	30	λ̄	λ̄	PRON
ijassa-1639	113	31	)	)	PUNCT
ijassa-1639	113	32	with	with	ADP
ijassa-1639	113	33	some	some	DET
ijassa-1639	113	34	λ̄	λ̄	ADP
ijassa-1639	113	35	∈	∈	PROPN
ijassa-1639	113	36	rm	rm	NOUN
ijassa-1639	113	37	is	be	AUX
ijassa-1639	113	38	a	a	DET
ijassa-1639	113	39	solution	solution	NOUN
ijassa-1639	113	40	of	of	ADP
ijassa-1639	113	41	(	(	PUNCT
ijassa-1639	113	42	2.2	2.2	NUM
ijassa-1639	113	43	)	)	PUNCT
ijassa-1639	113	44	,	,	PUNCT
ijassa-1639	113	45	where	where	SCONJ
ijassa-1639	113	46	the	the	DET
ijassa-1639	113	47	notation	notation	NOUN
ijassa-1639	113	48	introduces	introduce	VERB
ijassa-1639	113	49	in	in	ADP
ijassa-1639	113	50	section	section	NOUN
ijassa-1639	113	51	2	2	NUM
ijassa-1639	113	52	for	for	ADP
ijassa-1639	113	53	gnep	gnep	NOUN
ijassa-1639	113	54	is	be	AUX
ijassa-1639	113	55	employed	employ	VERB
ijassa-1639	113	56	.	.	PUNCT
ijassa-1639	114	1	let	let	VERB
ijassa-1639	114	2	φ	φ	PROPN
ijassa-1639	114	3	be	be	AUX
ijassa-1639	114	4	defined	define	VERB
ijassa-1639	114	5	in	in	ADP
ijassa-1639	114	6	(	(	PUNCT
ijassa-1639	114	7	2.5	2.5	NUM
ijassa-1639	114	8	)	)	PUNCT
ijassa-1639	114	9	,	,	PUNCT
ijassa-1639	114	10	with	with	ADP
ijassa-1639	114	11	its	its	PRON
ijassa-1639	114	12	smooth	smooth	ADJ
ijassa-1639	114	13	selection	selection	NOUN
ijassa-1639	114	14	mappings	mapping	NOUN
ijassa-1639	114	15	φj	φj	NOUN
ijassa-1639	114	16	,	,	PUNCT
ijassa-1639	114	17	j	j	PROPN
ijassa-1639	114	18	∈	∈	PROPN
ijassa-1639	114	19	{	{	PUNCT
ijassa-1639	114	20	1	1	NUM
ijassa-1639	114	21	,	,	PUNCT
ijassa-1639	114	22	.	.	PUNCT
ijassa-1639	114	23	.	.	PUNCT
ijassa-1639	115	1	.	.	PUNCT
ijassa-1639	116	1	2	2	NUM
ijassa-1639	116	2	m	m	NUM
ijassa-1639	116	3	}	}	PUNCT
ijassa-1639	116	4	,	,	PUNCT
ijassa-1639	116	5	defined	define	VERB
ijassa-1639	116	6	according	accord	VERB
ijassa-1639	116	7	to	to	ADP
ijassa-1639	116	8	(	(	PUNCT
ijassa-1639	116	9	2.7	2.7	NUM
ijassa-1639	116	10	)	)	PUNCT
ijassa-1639	116	11	,	,	PUNCT
ijassa-1639	116	12	and	and	CCONJ
ijassa-1639	116	13	let	let	VERB
ijassa-1639	116	14	p	p	PRON
ijassa-1639	116	15	be	be	AUX
ijassa-1639	116	16	defined	define	VERB
ijassa-1639	116	17	in	in	ADP
ijassa-1639	116	18	(	(	PUNCT
ijassa-1639	116	19	2.4	2.4	NUM
ijassa-1639	116	20	)	)	PUNCT
ijassa-1639	116	21	.	.	PUNCT
ijassa-1639	117	1	furthermore	furthermore	ADV
ijassa-1639	117	2	,	,	PUNCT
ijassa-1639	117	3	define	define	VERB
ijassa-1639	117	4	the	the	DET
ijassa-1639	117	5	index	index	NOUN
ijassa-1639	117	6	set	set	VERB
ijassa-1639	117	7	a	a	DET
ijassa-1639	117	8	=	=	X
ijassa-1639	117	9	{	{	PUNCT
ijassa-1639	117	10	i	i	NOUN
ijassa-1639	117	11	∈	∈	PROPN
ijassa-1639	117	12	{	{	PUNCT
ijassa-1639	117	13	1	1	NUM
ijassa-1639	117	14	,	,	PUNCT
ijassa-1639	117	15	.	.	PUNCT
ijassa-1639	117	16	.	.	PUNCT
ijassa-1639	118	1	.	.	PUNCT
ijassa-1639	119	1	,	,	PUNCT
ijassa-1639	119	2	m	m	VERB
ijassa-1639	119	3	}	}	PUNCT
ijassa-1639	119	4	|	|	ADV
ijassa-1639	119	5	gi(x̄	gi(x̄	PROPN
ijassa-1639	119	6	)	)	PUNCT
ijassa-1639	119	7	=	=	PUNCT
ijassa-1639	119	8	0	0	NUM
ijassa-1639	119	9	}	}	PUNCT
ijassa-1639	119	10	,	,	PUNCT
ijassa-1639	119	11	and	and	CCONJ
ijassa-1639	119	12	its	its	PRON
ijassa-1639	119	13	partitions	partition	NOUN
ijassa-1639	119	14	a+	a+	PUNCT
ijassa-1639	120	1	=	=	SYM
ijassa-1639	120	2	{	{	PUNCT
ijassa-1639	120	3	i	i	NOUN
ijassa-1639	120	4	∈	∈	VERB
ijassa-1639	120	5	a	a	DET
ijassa-1639	120	6	|	|	ADV
ijassa-1639	120	7	∃	∃	NOUN
ijassa-1639	120	8	ν	ν	X
ijassa-1639	120	9	∈	∈	PROPN
ijassa-1639	120	10	{	{	PUNCT
ijassa-1639	120	11	1	1	NUM
ijassa-1639	120	12	,	,	PUNCT
ijassa-1639	120	13	.	.	PUNCT
ijassa-1639	120	14	.	.	PUNCT
ijassa-1639	121	1	.	.	PUNCT
ijassa-1639	122	1	,	,	PUNCT
ijassa-1639	122	2	n	n	CCONJ
ijassa-1639	122	3	}	}	PUNCT
ijassa-1639	122	4	:	:	PUNCT
ijassa-1639	123	1	λ̄ν	λ̄ν	X
ijassa-1639	123	2	i	i	PRON
ijassa-1639	123	3	>	>	X
ijassa-1639	123	4	0	0	NUM
ijassa-1639	123	5	}	}	PUNCT
ijassa-1639	123	6	,	,	PUNCT
ijassa-1639	123	7	a0	a0	PROPN
ijassa-1639	123	8	=	=	PUNCT
ijassa-1639	123	9	a	a	DET
ijassa-1639	123	10	\	\	NOUN
ijassa-1639	123	11	a+	a+	NOUN
ijassa-1639	123	12	,	,	PUNCT
ijassa-1639	123	13	and	and	CCONJ
ijassa-1639	123	14	aν	aν	X
ijassa-1639	124	1	+	+	NOUN
ijassa-1639	124	2	=	=	SYM
ijassa-1639	124	3	{	{	PUNCT
ijassa-1639	124	4	i	i	NOUN
ijassa-1639	124	5	∈	∈	VERB
ijassa-1639	125	1	a	a	DET
ijassa-1639	125	2	|	|	NOUN
ijassa-1639	126	1	λ̄ν	λ̄ν	VERB
ijassa-1639	126	2	i	i	PRON
ijassa-1639	126	3	>	>	X
ijassa-1639	126	4	0	0	NUM
ijassa-1639	126	5	}	}	PUNCT
ijassa-1639	126	6	,	,	PUNCT
ijassa-1639	126	7	aν	aν	NOUN
ijassa-1639	126	8	0	0	NUM
ijassa-1639	126	9	=	=	PUNCT
ijassa-1639	126	10	a	a	DET
ijassa-1639	126	11	\	\	PROPN
ijassa-1639	126	12	aν	aν	NOUN
ijassa-1639	127	1	+	+	PROPN
ijassa-1639	127	2	,	,	PUNCT
ijassa-1639	127	3	for	for	ADP
ijassa-1639	127	4	every	every	DET
ijassa-1639	127	5	ν	ν	X
ijassa-1639	127	6	∈	∈	PROPN
ijassa-1639	127	7	{	{	PUNCT
ijassa-1639	127	8	1	1	NUM
ijassa-1639	127	9	,	,	PUNCT
ijassa-1639	127	10	.	.	PUNCT
ijassa-1639	127	11	.	.	PUNCT
ijassa-1639	128	1	.	.	PUNCT
ijassa-1639	128	2	,	,	PUNCT
ijassa-1639	128	3	n	n	CCONJ
ijassa-1639	128	4	}	}	PUNCT
ijassa-1639	128	5	.	.	PUNCT
ijassa-1639	129	1	if	if	SCONJ
ijassa-1639	129	2	for	for	ADP
ijassa-1639	129	3	any	any	DET
ijassa-1639	129	4	i	i	PROPN
ijassa-1639	129	5	⊂	⊂	PROPN
ijassa-1639	129	6	a0	a0	PROPN
ijassa-1639	129	7	and	and	CCONJ
ijassa-1639	129	8	any	any	DET
ijassa-1639	129	9	iν	iν	NOUN
ijassa-1639	129	10	⊂	⊂	ADJ
ijassa-1639	129	11	aν	aν	NOUN
ijassa-1639	129	12	0	0	NUM
ijassa-1639	129	13	,	,	PUNCT
ijassa-1639	129	14	ν	ν	PROPN
ijassa-1639	129	15	∈	∈	PROPN
ijassa-1639	129	16	{	{	PUNCT
ijassa-1639	129	17	1	1	NUM
ijassa-1639	129	18	,	,	PUNCT
ijassa-1639	129	19	.	.	PUNCT
ijassa-1639	129	20	.	.	PUNCT
ijassa-1639	130	1	.	.	PUNCT
ijassa-1639	131	1	,	,	PUNCT
ijassa-1639	131	2	n	n	CCONJ
ijassa-1639	131	3	}	}	PUNCT
ijassa-1639	131	4	,	,	PUNCT
ijassa-1639	131	5	the	the	DET
ijassa-1639	131	6	matrices	matrices	ADJ
ijassa-1639	131	7	∂l	∂l	PROPN
ijassa-1639	131	8	∂x	∂x	PROPN
ijassa-1639	131	9	(	(	PUNCT
ijassa-1639	131	10	x	x	NOUN
ijassa-1639	131	11	,	,	PUNCT
ijassa-1639	131	12	λ	λ	X
ijassa-1639	131	13	)	)	PUNCT
ijassa-1639	131	14	(	(	PUNCT
ijassa-1639	131	15	∂ga1	∂ga1	NUM
ijassa-1639	131	16	+	+	NOUN
ijassa-1639	131	17	∪i1	∪i1	NOUN
ijassa-1639	131	18	∂x1	∂x1	NOUN
ijassa-1639	131	19	(	(	PUNCT
ijassa-1639	131	20	x	x	NOUN
ijassa-1639	131	21	)	)	PUNCT
ijassa-1639	131	22	)	)	PUNCT
ijassa-1639	131	23	⊤	⊤	NOUN
ijassa-1639	131	24	0	0	NUM
ijassa-1639	131	25	.	.	PUNCT
ijassa-1639	131	26	.	.	PUNCT
ijassa-1639	132	1	.	.	PUNCT
ijassa-1639	133	1	0	0	NUM
ijassa-1639	133	2	0	0	NUM
ijassa-1639	134	1	(	(	PUNCT
ijassa-1639	134	2	∂ga2	∂ga2	NOUN
ijassa-1639	134	3	+	+	ADP
ijassa-1639	134	4	∪i2	∪i2	ADV
ijassa-1639	134	5	∂x2	∂x2	NOUN
ijassa-1639	134	6	(	(	PUNCT
ijassa-1639	134	7	x	x	NOUN
ijassa-1639	134	8	)	)	PUNCT
ijassa-1639	134	9	)	)	PUNCT
ijassa-1639	134	10	⊤	⊤	NOUN
ijassa-1639	134	11	.	.	PUNCT
ijassa-1639	134	12	.	.	PUNCT
ijassa-1639	135	1	.	.	PUNCT
ijassa-1639	136	1	0	0	NUM
ijassa-1639	136	2	...	...	PUNCT
ijassa-1639	136	3	...	...	PUNCT
ijassa-1639	136	4	.	.	PUNCT
ijassa-1639	136	5	.	.	PUNCT
ijassa-1639	136	6	.	.	PUNCT
ijassa-1639	137	1	...	...	PUNCT
ijassa-1639	137	2	0	0	PUNCT
ijassa-1639	137	3	.	.	PUNCT
ijassa-1639	137	4	.	.	PUNCT
ijassa-1639	137	5	.	.	PUNCT
ijassa-1639	137	6	.	.	PUNCT
ijassa-1639	137	7	.	.	PUNCT
ijassa-1639	137	8	.	.	PUNCT
ijassa-1639	138	1	(	(	PUNCT
ijassa-1639	138	2	∂gan	∂gan	VERB
ijassa-1639	138	3	+	+	VERB
ijassa-1639	138	4	∪in	∪in	PROPN
ijassa-1639	138	5	∂xn	∂xn	PROPN
ijassa-1639	138	6	(	(	PUNCT
ijassa-1639	138	7	x	x	NOUN
ijassa-1639	138	8	)	)	PUNCT
ijassa-1639	138	9	)	)	PUNCT
ijassa-1639	138	10	⊤	⊤	PROPN
ijassa-1639	138	11	g′a+∪i(x	g′a+∪i(x	NOUN
ijassa-1639	138	12	)	)	PUNCT
ijassa-1639	138	13	0	0	NUM
ijassa-1639	139	1			NOUN
ijassa-1639	139	2	have	have	VERB
ijassa-1639	139	3	the	the	DET
ijassa-1639	139	4	same	same	ADJ
ijassa-1639	139	5	rank	rank	NOUN
ijassa-1639	139	6	for	for	ADP
ijassa-1639	139	7	all	all	DET
ijassa-1639	139	8	(	(	PUNCT
ijassa-1639	139	9	x	x	NOUN
ijassa-1639	139	10	,	,	PUNCT
ijassa-1639	139	11	λ	λ	NOUN
ijassa-1639	139	12	)	)	PUNCT
ijassa-1639	139	13	∈	∈	PROPN
ijassa-1639	139	14	rn	rn	PROPN
ijassa-1639	139	15	×	×	PROPN
ijassa-1639	139	16	rm	rm	PROPN
ijassa-1639	139	17	near	near	ADV
ijassa-1639	139	18	(	(	PUNCT
ijassa-1639	139	19	x̄	x̄	NOUN
ijassa-1639	139	20	,	,	PUNCT
ijassa-1639	139	21	λ̄	λ̄	PRON
ijassa-1639	139	22	)	)	PUNCT
ijassa-1639	139	23	,	,	PUNCT
ijassa-1639	139	24	then	then	ADV
ijassa-1639	139	25	the	the	DET
ijassa-1639	139	26	piecewise	piecewise	NOUN
ijassa-1639	139	27	constrained	constrain	VERB
ijassa-1639	139	28	error	error	NOUN
ijassa-1639	139	29	bound	bind	VERB
ijassa-1639	139	30	condition	condition	NOUN
ijassa-1639	139	31	(	(	PUNCT
ijassa-1639	139	32	3.16	3.16	NUM
ijassa-1639	139	33	)	)	PUNCT
ijassa-1639	139	34	holds	hold	VERB
ijassa-1639	139	35	.	.	PUNCT
ijassa-1639	140	1	copyright	copyright	NOUN
ijassa-1639	140	2	©	©	PROPN
ijassa-1639	140	3	2024	2024	NUM
ijassa-1639	140	4	assa	assa	NOUN
ijassa-1639	140	5	.	.	PUNCT
ijassa-1639	141	1	adv	adv	PROPN
ijassa-1639	141	2	syst	syst	PROPN
ijassa-1639	141	3	sci	sci	PROPN
ijassa-1639	141	4	appl	appl	PROPN
ijassa-1639	141	5	(	(	PUNCT
ijassa-1639	141	6	2024	2024	NUM
ijassa-1639	141	7	)	)	PUNCT
ijassa-1639	141	8	24	24	NUM
ijassa-1639	141	9	a.	a.	PROPN
ijassa-1639	141	10	f.	f.	PROPN
ijassa-1639	141	11	izmailov	izmailov	PROPN
ijassa-1639	141	12	,	,	PUNCT
ijassa-1639	141	13	e.	e.	PROPN
ijassa-1639	141	14	i.	i.	PROPN
ijassa-1639	141	15	uskov	uskov	PROPN
ijassa-1639	141	16	,	,	PUNCT
ijassa-1639	141	17	yan	yan	PROPN
ijassa-1639	141	18	zhibai	zhibai	PROPN
ijassa-1639	141	19	corollary	corollary	PROPN
ijassa-1639	141	20	3.1	3.1	NUM
ijassa-1639	141	21	:	:	PUNCT
ijassa-1639	141	22	under	under	ADP
ijassa-1639	141	23	the	the	DET
ijassa-1639	141	24	assumptions	assumption	NOUN
ijassa-1639	141	25	of	of	ADP
ijassa-1639	141	26	proposition	proposition	NOUN
ijassa-1639	141	27	3.1	3.1	NUM
ijassa-1639	141	28	,	,	PUNCT
ijassa-1639	141	29	if	if	SCONJ
ijassa-1639	141	30	the	the	DET
ijassa-1639	141	31	matrix	matrix	ADJ
ijassa-1639	141	32	∂l	∂l	PROPN
ijassa-1639	141	33	∂x	∂x	PROPN
ijassa-1639	141	34	(	(	PUNCT
ijassa-1639	141	35	x̄	x̄	NOUN
ijassa-1639	141	36	,	,	PUNCT
ijassa-1639	141	37	λ̄	λ̄	NUM
ijassa-1639	141	38	)	)	PUNCT
ijassa-1639	141	39	(	(	PUNCT
ijassa-1639	141	40	∂ga1	∂ga1	NUM
ijassa-1639	141	41	+	+	NUM
ijassa-1639	141	42	∂x1	∂x1	NOUN
ijassa-1639	141	43	(	(	PUNCT
ijassa-1639	141	44	x̄	x̄	PROPN
ijassa-1639	141	45	)	)	PUNCT
ijassa-1639	141	46	)	)	PUNCT
ijassa-1639	141	47	⊤	⊤	NOUN
ijassa-1639	141	48	0	0	NUM
ijassa-1639	141	49	.	.	PUNCT
ijassa-1639	141	50	.	.	PUNCT
ijassa-1639	141	51	.	.	PUNCT
ijassa-1639	142	1	0	0	NUM
ijassa-1639	142	2	0	0	NUM
ijassa-1639	143	1	(	(	PUNCT
ijassa-1639	143	2	∂ga2	∂ga2	X
ijassa-1639	143	3	+	+	PUNCT
ijassa-1639	143	4	∂x2	∂x2	NOUN
ijassa-1639	143	5	(	(	PUNCT
ijassa-1639	143	6	x̄	x̄	PROPN
ijassa-1639	143	7	)	)	PUNCT
ijassa-1639	143	8	)	)	PUNCT
ijassa-1639	143	9	⊤	⊤	NOUN
ijassa-1639	143	10	.	.	PUNCT
ijassa-1639	143	11	.	.	PUNCT
ijassa-1639	144	1	.	.	PUNCT
ijassa-1639	145	1	0	0	NUM
ijassa-1639	145	2	...	...	PUNCT
ijassa-1639	145	3	...	...	PUNCT
ijassa-1639	145	4	.	.	PUNCT
ijassa-1639	145	5	.	.	PUNCT
ijassa-1639	145	6	.	.	PUNCT
ijassa-1639	146	1	...	...	PUNCT
ijassa-1639	146	2	0	0	PUNCT
ijassa-1639	146	3	.	.	PUNCT
ijassa-1639	146	4	.	.	PUNCT
ijassa-1639	146	5	.	.	PUNCT
ijassa-1639	146	6	.	.	PUNCT
ijassa-1639	146	7	.	.	PUNCT
ijassa-1639	146	8	.	.	PUNCT
ijassa-1639	147	1	(	(	PUNCT
ijassa-1639	147	2	∂gan	∂gan	VERB
ijassa-1639	147	3	+	+	CCONJ
ijassa-1639	147	4	∂xn	∂xn	PROPN
ijassa-1639	147	5	(	(	PUNCT
ijassa-1639	147	6	x̄	x̄	PROPN
ijassa-1639	147	7	)	)	PUNCT
ijassa-1639	147	8	)	)	PUNCT
ijassa-1639	147	9	⊤	⊤	PROPN
ijassa-1639	147	10	g′a(x̄	g′a(x̄	PROPN
ijassa-1639	147	11	)	)	PUNCT
ijassa-1639	147	12	0	0	NUM
ijassa-1639	148	1			NOUN
ijassa-1639	148	2	has	have	VERB
ijassa-1639	148	3	full	full	ADJ
ijassa-1639	148	4	row	row	NOUN
ijassa-1639	148	5	rank	rank	NOUN
ijassa-1639	148	6	,	,	PUNCT
ijassa-1639	148	7	then	then	ADV
ijassa-1639	148	8	the	the	DET
ijassa-1639	148	9	piecewise	piecewise	NOUN
ijassa-1639	148	10	constrained	constrain	VERB
ijassa-1639	148	11	error	error	NOUN
ijassa-1639	148	12	bound	bind	VERB
ijassa-1639	148	13	condition	condition	NOUN
ijassa-1639	148	14	(	(	PUNCT
ijassa-1639	148	15	3.16	3.16	NUM
ijassa-1639	148	16	)	)	PUNCT
ijassa-1639	148	17	holds	hold	VERB
ijassa-1639	148	18	.	.	PUNCT
ijassa-1639	149	1	the	the	DET
ijassa-1639	149	2	sufficient	sufficient	ADJ
ijassa-1639	149	3	condition	condition	NOUN
ijassa-1639	149	4	for	for	ADP
ijassa-1639	149	5	the	the	DET
ijassa-1639	149	6	piecewise	piecewise	NOUN
ijassa-1639	149	7	constrained	constrain	VERB
ijassa-1639	149	8	error	error	NOUN
ijassa-1639	149	9	bound	bind	VERB
ijassa-1639	149	10	in	in	ADP
ijassa-1639	149	11	proposition	proposition	NOUN
ijassa-1639	149	12	3.1	3.1	NUM
ijassa-1639	149	13	is	be	AUX
ijassa-1639	149	14	automatically	automatically	ADV
ijassa-1639	149	15	satisfied	satisfied	ADJ
ijassa-1639	149	16	if	if	SCONJ
ijassa-1639	149	17	fν	fν	NOUN
ijassa-1639	149	18	is	be	AUX
ijassa-1639	149	19	quadratic	quadratic	ADJ
ijassa-1639	149	20	and	and	CCONJ
ijassa-1639	149	21	gν	gν	PROPN
ijassa-1639	149	22	is	be	AUX
ijassa-1639	149	23	affine	affine	ADJ
ijassa-1639	149	24	,	,	PUNCT
ijassa-1639	149	25	for	for	ADP
ijassa-1639	149	26	all	all	PRON
ijassa-1639	149	27	ν	ν	X
ijassa-1639	149	28	∈	∈	PROPN
ijassa-1639	149	29	{	{	PUNCT
ijassa-1639	149	30	1	1	NUM
ijassa-1639	149	31	,	,	PUNCT
ijassa-1639	149	32	.	.	PUNCT
ijassa-1639	149	33	.	.	PUNCT
ijassa-1639	150	1	.	.	PUNCT
ijassa-1639	150	2	,	,	PUNCT
ijassa-1639	150	3	n	n	CCONJ
ijassa-1639	150	4	}	}	PUNCT
ijassa-1639	150	5	.	.	PUNCT
ijassa-1639	151	1	observe	observe	VERB
ijassa-1639	151	2	also	also	ADV
ijassa-1639	151	3	that	that	SCONJ
ijassa-1639	151	4	any	any	DET
ijassa-1639	151	5	strict	strict	ADJ
ijassa-1639	151	6	complementarity	complementarity	NOUN
ijassa-1639	151	7	-	-	PUNCT
ijassa-1639	151	8	like	like	ADJ
ijassa-1639	151	9	conditions	condition	NOUN
ijassa-1639	151	10	are	be	AUX
ijassa-1639	151	11	neither	neither	ADV
ijassa-1639	151	12	involved	involve	VERB
ijassa-1639	151	13	in	in	ADP
ijassa-1639	151	14	proposition	proposition	NOUN
ijassa-1639	151	15	3.1	3.1	NUM
ijassa-1639	151	16	,	,	PUNCT
ijassa-1639	151	17	nor	nor	CCONJ
ijassa-1639	151	18	in	in	ADP
ijassa-1639	151	19	its	its	PRON
ijassa-1639	151	20	corollary	corollary	ADJ
ijassa-1639	151	21	3.1	3.1	NUM
ijassa-1639	151	22	.	.	NOUN
ijassa-1639	151	23	4	4	NUM
ijassa-1639	151	24	.	.	X
ijassa-1639	151	25	numerical	numerical	PROPN
ijassa-1639	151	26	results	result	NOUN
ijassa-1639	151	27	the	the	DET
ijassa-1639	151	28	test	test	NOUN
ijassa-1639	151	29	set	set	VERB
ijassa-1639	151	30	used	use	VERB
ijassa-1639	151	31	for	for	ADP
ijassa-1639	151	32	the	the	DET
ijassa-1639	151	33	numerical	numerical	ADJ
ijassa-1639	151	34	comparisons	comparison	NOUN
ijassa-1639	151	35	presented	present	VERB
ijassa-1639	151	36	below	below	ADV
ijassa-1639	151	37	is	be	AUX
ijassa-1639	151	38	a	a	DET
ijassa-1639	151	39	collection	collection	NOUN
ijassa-1639	151	40	of	of	ADP
ijassa-1639	151	41	gneps	gneps	NOUN
ijassa-1639	151	42	from	from	ADP
ijassa-1639	151	43	[	[	X
ijassa-1639	151	44	5	5	NUM
ijassa-1639	151	45	]	]	PUNCT
ijassa-1639	151	46	,	,	PUNCT
ijassa-1639	151	47	later	later	ADV
ijassa-1639	151	48	also	also	ADV
ijassa-1639	151	49	used	use	VERB
ijassa-1639	151	50	in	in	ADP
ijassa-1639	151	51	[	[	X
ijassa-1639	151	52	4	4	NUM
ijassa-1639	151	53	,	,	PUNCT
ijassa-1639	151	54	13	13	NUM
ijassa-1639	151	55	]	]	PUNCT
ijassa-1639	151	56	.	.	PUNCT
ijassa-1639	152	1	information	information	NOUN
ijassa-1639	152	2	about	about	ADP
ijassa-1639	152	3	these	these	DET
ijassa-1639	152	4	test	test	NOUN
ijassa-1639	152	5	problems	problem	NOUN
ijassa-1639	152	6	and	and	CCONJ
ijassa-1639	152	7	references	reference	NOUN
ijassa-1639	152	8	to	to	ADP
ijassa-1639	152	9	their	their	PRON
ijassa-1639	152	10	sources	source	NOUN
ijassa-1639	152	11	and	and	CCONJ
ijassa-1639	152	12	detailed	detailed	ADJ
ijassa-1639	152	13	descriptions	description	NOUN
ijassa-1639	152	14	are	be	AUX
ijassa-1639	152	15	provided	provide	VERB
ijassa-1639	152	16	in	in	ADP
ijassa-1639	152	17	[	[	X
ijassa-1639	152	18	5	5	NUM
ijassa-1639	152	19	]	]	PUNCT
ijassa-1639	152	20	.	.	PUNCT
ijassa-1639	153	1	for	for	ADP
ijassa-1639	153	2	each	each	DET
ijassa-1639	153	3	test	test	NOUN
ijassa-1639	153	4	problem	problem	NOUN
ijassa-1639	153	5	,	,	PUNCT
ijassa-1639	153	6	20	20	NUM
ijassa-1639	153	7	random	random	ADJ
ijassa-1639	153	8	starting	starting	NOUN
ijassa-1639	153	9	points	point	NOUN
ijassa-1639	153	10	were	be	AUX
ijassa-1639	153	11	used	use	VERB
ijassa-1639	153	12	(	(	PUNCT
ijassa-1639	153	13	the	the	DET
ijassa-1639	153	14	same	same	ADJ
ijassa-1639	153	15	for	for	ADP
ijassa-1639	153	16	all	all	DET
ijassa-1639	153	17	algorithms	algorithm	NOUN
ijassa-1639	153	18	involved	involve	VERB
ijassa-1639	153	19	,	,	PUNCT
ijassa-1639	153	20	with	with	ADP
ijassa-1639	153	21	random	random	ADJ
ijassa-1639	153	22	components	component	NOUN
ijassa-1639	153	23	of	of	ADP
ijassa-1639	153	24	x0	x0	PROPN
ijassa-1639	153	25	distributed	distribute	VERB
ijassa-1639	153	26	uniformly	uniformly	ADV
ijassa-1639	153	27	within	within	ADP
ijassa-1639	153	28	(	(	PUNCT
ijassa-1639	153	29	0.1	0.1	NUM
ijassa-1639	153	30	,	,	PUNCT
ijassa-1639	153	31	20	20	NUM
ijassa-1639	153	32	)	)	PUNCT
ijassa-1639	153	33	,	,	PUNCT
ijassa-1639	153	34	which	which	PRON
ijassa-1639	153	35	guarantees	guarantee	VERB
ijassa-1639	153	36	that	that	SCONJ
ijassa-1639	153	37	all	all	DET
ijassa-1639	153	38	the	the	DET
ijassa-1639	153	39	functions	function	NOUN
ijassa-1639	153	40	appearing	appear	VERB
ijassa-1639	153	41	in	in	ADP
ijassa-1639	153	42	all	all	DET
ijassa-1639	153	43	test	test	NOUN
ijassa-1639	153	44	problems	problem	NOUN
ijassa-1639	153	45	are	be	AUX
ijassa-1639	153	46	well	well	ADV
ijassa-1639	153	47	-	-	PUNCT
ijassa-1639	153	48	defined	define	VERB
ijassa-1639	153	49	at	at	ADP
ijassa-1639	153	50	x0	x0	PROPN
ijassa-1639	153	51	.	.	PUNCT
ijassa-1639	154	1	furthermore	furthermore	ADV
ijassa-1639	154	2	,	,	PUNCT
ijassa-1639	154	3	λ0	λ0	NOUN
ijassa-1639	154	4	and	and	CCONJ
ijassa-1639	154	5	y0	y0	NOUN
ijassa-1639	154	6	were	be	AUX
ijassa-1639	154	7	chosen	choose	VERB
ijassa-1639	154	8	according	accord	VERB
ijassa-1639	154	9	to	to	ADP
ijassa-1639	154	10	[	[	X
ijassa-1639	154	11	13	13	NUM
ijassa-1639	154	12	,	,	PUNCT
ijassa-1639	154	13	section	section	NOUN
ijassa-1639	154	14	5	5	NUM
ijassa-1639	154	15	]	]	PUNCT
ijassa-1639	154	16	.	.	PUNCT
ijassa-1639	155	1	throughout	throughout	ADP
ijassa-1639	155	2	the	the	DET
ijassa-1639	155	3	rest	rest	NOUN
ijassa-1639	155	4	of	of	ADP
ijassa-1639	155	5	this	this	DET
ijassa-1639	155	6	section	section	NOUN
ijassa-1639	155	7	,	,	PUNCT
ijassa-1639	155	8	p	p	PROPN
ijassa-1639	155	9	is	be	AUX
ijassa-1639	155	10	defined	define	VERB
ijassa-1639	155	11	according	accord	VERB
ijassa-1639	155	12	to	to	ADP
ijassa-1639	155	13	(	(	PUNCT
ijassa-1639	155	14	2.4	2.4	NUM
ijassa-1639	155	15	)	)	PUNCT
ijassa-1639	155	16	.	.	PUNCT
ijassa-1639	156	1	we	we	PRON
ijassa-1639	156	2	compared	compare	VERB
ijassa-1639	156	3	the	the	DET
ijassa-1639	156	4	performance	performance	NOUN
ijassa-1639	156	5	of	of	ADP
ijassa-1639	156	6	algorithm	algorithm	NOUN
ijassa-1639	156	7	3.1	3.1	NUM
ijassa-1639	156	8	applied	apply	VERB
ijassa-1639	156	9	to	to	ADP
ijassa-1639	156	10	(	(	PUNCT
ijassa-1639	156	11	2.3	2.3	NUM
ijassa-1639	156	12	)	)	PUNCT
ijassa-1639	156	13	with	with	ADP
ijassa-1639	156	14	φ	φ	PROPN
ijassa-1639	156	15	defined	define	VERB
ijassa-1639	156	16	in	in	ADP
ijassa-1639	156	17	(	(	PUNCT
ijassa-1639	156	18	2.5	2.5	NUM
ijassa-1639	156	19	)	)	PUNCT
ijassa-1639	156	20	(	(	PUNCT
ijassa-1639	156	21	abbreviated	abbreviate	VERB
ijassa-1639	156	22	below	below	ADV
ijassa-1639	156	23	as	as	ADP
ijassa-1639	156	24	pwlm	pwlm	PROPN
ijassa-1639	156	25	)	)	PUNCT
ijassa-1639	156	26	with	with	ADP
ijassa-1639	156	27	the	the	DET
ijassa-1639	156	28	following	following	ADJ
ijassa-1639	156	29	alternatives	alternative	NOUN
ijassa-1639	156	30	:	:	PUNCT
ijassa-1639	156	31	•	•	NOUN
ijassa-1639	156	32	globalized	globalize	VERB
ijassa-1639	156	33	lp	lp	PROPN
ijassa-1639	156	34	-	-	PUNCT
ijassa-1639	156	35	newton	newton	PROPN
ijassa-1639	156	36	method	method	NOUN
ijassa-1639	156	37	from	from	ADP
ijassa-1639	156	38	[	[	X
ijassa-1639	156	39	13	13	NUM
ijassa-1639	156	40	,	,	PUNCT
ijassa-1639	156	41	algorithm	algorithm	NOUN
ijassa-1639	156	42	1	1	NUM
ijassa-1639	156	43	]	]	PUNCT
ijassa-1639	156	44	supplied	supply	VERB
ijassa-1639	156	45	with	with	ADP
ijassa-1639	156	46	all	all	DET
ijassa-1639	156	47	the	the	DET
ijassa-1639	156	48	performance	performance	NOUN
ijassa-1639	156	49	-	-	PUNCT
ijassa-1639	156	50	improving	improve	VERB
ijassa-1639	156	51	modification	modification	NOUN
ijassa-1639	156	52	proposed	propose	VERB
ijassa-1639	156	53	in	in	ADP
ijassa-1639	156	54	[	[	X
ijassa-1639	156	55	13	13	NUM
ijassa-1639	156	56	,	,	PUNCT
ijassa-1639	156	57	section	section	NOUN
ijassa-1639	156	58	5	5	NUM
ijassa-1639	156	59	]	]	PUNCT
ijassa-1639	156	60	,	,	PUNCT
ijassa-1639	156	61	and	and	CCONJ
ijassa-1639	156	62	applied	apply	VERB
ijassa-1639	156	63	to	to	ADP
ijassa-1639	156	64	the	the	DET
ijassa-1639	156	65	same	same	ADJ
ijassa-1639	156	66	instances	instance	NOUN
ijassa-1639	156	67	of	of	ADP
ijassa-1639	156	68	(	(	PUNCT
ijassa-1639	156	69	2.3	2.3	NUM
ijassa-1639	156	70	)	)	PUNCT
ijassa-1639	156	71	as	as	ADP
ijassa-1639	156	72	pwlm	pwlm	PROPN
ijassa-1639	156	73	(	(	PUNCT
ijassa-1639	156	74	abbreviated	abbreviate	VERB
ijassa-1639	156	75	as	as	ADP
ijassa-1639	156	76	pwlpn	pwlpn	NOUN
ijassa-1639	156	77	)	)	PUNCT
ijassa-1639	156	78	.	.	PUNCT
ijassa-1639	157	1	•	•	NOUN
ijassa-1639	157	2	the	the	DET
ijassa-1639	157	3	lm	lm	ADJ
ijassa-1639	157	4	method	method	NOUN
ijassa-1639	157	5	globalized	globalize	VERB
ijassa-1639	157	6	according	accord	VERB
ijassa-1639	157	7	to	to	ADP
ijassa-1639	157	8	algorithm	algorithm	NOUN
ijassa-1639	157	9	3.1	3.1	NUM
ijassa-1639	157	10	,	,	PUNCT
ijassa-1639	157	11	but	but	CCONJ
ijassa-1639	157	12	applied	apply	VERB
ijassa-1639	157	13	to	to	ADP
ijassa-1639	157	14	(	(	PUNCT
ijassa-1639	157	15	2.3	2.3	NUM
ijassa-1639	157	16	)	)	PUNCT
ijassa-1639	157	17	with	with	ADP
ijassa-1639	157	18	smooth	smooth	ADJ
ijassa-1639	157	19	φ	φ	PROPN
ijassa-1639	157	20	defined	define	VERB
ijassa-1639	157	21	in	in	ADP
ijassa-1639	157	22	(	(	PUNCT
ijassa-1639	157	23	2.6	2.6	NUM
ijassa-1639	157	24	)	)	PUNCT
ijassa-1639	157	25	(	(	PUNCT
ijassa-1639	157	26	abbreviated	abbreviate	VERB
ijassa-1639	157	27	as	as	ADP
ijassa-1639	157	28	lm	lm	NOUN
ijassa-1639	157	29	-	-	PUNCT
ijassa-1639	157	30	had	have	AUX
ijassa-1639	157	31	)	)	PUNCT
ijassa-1639	157	32	.	.	PUNCT
ijassa-1639	158	1	•	•	NUM
ijassa-1639	158	2	globalized	globalize	VERB
ijassa-1639	158	3	lp	lp	PROPN
ijassa-1639	158	4	-	-	PUNCT
ijassa-1639	158	5	newton	newton	PROPN
ijassa-1639	158	6	method	method	NOUN
ijassa-1639	158	7	,	,	PUNCT
ijassa-1639	158	8	the	the	DET
ijassa-1639	158	9	same	same	ADJ
ijassa-1639	158	10	as	as	ADP
ijassa-1639	158	11	pwlpn	pwlpn	NOUN
ijassa-1639	158	12	,	,	PUNCT
ijassa-1639	158	13	but	but	CCONJ
ijassa-1639	158	14	applied	apply	VERB
ijassa-1639	158	15	to	to	ADP
ijassa-1639	158	16	(	(	PUNCT
ijassa-1639	158	17	2.3	2.3	NUM
ijassa-1639	158	18	)	)	PUNCT
ijassa-1639	158	19	with	with	ADP
ijassa-1639	158	20	smooth	smooth	ADJ
ijassa-1639	158	21	φ	φ	PROPN
ijassa-1639	158	22	defined	define	VERB
ijassa-1639	158	23	in	in	ADP
ijassa-1639	158	24	(	(	PUNCT
ijassa-1639	158	25	2.6	2.6	NUM
ijassa-1639	158	26	)	)	PUNCT
ijassa-1639	158	27	(	(	PUNCT
ijassa-1639	158	28	abbreviated	abbreviate	VERB
ijassa-1639	158	29	as	as	ADP
ijassa-1639	158	30	lpn	lpn	NOUN
ijassa-1639	158	31	-	-	PUNCT
ijassa-1639	158	32	had	have	AUX
ijassa-1639	158	33	)	)	PUNCT
ijassa-1639	158	34	.	.	PUNCT
ijassa-1639	159	1	in	in	ADP
ijassa-1639	159	2	case	case	NOUN
ijassa-1639	159	3	of	of	ADP
ijassa-1639	159	4	a	a	DET
ijassa-1639	159	5	smooth	smooth	ADJ
ijassa-1639	159	6	φ	φ	NOUN
ijassa-1639	159	7	from	from	ADP
ijassa-1639	159	8	(	(	PUNCT
ijassa-1639	159	9	2.6	2.6	NUM
ijassa-1639	159	10	)	)	PUNCT
ijassa-1639	159	11	,	,	PUNCT
ijassa-1639	159	12	(	(	PUNCT
ijassa-1639	159	13	3.9	3.9	NUM
ijassa-1639	159	14	)	)	PUNCT
ijassa-1639	159	15	implies	imply	VERB
ijassa-1639	159	16	that	that	SCONJ
ijassa-1639	159	17	g(u	g(u	PROPN
ijassa-1639	159	18	)	)	PUNCT
ijassa-1639	159	19	at	at	ADP
ijassa-1639	159	20	any	any	DET
ijassa-1639	159	21	u	u	NOUN
ijassa-1639	159	22	=	=	PUNCT
ijassa-1639	159	23	(	(	PUNCT
ijassa-1639	159	24	x	x	X
ijassa-1639	159	25	,	,	PUNCT
ijassa-1639	159	26	λ	λ	PROPN
ijassa-1639	159	27	,	,	PUNCT
ijassa-1639	159	28	y	y	NOUN
ijassa-1639	159	29	)	)	PUNCT
ijassa-1639	159	30	∈	∈	PROPN
ijassa-1639	159	31	rp	rp	NOUN
ijassa-1639	159	32	equals	equal	VERB
ijassa-1639	159	33	φ′(u	φ′(u	PROPN
ijassa-1639	159	34	)	)	PUNCT
ijassa-1639	159	35	.	.	PUNCT
ijassa-1639	160	1	for	for	ADP
ijassa-1639	160	2	φ	φ	PROPN
ijassa-1639	160	3	from	from	ADP
ijassa-1639	160	4	(	(	PUNCT
ijassa-1639	160	5	2.5	2.5	NUM
ijassa-1639	160	6	)	)	PUNCT
ijassa-1639	160	7	,	,	PUNCT
ijassa-1639	160	8	the	the	DET
ijassa-1639	160	9	values	value	NOUN
ijassa-1639	160	10	of	of	ADP
ijassa-1639	160	11	a	a	DET
ijassa-1639	160	12	mapping	mapping	NOUN
ijassa-1639	160	13	g	g	NOUN
ijassa-1639	160	14	satisfying	satisfy	VERB
ijassa-1639	160	15	(	(	PUNCT
ijassa-1639	160	16	3.9	3.9	NUM
ijassa-1639	160	17	)	)	PUNCT
ijassa-1639	160	18	were	be	AUX
ijassa-1639	160	19	computed	compute	VERB
ijassa-1639	160	20	according	accord	VERB
ijassa-1639	160	21	to	to	ADP
ijassa-1639	160	22	the	the	DET
ijassa-1639	160	23	following	follow	VERB
ijassa-1639	160	24	rule	rule	NOUN
ijassa-1639	160	25	:	:	PUNCT
ijassa-1639	160	26	for	for	ADP
ijassa-1639	160	27	every	every	DET
ijassa-1639	160	28	i	i	PROPN
ijassa-1639	160	29	∈	∈	PROPN
ijassa-1639	160	30	{	{	PUNCT
ijassa-1639	160	31	1	1	NUM
ijassa-1639	160	32	,	,	PUNCT
ijassa-1639	160	33	.	.	PUNCT
ijassa-1639	160	34	.	.	PUNCT
ijassa-1639	161	1	.	.	PUNCT
ijassa-1639	162	1	,	,	PUNCT
ijassa-1639	162	2	m	m	VERB
ijassa-1639	162	3	}	}	PUNCT
ijassa-1639	162	4	,	,	PUNCT
ijassa-1639	162	5	if	if	SCONJ
ijassa-1639	162	6	λi	λi	INTJ
ijassa-1639	162	7	>	>	X
ijassa-1639	162	8	yi	yi	PROPN
ijassa-1639	162	9	,	,	PUNCT
ijassa-1639	162	10	then	then	ADV
ijassa-1639	162	11	the	the	DET
ijassa-1639	162	12	(	(	PUNCT
ijassa-1639	162	13	n+m+	n+m+	X
ijassa-1639	162	14	i)-th	i)-th	NOUN
ijassa-1639	162	15	row	row	NOUN
ijassa-1639	162	16	of	of	ADP
ijassa-1639	162	17	g(u	g(u	PROPN
ijassa-1639	162	18	)	)	PUNCT
ijassa-1639	162	19	is	be	AUX
ijassa-1639	162	20	gn+m+i(u	gn+m+i(u	NOUN
ijassa-1639	162	21	)	)	PUNCT
ijassa-1639	163	1	=	=	PUNCT
ijassa-1639	163	2	(	(	PUNCT
ijassa-1639	163	3	0	0	NUM
ijassa-1639	163	4	,	,	PUNCT
ijassa-1639	163	5	ei	ei	NOUN
ijassa-1639	163	6	)	)	PUNCT
ijassa-1639	163	7	,	,	PUNCT
ijassa-1639	163	8	with	with	ADP
ijassa-1639	163	9	ei	ei	X
ijassa-1639	163	10	being	be	AUX
ijassa-1639	163	11	the	the	DET
ijassa-1639	163	12	i	i	PROPN
ijassa-1639	163	13	-	-	PUNCT
ijassa-1639	163	14	th	th	X
ijassa-1639	163	15	element	element	NOUN
ijassa-1639	163	16	of	of	ADP
ijassa-1639	163	17	the	the	DET
ijassa-1639	163	18	standard	standard	ADJ
ijassa-1639	163	19	basis	basis	NOUN
ijassa-1639	163	20	in	in	ADP
ijassa-1639	163	21	rm	rm	NOUN
ijassa-1639	163	22	;	;	PUNCT
ijassa-1639	163	23	otherwise	otherwise	ADV
ijassa-1639	163	24	gn+m+i(u	gn+m+i(u	PROPN
ijassa-1639	163	25	)	)	PUNCT
ijassa-1639	164	1	=	=	PUNCT
ijassa-1639	164	2	(	(	PUNCT
ijassa-1639	164	3	ei	ei	NOUN
ijassa-1639	164	4	,	,	PUNCT
ijassa-1639	164	5	0	0	NUM
ijassa-1639	164	6	)	)	PUNCT
ijassa-1639	164	7	;	;	PUNCT
ijassa-1639	164	8	the	the	DET
ijassa-1639	164	9	other	other	ADJ
ijassa-1639	164	10	rows	row	NOUN
ijassa-1639	164	11	of	of	ADP
ijassa-1639	164	12	g(u	g(u	PROPN
ijassa-1639	164	13	)	)	PUNCT
ijassa-1639	164	14	are	be	AUX
ijassa-1639	164	15	the	the	DET
ijassa-1639	164	16	gradients	gradient	NOUN
ijassa-1639	164	17	of	of	ADP
ijassa-1639	164	18	the	the	DET
ijassa-1639	164	19	corresponding	correspond	VERB
ijassa-1639	164	20	(	(	PUNCT
ijassa-1639	164	21	smooth	smooth	ADJ
ijassa-1639	164	22	)	)	PUNCT
ijassa-1639	164	23	components	component	NOUN
ijassa-1639	164	24	of	of	ADP
ijassa-1639	164	25	φ	φ	PROPN
ijassa-1639	164	26	.	.	PUNCT
ijassa-1639	165	1	the	the	DET
ijassa-1639	165	2	experiments	experiment	NOUN
ijassa-1639	165	3	were	be	AUX
ijassa-1639	165	4	performed	perform	VERB
ijassa-1639	165	5	in	in	ADP
ijassa-1639	165	6	matlab	matlab	PROPN
ijassa-1639	165	7	,	,	PUNCT
ijassa-1639	165	8	with	with	ADP
ijassa-1639	165	9	its	its	PRON
ijassa-1639	165	10	built	build	VERB
ijassa-1639	165	11	-	-	PUNCT
ijassa-1639	165	12	in	in	ADP
ijassa-1639	165	13	solver	solver	NOUN
ijassa-1639	165	14	quadprog	quadprog	NOUN
ijassa-1639	165	15	used	use	VERB
ijassa-1639	165	16	for	for	ADP
ijassa-1639	165	17	quadratic	quadratic	ADJ
ijassa-1639	165	18	programming	programming	NOUN
ijassa-1639	165	19	subproblems	subproblem	NOUN
ijassa-1639	165	20	of	of	ADP
ijassa-1639	165	21	pwlm	pwlm	PROPN
ijassa-1639	165	22	and	and	CCONJ
ijassa-1639	165	23	lm	lm	NOUN
ijassa-1639	165	24	-	-	PUNCT
ijassa-1639	165	25	had	have	VERB
ijassa-1639	165	26	,	,	PUNCT
ijassa-1639	165	27	and	and	CCONJ
ijassa-1639	165	28	linprog	linprog	VERB
ijassa-1639	165	29	for	for	ADP
ijassa-1639	165	30	copyright	copyright	NOUN
ijassa-1639	165	31	©	©	PROPN
ijassa-1639	165	32	2024	2024	NUM
ijassa-1639	165	33	assa	assa	NOUN
ijassa-1639	165	34	.	.	PUNCT
ijassa-1639	166	1	adv	adv	PROPN
ijassa-1639	166	2	syst	syst	PROPN
ijassa-1639	166	3	sci	sci	PROPN
ijassa-1639	166	4	appl	appl	PROPN
ijassa-1639	166	5	(	(	PUNCT
ijassa-1639	166	6	2024	2024	NUM
ijassa-1639	166	7	)	)	PUNCT
ijassa-1639	166	8	piecewise	piecewise	NOUN
ijassa-1639	166	9	levenberg	levenberg	PROPN
ijassa-1639	166	10	–	–	PUNCT
ijassa-1639	166	11	marquardt	marquardt	PROPN
ijassa-1639	166	12	method	method	NOUN
ijassa-1639	166	13	for	for	ADP
ijassa-1639	166	14	gneps	gneps	NOUN
ijassa-1639	166	15	25	25	NUM
ijassa-1639	166	16	100	100	NUM
ijassa-1639	166	17	101	101	NUM
ijassa-1639	166	18	0	0	NUM
ijassa-1639	166	19	0.2	0.2	NUM
ijassa-1639	166	20	0.4	0.4	NUM
ijassa-1639	166	21	0.6	0.6	NUM
ijassa-1639	166	22	0.8	0.8	NUM
ijassa-1639	166	23	1	1	NUM
ijassa-1639	166	24	pwlm	pwlm	NOUN
ijassa-1639	166	25	1e-5	1e-5	PROPN
ijassa-1639	166	26	pwlm	pwlm	PROPN
ijassa-1639	166	27	1e-8	1e-8	NUM
ijassa-1639	166	28	pwlm	pwlm	NOUN
ijassa-1639	166	29	1e-10	1e-10	NUM
ijassa-1639	166	30	(	(	PUNCT
ijassa-1639	166	31	a	a	NOUN
ijassa-1639	166	32	)	)	PUNCT
ijassa-1639	166	33	for	for	ADP
ijassa-1639	166	34	“	"	PUNCT
ijassa-1639	166	35	min	min	NOUN
ijassa-1639	166	36	”	"	PUNCT
ijassa-1639	166	37	reformulation	reformulation	NOUN
ijassa-1639	166	38	100	100	NUM
ijassa-1639	166	39	101	101	NUM
ijassa-1639	166	40	0	0	NUM
ijassa-1639	166	41	0.2	0.2	NUM
ijassa-1639	166	42	0.4	0.4	NUM
ijassa-1639	166	43	0.6	0.6	NUM
ijassa-1639	166	44	0.8	0.8	NUM
ijassa-1639	166	45	1	1	NUM
ijassa-1639	166	46	lm	lm	NOUN
ijassa-1639	166	47	-	-	PUNCT
ijassa-1639	166	48	had	have	VERB
ijassa-1639	166	49	1e-5	1e-5	NUM
ijassa-1639	166	50	lm	lm	NOUN
ijassa-1639	166	51	-	-	PUNCT
ijassa-1639	166	52	had	have	VERB
ijassa-1639	166	53	1e-8	1e-8	NUM
ijassa-1639	166	54	lm	lm	NOUN
ijassa-1639	166	55	-	-	PUNCT
ijassa-1639	166	56	had	have	VERB
ijassa-1639	166	57	1e-10	1e-10	NUM
ijassa-1639	166	58	(	(	PUNCT
ijassa-1639	166	59	b	b	NOUN
ijassa-1639	166	60	)	)	PUNCT
ijassa-1639	166	61	for	for	ADP
ijassa-1639	166	62	hadamard	hadamard	ADJ
ijassa-1639	166	63	product	product	NOUN
ijassa-1639	166	64	-	-	PUNCT
ijassa-1639	166	65	based	base	VERB
ijassa-1639	166	66	reformulation	reformulation	ADJ
ijassa-1639	166	67	fig	fig	NOUN
ijassa-1639	166	68	.	.	PUNCT
ijassa-1639	167	1	4.1	4.1	NUM
ijassa-1639	167	2	.	.	PUNCT
ijassa-1639	167	3	comparison	comparison	NOUN
ijassa-1639	167	4	by	by	ADP
ijassa-1639	167	5	average	average	ADJ
ijassa-1639	167	6	iteration	iteration	NOUN
ijassa-1639	167	7	counts	count	NOUN
ijassa-1639	167	8	(	(	PUNCT
ijassa-1639	167	9	the	the	DET
ijassa-1639	167	10	same	same	ADJ
ijassa-1639	167	11	as	as	ADP
ijassa-1639	167	12	evaluations	evaluation	NOUN
ijassa-1639	167	13	of	of	ADP
ijassa-1639	167	14	g	g	NOUN
ijassa-1639	167	15	)	)	PUNCT
ijassa-1639	167	16	for	for	ADP
ijassa-1639	167	17	different	different	ADJ
ijassa-1639	167	18	values	value	NOUN
ijassa-1639	167	19	of	of	ADP
ijassa-1639	167	20	σ̄.	σ̄.	NUM
ijassa-1639	167	21	100	100	NUM
ijassa-1639	167	22	101	101	NUM
ijassa-1639	167	23	0	0	NUM
ijassa-1639	167	24	0.2	0.2	NUM
ijassa-1639	167	25	0.4	0.4	NUM
ijassa-1639	167	26	0.6	0.6	NUM
ijassa-1639	167	27	0.8	0.8	NUM
ijassa-1639	167	28	1	1	NUM
ijassa-1639	167	29	pwlm	pwlm	NOUN
ijassa-1639	167	30	1e-10	1e-10	NUM
ijassa-1639	167	31	pwlpn	pwlpn	NOUN
ijassa-1639	167	32	lm	lm	VERB
ijassa-1639	167	33	-	-	PUNCT
ijassa-1639	167	34	had	have	VERB
ijassa-1639	167	35	1e-10	1e-10	NUM
ijassa-1639	167	36	lpn	lpn	NOUN
ijassa-1639	167	37	-	-	PUNCT
ijassa-1639	167	38	had	have	AUX
ijassa-1639	167	39	(	(	PUNCT
ijassa-1639	167	40	a	a	NOUN
ijassa-1639	167	41	)	)	PUNCT
ijassa-1639	167	42	by	by	ADP
ijassa-1639	167	43	average	average	ADJ
ijassa-1639	167	44	iteration	iteration	NOUN
ijassa-1639	167	45	counts	count	VERB
ijassa-1639	167	46	100	100	NUM
ijassa-1639	167	47	101	101	NUM
ijassa-1639	167	48	0	0	NUM
ijassa-1639	167	49	0.2	0.2	NUM
ijassa-1639	167	50	0.4	0.4	NUM
ijassa-1639	167	51	0.6	0.6	NUM
ijassa-1639	167	52	0.8	0.8	NUM
ijassa-1639	167	53	1	1	NUM
ijassa-1639	167	54	pwlm	pwlm	NOUN
ijassa-1639	167	55	1e-10	1e-10	NUM
ijassa-1639	167	56	pwlpn	pwlpn	NOUN
ijassa-1639	167	57	lm	lm	VERB
ijassa-1639	167	58	-	-	PUNCT
ijassa-1639	167	59	had	have	VERB
ijassa-1639	167	60	1e-10	1e-10	NUM
ijassa-1639	167	61	lpn	lpn	NOUN
ijassa-1639	167	62	-	-	PUNCT
ijassa-1639	167	63	had	have	AUX
ijassa-1639	167	64	(	(	PUNCT
ijassa-1639	167	65	b	b	NOUN
ijassa-1639	167	66	)	)	PUNCT
ijassa-1639	167	67	by	by	ADP
ijassa-1639	167	68	average	average	ADJ
ijassa-1639	167	69	evaluations	evaluation	NOUN
ijassa-1639	167	70	of	of	ADP
ijassa-1639	167	71	φ	φ	PROPN
ijassa-1639	167	72	fig	fig	NOUN
ijassa-1639	167	73	.	.	PUNCT
ijassa-1639	168	1	4.2	4.2	NUM
ijassa-1639	168	2	.	.	PUNCT
ijassa-1639	168	3	comparison	comparison	NOUN
ijassa-1639	168	4	of	of	ADP
ijassa-1639	168	5	different	different	ADJ
ijassa-1639	168	6	algorithms	algorithm	NOUN
ijassa-1639	168	7	.	.	PUNCT
ijassa-1639	169	1	linear	linear	ADJ
ijassa-1639	169	2	programming	programming	NOUN
ijassa-1639	169	3	subproblems	subproblem	NOUN
ijassa-1639	169	4	of	of	ADP
ijassa-1639	169	5	pwlpn	pwlpn	NOUN
ijassa-1639	169	6	and	and	CCONJ
ijassa-1639	169	7	lpn	lpn	PROPN
ijassa-1639	169	8	-	-	PUNCT
ijassa-1639	169	9	had	have	VERB
ijassa-1639	169	10	,	,	PUNCT
ijassa-1639	169	11	the	the	DET
ijassa-1639	169	12	former	former	ADJ
ijassa-1639	169	13	run	run	NOUN
ijassa-1639	169	14	with	with	ADP
ijassa-1639	169	15	option	option	NOUN
ijassa-1639	169	16	’	'	PUNCT
ijassa-1639	169	17	optimalitytolerance	optimalitytolerance	NOUN
ijassa-1639	169	18	’	'	PUNCT
ijassa-1639	169	19	,	,	PUNCT
ijassa-1639	169	20	1e-15	1e-15	NUM
ijassa-1639	169	21	,	,	PUNCT
ijassa-1639	169	22	and	and	CCONJ
ijassa-1639	169	23	the	the	DET
ijassa-1639	169	24	latter	latter	ADJ
ijassa-1639	169	25	with	with	ADP
ijassa-1639	169	26	options	option	NOUN
ijassa-1639	169	27	’	'	PUNCT
ijassa-1639	169	28	optimalitytolerance	optimalitytolerance	NOUN
ijassa-1639	169	29	’	'	PUNCT
ijassa-1639	169	30	,	,	PUNCT
ijassa-1639	169	31	1e-8	1e-8	NUM
ijassa-1639	169	32	,	,	PUNCT
ijassa-1639	169	33	’	'	PUNCT
ijassa-1639	169	34	constrainttolerance	constrainttolerance	NOUN
ijassa-1639	169	35	’	'	PUNCT
ijassa-1639	169	36	,	,	PUNCT
ijassa-1639	169	37	1e-8	1e-8	NUM
ijassa-1639	169	38	.	.	PUNCT
ijassa-1639	170	1	the	the	DET
ijassa-1639	170	2	parameters	parameter	NOUN
ijassa-1639	170	3	in	in	ADP
ijassa-1639	170	4	algorithm	algorithm	PROPN
ijassa-1639	170	5	3.1	3.1	NUM
ijassa-1639	170	6	:	:	PUNCT
ijassa-1639	170	7	were	be	AUX
ijassa-1639	170	8	chosen	choose	VERB
ijassa-1639	170	9	as	as	SCONJ
ijassa-1639	170	10	follows	follow	VERB
ijassa-1639	170	11	:	:	PUNCT
ijassa-1639	170	12	θ	θ	NOUN
ijassa-1639	170	13	=	=	SYM
ijassa-1639	170	14	2	2	NUM
ijassa-1639	170	15	,	,	PUNCT
ijassa-1639	170	16	ε	ε	PROPN
ijassa-1639	170	17	=	=	SYM
ijassa-1639	170	18	0.001	0.001	NUM
ijassa-1639	170	19	,	,	PUNCT
ijassa-1639	170	20	κ	κ	X
ijassa-1639	170	21	=	=	PROPN
ijassa-1639	170	22	0.5	0.5	NUM
ijassa-1639	170	23	.	.	PUNCT
ijassa-1639	171	1	the	the	DET
ijassa-1639	171	2	parameters	parameter	NOUN
ijassa-1639	171	3	of	of	ADP
ijassa-1639	171	4	the	the	DET
ijassa-1639	171	5	globalized	globalized	ADJ
ijassa-1639	171	6	lp	lp	PROPN
ijassa-1639	171	7	-	-	PUNCT
ijassa-1639	171	8	newton	newton	PROPN
ijassa-1639	171	9	methods	method	NOUN
ijassa-1639	171	10	were	be	AUX
ijassa-1639	171	11	chosen	choose	VERB
ijassa-1639	171	12	according	accord	VERB
ijassa-1639	171	13	to	to	ADP
ijassa-1639	171	14	[	[	X
ijassa-1639	171	15	13	13	NUM
ijassa-1639	171	16	,	,	PUNCT
ijassa-1639	171	17	section	section	NOUN
ijassa-1639	171	18	5	5	NUM
ijassa-1639	171	19	]	]	PUNCT
ijassa-1639	171	20	.	.	PUNCT
ijassa-1639	172	1	in	in	ADP
ijassa-1639	172	2	order	order	NOUN
ijassa-1639	172	3	to	to	PART
ijassa-1639	172	4	avoid	avoid	VERB
ijassa-1639	172	5	large	large	ADJ
ijassa-1639	172	6	values	value	NOUN
ijassa-1639	172	7	of	of	ADP
ijassa-1639	172	8	the	the	DET
ijassa-1639	172	9	regularization	regularization	NOUN
ijassa-1639	172	10	parameter	parameter	NOUN
ijassa-1639	172	11	far	far	ADV
ijassa-1639	172	12	from	from	ADP
ijassa-1639	172	13	solutions	solution	NOUN
ijassa-1639	172	14	,	,	PUNCT
ijassa-1639	172	15	the	the	DET
ijassa-1639	172	16	rule	rule	NOUN
ijassa-1639	172	17	for	for	ADP
ijassa-1639	172	18	it	it	PRON
ijassa-1639	172	19	in	in	ADP
ijassa-1639	172	20	step	step	NOUN
ijassa-1639	172	21	2	2	NUM
ijassa-1639	172	22	of	of	ADP
ijassa-1639	172	23	algorithm	algorithm	NOUN
ijassa-1639	172	24	3.1	3.1	NUM
ijassa-1639	172	25	was	be	AUX
ijassa-1639	172	26	replaced	replace	VERB
ijassa-1639	172	27	by	by	ADP
ijassa-1639	172	28	σ(uk	σ(uk	NOUN
ijassa-1639	172	29	)	)	PUNCT
ijassa-1639	172	30	=	=	SYM
ijassa-1639	172	31	min{σ̄	min{σ̄	NOUN
ijassa-1639	172	32	,	,	PUNCT
ijassa-1639	172	33	∥φ(uk)∥θ	∥φ(uk)∥θ	NOUN
ijassa-1639	172	34	}	}	PUNCT
ijassa-1639	172	35	,	,	PUNCT
ijassa-1639	172	36	where	where	SCONJ
ijassa-1639	172	37	several	several	ADJ
ijassa-1639	172	38	different	different	ADJ
ijassa-1639	172	39	values	value	NOUN
ijassa-1639	172	40	of	of	ADP
ijassa-1639	172	41	σ̄	σ̄	PROPN
ijassa-1639	172	42	>	>	X
ijassa-1639	172	43	0	0	NUM
ijassa-1639	172	44	were	be	AUX
ijassa-1639	172	45	tied	tie	VERB
ijassa-1639	172	46	.	.	PUNCT
ijassa-1639	173	1	runs	run	NOUN
ijassa-1639	173	2	were	be	AUX
ijassa-1639	173	3	declared	declare	VERB
ijassa-1639	173	4	successful	successful	ADJ
ijassa-1639	173	5	when	when	SCONJ
ijassa-1639	173	6	terminated	terminate	VERB
ijassa-1639	173	7	because	because	SCONJ
ijassa-1639	173	8	of	of	ADP
ijassa-1639	173	9	∥φ(uk)∥∞	∥φ(uk)∥∞	NOUN
ijassa-1639	173	10	≤	≤	ADJ
ijassa-1639	173	11	10−6	10−6	NUM
ijassa-1639	173	12	,	,	PUNCT
ijassa-1639	173	13	within	within	ADP
ijassa-1639	173	14	1000	1000	NUM
ijassa-1639	173	15	iterations	iteration	NOUN
ijassa-1639	173	16	,	,	PUNCT
ijassa-1639	173	17	where	where	SCONJ
ijassa-1639	173	18	for	for	ADP
ijassa-1639	173	19	all	all	DET
ijassa-1639	173	20	the	the	DET
ijassa-1639	173	21	algorithms	algorithm	NOUN
ijassa-1639	173	22	involved	involve	VERB
ijassa-1639	173	23	,	,	PUNCT
ijassa-1639	173	24	φ	φ	PROPN
ijassa-1639	173	25	defined	define	VERB
ijassa-1639	173	26	in	in	ADP
ijassa-1639	173	27	(	(	PUNCT
ijassa-1639	173	28	2.5	2.5	NUM
ijassa-1639	173	29	)	)	PUNCT
ijassa-1639	173	30	was	be	AUX
ijassa-1639	173	31	used	use	VERB
ijassa-1639	173	32	in	in	ADP
ijassa-1639	173	33	this	this	DET
ijassa-1639	173	34	stopping	stopping	NOUN
ijassa-1639	173	35	test	test	NOUN
ijassa-1639	173	36	.	.	PUNCT
ijassa-1639	174	1	otherwise	otherwise	ADV
ijassa-1639	174	2	,	,	PUNCT
ijassa-1639	174	3	failure	failure	NOUN
ijassa-1639	174	4	was	be	AUX
ijassa-1639	174	5	declared	declare	VERB
ijassa-1639	174	6	,	,	PUNCT
ijassa-1639	174	7	as	as	ADV
ijassa-1639	174	8	well	well	ADV
ijassa-1639	174	9	as	as	ADP
ijassa-1639	174	10	in	in	ADP
ijassa-1639	174	11	the	the	DET
ijassa-1639	174	12	cases	case	NOUN
ijassa-1639	174	13	when	when	SCONJ
ijassa-1639	174	14	the	the	DET
ijassa-1639	174	15	backtracking	backtrack	VERB
ijassa-1639	174	16	procedure	procedure	NOUN
ijassa-1639	174	17	in	in	ADP
ijassa-1639	174	18	step	step	NOUN
ijassa-1639	174	19	3	3	NUM
ijassa-1639	174	20	of	of	ADP
ijassa-1639	174	21	algorithm	algorithm	PROPN
ijassa-1639	174	22	3.1	3.1	NUM
ijassa-1639	174	23	was	be	AUX
ijassa-1639	174	24	producing	produce	VERB
ijassa-1639	174	25	the	the	DET
ijassa-1639	174	26	trial	trial	NOUN
ijassa-1639	174	27	stepsize	stepsize	NOUN
ijassa-1639	174	28	parameter	parameter	NOUN
ijassa-1639	174	29	copyright	copyright	NOUN
ijassa-1639	174	30	©	©	PROPN
ijassa-1639	174	31	2024	2024	NUM
ijassa-1639	174	32	assa	assa	NOUN
ijassa-1639	174	33	.	.	PUNCT
ijassa-1639	175	1	adv	adv	PROPN
ijassa-1639	175	2	syst	syst	PROPN
ijassa-1639	175	3	sci	sci	PROPN
ijassa-1639	175	4	appl	appl	PROPN
ijassa-1639	175	5	(	(	PUNCT
ijassa-1639	175	6	2024	2024	NUM
ijassa-1639	175	7	)	)	PUNCT
ijassa-1639	175	8	26	26	NUM
ijassa-1639	175	9	a.	a.	NOUN
ijassa-1639	175	10	f.	f.	PROPN
ijassa-1639	175	11	izmailov	izmailov	PROPN
ijassa-1639	175	12	,	,	PUNCT
ijassa-1639	175	13	e.	e.	PROPN
ijassa-1639	175	14	i.	i.	PROPN
ijassa-1639	175	15	uskov	uskov	PROPN
ijassa-1639	175	16	,	,	PUNCT
ijassa-1639	175	17	yan	yan	PROPN
ijassa-1639	175	18	zhibai	zhibai	PROPN
ijassa-1639	175	19	100	100	NUM
ijassa-1639	175	20	101	101	NUM
ijassa-1639	175	21	0	0	NUM
ijassa-1639	175	22	0.2	0.2	NUM
ijassa-1639	175	23	0.4	0.4	NUM
ijassa-1639	175	24	0.6	0.6	NUM
ijassa-1639	175	25	0.8	0.8	NUM
ijassa-1639	175	26	1	1	NUM
ijassa-1639	175	27	pwlm	pwlm	NOUN
ijassa-1639	175	28	1e-10	1e-10	NUM
ijassa-1639	175	29	pwlpn	pwlpn	NOUN
ijassa-1639	175	30	lm	lm	VERB
ijassa-1639	175	31	-	-	PUNCT
ijassa-1639	175	32	had	have	VERB
ijassa-1639	175	33	1e-10	1e-10	NUM
ijassa-1639	175	34	lpn	lpn	NOUN
ijassa-1639	175	35	-	-	PUNCT
ijassa-1639	175	36	had	have	AUX
ijassa-1639	175	37	(	(	PUNCT
ijassa-1639	175	38	a	a	X
ijassa-1639	175	39	)	)	PUNCT
ijassa-1639	175	40	all	all	DET
ijassa-1639	175	41	test	test	NOUN
ijassa-1639	175	42	problems	problem	NOUN
ijassa-1639	175	43	100	100	NUM
ijassa-1639	175	44	101	101	NUM
ijassa-1639	175	45	0	0	NUM
ijassa-1639	175	46	0.2	0.2	NUM
ijassa-1639	175	47	0.4	0.4	NUM
ijassa-1639	175	48	0.6	0.6	NUM
ijassa-1639	175	49	0.8	0.8	NUM
ijassa-1639	175	50	1	1	NUM
ijassa-1639	175	51	pwlm	pwlm	NOUN
ijassa-1639	175	52	1e-10	1e-10	NUM
ijassa-1639	175	53	pwlpn	pwlpn	NOUN
ijassa-1639	175	54	lm	lm	VERB
ijassa-1639	175	55	-	-	PUNCT
ijassa-1639	175	56	had	have	VERB
ijassa-1639	175	57	1e-10	1e-10	NUM
ijassa-1639	175	58	lpn	lpn	NOUN
ijassa-1639	175	59	-	-	PUNCT
ijassa-1639	175	60	had	have	AUX
ijassa-1639	175	61	(	(	PUNCT
ijassa-1639	175	62	b	b	NOUN
ijassa-1639	175	63	)	)	PUNCT
ijassa-1639	175	64	large	large	ADJ
ijassa-1639	175	65	test	test	NOUN
ijassa-1639	175	66	problems	problem	NOUN
ijassa-1639	175	67	fig	fig	NOUN
ijassa-1639	175	68	.	.	PUNCT
ijassa-1639	176	1	4.3	4.3	NUM
ijassa-1639	176	2	.	.	PUNCT
ijassa-1639	176	3	comparison	comparison	NOUN
ijassa-1639	176	4	by	by	ADP
ijassa-1639	176	5	time	time	NOUN
ijassa-1639	176	6	.	.	PUNCT
ijassa-1639	177	1	value	value	NOUN
ijassa-1639	177	2	α	α	NOUN
ijassa-1639	177	3	≤	≤	NUM
ijassa-1639	177	4	10−13	10−13	NUM
ijassa-1639	177	5	,	,	PUNCT
ijassa-1639	177	6	and	and	CCONJ
ijassa-1639	177	7	also	also	ADV
ijassa-1639	177	8	when	when	SCONJ
ijassa-1639	177	9	∥((φj)′(uk))⊤φ(uk)∥	∥((φj)′(uk))⊤φ(uk)∥	VERB
ijassa-1639	177	10	≤	≤	NOUN
ijassa-1639	177	11	10−12	10−12	NOUN
ijassa-1639	177	12	was	be	AUX
ijassa-1639	177	13	encountered	encounter	VERB
ijassa-1639	177	14	for	for	ADP
ijassa-1639	177	15	j	j	PROPN
ijassa-1639	177	16	∈	∈	PROPN
ijassa-1639	177	17	a(uk	a(uk	PROPN
ijassa-1639	177	18	)	)	PUNCT
ijassa-1639	177	19	such	such	ADJ
ijassa-1639	177	20	that	that	SCONJ
ijassa-1639	177	21	g(uk	g(uk	PROPN
ijassa-1639	177	22	)	)	PUNCT
ijassa-1639	177	23	=	=	SYM
ijassa-1639	177	24	(	(	PUNCT
ijassa-1639	177	25	φj)′(uk	φj)′(uk	PROPN
ijassa-1639	177	26	)	)	PUNCT
ijassa-1639	177	27	,	,	PUNCT
ijassa-1639	177	28	and	and	CCONJ
ijassa-1639	177	29	in	in	ADP
ijassa-1639	177	30	particular	particular	ADJ
ijassa-1639	177	31	,	,	PUNCT
ijassa-1639	177	32	the	the	DET
ijassa-1639	177	33	stationarity	stationarity	NOUN
ijassa-1639	177	34	condition	condition	NOUN
ijassa-1639	177	35	(	(	PUNCT
ijassa-1639	177	36	3.14	3.14	NUM
ijassa-1639	177	37	)	)	PUNCT
ijassa-1639	177	38	was	be	AUX
ijassa-1639	177	39	approximately	approximately	ADV
ijassa-1639	177	40	satisfied	satisfied	ADJ
ijassa-1639	177	41	.	.	PUNCT
ijassa-1639	178	1	for	for	ADP
ijassa-1639	178	2	the	the	DET
ijassa-1639	178	3	lp	lp	PROPN
ijassa-1639	178	4	-	-	PUNCT
ijassa-1639	178	5	newton	newton	NOUN
ijassa-1639	178	6	-	-	PUNCT
ijassa-1639	178	7	based	base	VERB
ijassa-1639	178	8	algorithms	algorithm	NOUN
ijassa-1639	178	9	,	,	PUNCT
ijassa-1639	178	10	similar	similar	ADJ
ijassa-1639	178	11	rules	rule	NOUN
ijassa-1639	178	12	were	be	AUX
ijassa-1639	178	13	adopted	adopt	VERB
ijassa-1639	178	14	,	,	PUNCT
ijassa-1639	178	15	but	but	CCONJ
ijassa-1639	178	16	the	the	DET
ijassa-1639	178	17	approximate	approximate	ADJ
ijassa-1639	178	18	stationarity	stationarity	NOUN
ijassa-1639	178	19	test	test	NOUN
ijassa-1639	178	20	was	be	AUX
ijassa-1639	178	21	replaced	replace	VERB
ijassa-1639	178	22	by	by	ADP
ijassa-1639	178	23	|∆(uk)|	|∆(uk)|	NOUN
ijassa-1639	178	24	≤	≤	NOUN
ijassa-1639	178	25	10−12	10−12	NOUN
ijassa-1639	178	26	,	,	PUNCT
ijassa-1639	178	27	where	where	SCONJ
ijassa-1639	178	28	the	the	DET
ijassa-1639	178	29	quantity	quantity	NOUN
ijassa-1639	178	30	∆(uk	∆(uk	NOUN
ijassa-1639	178	31	)	)	PUNCT
ijassa-1639	178	32	estimating	estimate	VERB
ijassa-1639	178	33	from	from	ADP
ijassa-1639	178	34	above	above	ADP
ijassa-1639	178	35	the	the	DET
ijassa-1639	178	36	directional	directional	ADJ
ijassa-1639	178	37	derivative	derivative	NOUN
ijassa-1639	178	38	of	of	ADP
ijassa-1639	178	39	the	the	DET
ijassa-1639	178	40	merit	merit	NOUN
ijassa-1639	178	41	function	function	NOUN
ijassa-1639	178	42	is	be	AUX
ijassa-1639	178	43	defined	define	VERB
ijassa-1639	178	44	according	accord	VERB
ijassa-1639	178	45	to	to	ADP
ijassa-1639	178	46	[	[	X
ijassa-1639	178	47	13	13	NUM
ijassa-1639	178	48	,	,	PUNCT
ijassa-1639	178	49	(	(	PUNCT
ijassa-1639	178	50	2.3	2.3	NUM
ijassa-1639	178	51	)	)	PUNCT
ijassa-1639	178	52	]	]	PUNCT
ijassa-1639	178	53	,	,	PUNCT
ijassa-1639	178	54	where	where	SCONJ
ijassa-1639	178	55	γ(uk	γ(uk	X
ijassa-1639	178	56	)	)	PUNCT
ijassa-1639	178	57	is	be	AUX
ijassa-1639	178	58	taken	take	VERB
ijassa-1639	178	59	the	the	DET
ijassa-1639	178	60	optimal	optimal	ADJ
ijassa-1639	178	61	value	value	NOUN
ijassa-1639	178	62	of	of	ADP
ijassa-1639	178	63	the	the	DET
ijassa-1639	178	64	lp	lp	PROPN
ijassa-1639	178	65	-	-	PUNCT
ijassa-1639	178	66	newton	newton	PROPN
ijassa-1639	178	67	subproblem	subproblem	NOUN
ijassa-1639	178	68	.	.	PUNCT
ijassa-1639	179	1	it	it	PRON
ijassa-1639	179	2	turned	turn	VERB
ijassa-1639	179	3	out	out	ADP
ijassa-1639	179	4	that	that	SCONJ
ijassa-1639	179	5	in	in	ADP
ijassa-1639	179	6	order	order	NOUN
ijassa-1639	179	7	to	to	PART
ijassa-1639	179	8	achieve	achieve	VERB
ijassa-1639	179	9	reasonable	reasonable	ADJ
ijassa-1639	179	10	robustness	robustness	NOUN
ijassa-1639	179	11	of	of	ADP
ijassa-1639	179	12	the	the	DET
ijassa-1639	179	13	lm	lm	ADV
ijassa-1639	179	14	-	-	PUNCT
ijassa-1639	179	15	based	base	VERB
ijassa-1639	179	16	algorithms	algorithm	NOUN
ijassa-1639	179	17	,	,	PUNCT
ijassa-1639	179	18	σ̄	σ̄	PROPN
ijassa-1639	179	19	has	have	VERB
ijassa-1639	179	20	to	to	PART
ijassa-1639	179	21	be	be	AUX
ijassa-1639	179	22	taken	take	VERB
ijassa-1639	179	23	quite	quite	ADV
ijassa-1639	179	24	small	small	ADJ
ijassa-1639	179	25	:	:	PUNCT
ijassa-1639	179	26	larger	large	ADJ
ijassa-1639	179	27	values	value	NOUN
ijassa-1639	179	28	lead	lead	VERB
ijassa-1639	179	29	to	to	ADP
ijassa-1639	179	30	long	long	ADJ
ijassa-1639	179	31	series	series	NOUN
ijassa-1639	179	32	of	of	ADP
ijassa-1639	179	33	short	short	ADJ
ijassa-1639	179	34	steps	step	NOUN
ijassa-1639	179	35	far	far	ADV
ijassa-1639	179	36	from	from	ADP
ijassa-1639	179	37	solutions	solution	NOUN
ijassa-1639	179	38	,	,	PUNCT
ijassa-1639	179	39	and	and	CCONJ
ijassa-1639	179	40	this	this	PRON
ijassa-1639	179	41	often	often	ADV
ijassa-1639	179	42	ends	end	VERB
ijassa-1639	179	43	up	up	ADP
ijassa-1639	179	44	with	with	ADP
ijassa-1639	179	45	a	a	DET
ijassa-1639	179	46	failure	failure	NOUN
ijassa-1639	179	47	.	.	PUNCT
ijassa-1639	180	1	this	this	PRON
ijassa-1639	180	2	happens	happen	VERB
ijassa-1639	180	3	for	for	ADP
ijassa-1639	180	4	lm	lm	VERB
ijassa-1639	180	5	-	-	PUNCT
ijassa-1639	180	6	had	have	AUX
ijassa-1639	180	7	when	when	SCONJ
ijassa-1639	180	8	run	run	VERB
ijassa-1639	180	9	for	for	ADP
ijassa-1639	180	10	problems	problem	NOUN
ijassa-1639	180	11	a7	a7	PROPN
ijassa-1639	180	12	,	,	PUNCT
ijassa-1639	180	13	heu	heu	PROPN
ijassa-1639	180	14	,	,	PUNCT
ijassa-1639	180	15	tr1b	tr1b	PROPN
ijassa-1639	180	16	,	,	PUNCT
ijassa-1639	180	17	tr1c	tr1c	NOUN
ijassa-1639	180	18	,	,	PUNCT
ijassa-1639	180	19	and	and	CCONJ
ijassa-1639	180	20	for	for	ADP
ijassa-1639	180	21	pwlm	pwlm	NOUN
ijassa-1639	180	22	when	when	SCONJ
ijassa-1639	180	23	run	run	VERB
ijassa-1639	180	24	for	for	ADP
ijassa-1639	180	25	a10e	a10e	PROPN
ijassa-1639	180	26	,	,	PUNCT
ijassa-1639	180	27	tr1a	tr1a	PROPN
ijassa-1639	180	28	.	.	PUNCT
ijassa-1639	181	1	for	for	ADP
ijassa-1639	181	2	a10c	a10c	PROPN
ijassa-1639	181	3	and	and	CCONJ
ijassa-1639	181	4	a10d	a10d	NOUN
ijassa-1639	181	5	,	,	PUNCT
ijassa-1639	181	6	runs	run	NOUN
ijassa-1639	181	7	of	of	ADP
ijassa-1639	181	8	pwlm	pwlm	PROPN
ijassa-1639	181	9	are	be	AUX
ijassa-1639	181	10	generally	generally	ADV
ijassa-1639	181	11	successful	successful	ADJ
ijassa-1639	181	12	for	for	ADP
ijassa-1639	181	13	larger	large	ADJ
ijassa-1639	181	14	σ̄	σ̄	NOUN
ijassa-1639	181	15	as	as	ADV
ijassa-1639	181	16	well	well	ADV
ijassa-1639	181	17	,	,	PUNCT
ijassa-1639	181	18	but	but	CCONJ
ijassa-1639	181	19	taking	take	VERB
ijassa-1639	181	20	smaller	small	ADJ
ijassa-1639	181	21	values	value	NOUN
ijassa-1639	181	22	of	of	ADP
ijassa-1639	181	23	this	this	DET
ijassa-1639	181	24	parameter	parameter	NOUN
ijassa-1639	181	25	reduces	reduce	VERB
ijassa-1639	181	26	the	the	DET
ijassa-1639	181	27	iteration	iteration	NOUN
ijassa-1639	181	28	count	count	NOUN
ijassa-1639	181	29	significantly	significantly	ADV
ijassa-1639	181	30	.	.	PUNCT
ijassa-1639	182	1	our	our	PRON
ijassa-1639	182	2	numerical	numerical	ADJ
ijassa-1639	182	3	results	result	NOUN
ijassa-1639	182	4	are	be	AUX
ijassa-1639	182	5	presented	present	VERB
ijassa-1639	182	6	in	in	ADP
ijassa-1639	182	7	the	the	DET
ijassa-1639	182	8	form	form	NOUN
ijassa-1639	182	9	of	of	ADP
ijassa-1639	182	10	performance	performance	NOUN
ijassa-1639	182	11	profiles	profile	NOUN
ijassa-1639	182	12	originally	originally	ADV
ijassa-1639	182	13	proposed	propose	VERB
ijassa-1639	182	14	in	in	ADP
ijassa-1639	182	15	[	[	X
ijassa-1639	182	16	2	2	NUM
ijassa-1639	182	17	]	]	PUNCT
ijassa-1639	182	18	,	,	PUNCT
ijassa-1639	182	19	and	and	CCONJ
ijassa-1639	182	20	later	later	ADV
ijassa-1639	182	21	adapted	adapt	VERB
ijassa-1639	182	22	in	in	ADP
ijassa-1639	182	23	[	[	X
ijassa-1639	182	24	23	23	NUM
ijassa-1639	182	25	]	]	PUNCT
ijassa-1639	182	26	for	for	ADP
ijassa-1639	182	27	the	the	DET
ijassa-1639	182	28	case	case	NOUN
ijassa-1639	182	29	when	when	SCONJ
ijassa-1639	182	30	multiple	multiple	ADJ
ijassa-1639	182	31	starting	starting	NOUN
ijassa-1639	182	32	points	point	NOUN
ijassa-1639	182	33	are	be	AUX
ijassa-1639	182	34	used	use	VERB
ijassa-1639	182	35	for	for	ADP
ijassa-1639	182	36	every	every	DET
ijassa-1639	182	37	test	test	NOUN
ijassa-1639	182	38	problem	problem	NOUN
ijassa-1639	182	39	.	.	PUNCT
ijassa-1639	183	1	specifically	specifically	ADV
ijassa-1639	183	2	,	,	PUNCT
ijassa-1639	183	3	for	for	SCONJ
ijassa-1639	183	4	each	each	DET
ijassa-1639	183	5	algorithm	algorithm	NOUN
ijassa-1639	183	6	a	a	X
ijassa-1639	183	7	,	,	PUNCT
ijassa-1639	183	8	we	we	PRON
ijassa-1639	183	9	present	present	VERB
ijassa-1639	183	10	the	the	DET
ijassa-1639	183	11	plot	plot	NOUN
ijassa-1639	183	12	the	the	DET
ijassa-1639	183	13	function	function	NOUN
ijassa-1639	183	14	πa	πa	ADP
ijassa-1639	183	15	:	:	PUNCT
ijassa-1639	184	1	[	[	X
ijassa-1639	184	2	1	1	NUM
ijassa-1639	184	3	,	,	PUNCT
ijassa-1639	184	4	+	+	NOUN
ijassa-1639	184	5	∞	∞	NOUN
ijassa-1639	184	6	)	)	PUNCT
ijassa-1639	184	7	→	→	PUNCT
ijassa-1639	184	8	[	[	X
ijassa-1639	184	9	0	0	NUM
ijassa-1639	184	10	,	,	PUNCT
ijassa-1639	184	11	1	1	NUM
ijassa-1639	184	12	]	]	PUNCT
ijassa-1639	184	13	constructed	construct	VERB
ijassa-1639	184	14	as	as	SCONJ
ijassa-1639	184	15	follows	follow	VERB
ijassa-1639	184	16	.	.	PUNCT
ijassa-1639	185	1	let	let	VERB
ijassa-1639	185	2	ka	ka	PROPN
ijassa-1639	185	3	τ	τ	PROPN
ijassa-1639	185	4	be	be	AUX
ijassa-1639	185	5	the	the	DET
ijassa-1639	185	6	average	average	NOUN
ijassa-1639	185	7	of	of	ADP
ijassa-1639	185	8	some	some	DET
ijassa-1639	185	9	measure	measure	NOUN
ijassa-1639	185	10	of	of	ADP
ijassa-1639	185	11	efficiency	efficiency	NOUN
ijassa-1639	185	12	of	of	ADP
ijassa-1639	185	13	algorithm	algorithm	NOUN
ijassa-1639	185	14	a	a	PRON
ijassa-1639	185	15	on	on	ADP
ijassa-1639	185	16	problem	problem	NOUN
ijassa-1639	185	17	τ	τ	X
ijassa-1639	185	18	,	,	PUNCT
ijassa-1639	185	19	where	where	SCONJ
ijassa-1639	185	20	the	the	DET
ijassa-1639	185	21	average	average	NOUN
ijassa-1639	185	22	is	be	AUX
ijassa-1639	185	23	taken	take	VERB
ijassa-1639	185	24	over	over	ADP
ijassa-1639	185	25	successful	successful	ADJ
ijassa-1639	185	26	runs	run	NOUN
ijassa-1639	185	27	,	,	PUNCT
ijassa-1639	185	28	and	and	CCONJ
ijassa-1639	185	29	let	let	VERB
ijassa-1639	185	30	saτ	saτ	PRON
ijassa-1639	185	31	∈	∈	PROPN
ijassa-1639	186	1	[	[	X
ijassa-1639	186	2	0	0	NUM
ijassa-1639	186	3	,	,	PUNCT
ijassa-1639	186	4	1	1	NUM
ijassa-1639	186	5	]	]	PUNCT
ijassa-1639	186	6	stand	stand	VERB
ijassa-1639	186	7	for	for	ADP
ijassa-1639	186	8	the	the	DET
ijassa-1639	186	9	portion	portion	NOUN
ijassa-1639	186	10	of	of	ADP
ijassa-1639	186	11	successful	successful	ADJ
ijassa-1639	186	12	runs	run	NOUN
ijassa-1639	186	13	of	of	ADP
ijassa-1639	186	14	algorithm	algorithm	NOUN
ijassa-1639	186	15	a	a	PRON
ijassa-1639	186	16	on	on	ADP
ijassa-1639	186	17	problem	problem	NOUN
ijassa-1639	186	18	τ	τ	X
ijassa-1639	186	19	.	.	PUNCT
ijassa-1639	187	1	let	let	VERB
ijassa-1639	187	2	rτ	rτ	NOUN
ijassa-1639	187	3	be	be	AUX
ijassa-1639	187	4	the	the	DET
ijassa-1639	187	5	best	good	ADJ
ijassa-1639	187	6	(	(	PUNCT
ijassa-1639	187	7	say	say	INTJ
ijassa-1639	187	8	,	,	PUNCT
ijassa-1639	187	9	smallest	small	ADJ
ijassa-1639	187	10	)	)	PUNCT
ijassa-1639	187	11	value	value	NOUN
ijassa-1639	187	12	of	of	ADP
ijassa-1639	187	13	ka	ka	PROPN
ijassa-1639	187	14	τ	τ	PROPN
ijassa-1639	187	15	among	among	ADP
ijassa-1639	187	16	all	all	DET
ijassa-1639	187	17	the	the	DET
ijassa-1639	187	18	algorithms	algorithm	NOUN
ijassa-1639	187	19	.	.	PUNCT
ijassa-1639	188	1	then	then	ADV
ijassa-1639	188	2	for	for	ADP
ijassa-1639	188	3	each	each	DET
ijassa-1639	188	4	t	t	NOUN
ijassa-1639	188	5	∈	∈	PROPN
ijassa-1639	189	1	[	[	X
ijassa-1639	189	2	1	1	NUM
ijassa-1639	189	3	,	,	PUNCT
ijassa-1639	189	4	+	+	NOUN
ijassa-1639	189	5	∞	∞	NOUN
ijassa-1639	189	6	)	)	PUNCT
ijassa-1639	189	7	,	,	PUNCT
ijassa-1639	189	8	we	we	PRON
ijassa-1639	189	9	set	set	VERB
ijassa-1639	189	10	πa(t	πa(t	PUNCT
ijassa-1639	189	11	)	)	PUNCT
ijassa-1639	189	12	=	=	SYM
ijassa-1639	189	13	1	1	NUM
ijassa-1639	189	14	t	t	NOUN
ijassa-1639	189	15	∑	∑	PUNCT
ijassa-1639	189	16	τ∈ra(t	τ∈ra(t	PROPN
ijassa-1639	189	17	)	)	PUNCT
ijassa-1639	189	18	saτ	saτ	NOUN
ijassa-1639	189	19	,	,	PUNCT
ijassa-1639	189	20	where	where	SCONJ
ijassa-1639	189	21	t	t	NOUN
ijassa-1639	189	22	the	the	DET
ijassa-1639	189	23	overall	overall	ADJ
ijassa-1639	189	24	number	number	NOUN
ijassa-1639	189	25	of	of	ADP
ijassa-1639	189	26	problems	problem	NOUN
ijassa-1639	189	27	in	in	ADP
ijassa-1639	189	28	the	the	DET
ijassa-1639	189	29	test	test	NOUN
ijassa-1639	189	30	set	set	NOUN
ijassa-1639	189	31	,	,	PUNCT
ijassa-1639	189	32	and	and	CCONJ
ijassa-1639	189	33	ra(t	ra(t	NOUN
ijassa-1639	189	34	)	)	PUNCT
ijassa-1639	189	35	is	be	AUX
ijassa-1639	189	36	the	the	DET
ijassa-1639	189	37	subset	subset	NOUN
ijassa-1639	189	38	of	of	ADP
ijassa-1639	189	39	problems	problem	NOUN
ijassa-1639	189	40	for	for	ADP
ijassa-1639	189	41	which	which	PRON
ijassa-1639	189	42	the	the	DET
ijassa-1639	189	43	performance	performance	NOUN
ijassa-1639	189	44	of	of	ADP
ijassa-1639	189	45	algorithm	algorithm	NOUN
ijassa-1639	189	46	a	a	PRON
ijassa-1639	189	47	is	be	AUX
ijassa-1639	189	48	no	no	PRON
ijassa-1639	189	49	more	more	ADJ
ijassa-1639	189	50	than	than	ADP
ijassa-1639	189	51	t	t	PROPN
ijassa-1639	189	52	times	time	NOUN
ijassa-1639	189	53	worse	bad	ADJ
ijassa-1639	189	54	than	than	ADP
ijassa-1639	189	55	that	that	PRON
ijassa-1639	189	56	of	of	ADP
ijassa-1639	189	57	the	the	DET
ijassa-1639	189	58	best	good	ADJ
ijassa-1639	189	59	algorithm	algorithm	NOUN
ijassa-1639	189	60	:	:	PUNCT
ijassa-1639	189	61	ra(t	ra(t	X
ijassa-1639	189	62	)	)	PUNCT
ijassa-1639	189	63	=	=	SYM
ijassa-1639	190	1	{	{	PUNCT
ijassa-1639	190	2	τ	τ	PROPN
ijassa-1639	190	3	∈	∈	PROPN
ijassa-1639	190	4	{	{	PUNCT
ijassa-1639	190	5	1	1	NUM
ijassa-1639	190	6	,	,	PUNCT
ijassa-1639	190	7	.	.	PUNCT
ijassa-1639	190	8	.	.	PUNCT
ijassa-1639	190	9	.	.	PUNCT
ijassa-1639	191	1	,	,	PUNCT
ijassa-1639	191	2	t	t	X
ijassa-1639	191	3	}	}	PUNCT
ijassa-1639	191	4	|	|	ADV
ijassa-1639	191	5	ka	ka	PROPN
ijassa-1639	191	6	τ	τ	PROPN
ijassa-1639	191	7	≤	≤	ADJ
ijassa-1639	191	8	trτ	trτ	NOUN
ijassa-1639	191	9	}	}	PUNCT
ijassa-1639	191	10	.	.	PUNCT
ijassa-1639	192	1	in	in	ADP
ijassa-1639	192	2	particular	particular	ADJ
ijassa-1639	192	3	,	,	PUNCT
ijassa-1639	192	4	πa(t	πa(t	PUNCT
ijassa-1639	192	5	)	)	PUNCT
ijassa-1639	192	6	for	for	ADP
ijassa-1639	192	7	large	large	ADJ
ijassa-1639	192	8	t	t	PROPN
ijassa-1639	192	9	is	be	AUX
ijassa-1639	192	10	the	the	DET
ijassa-1639	192	11	average	average	ADJ
ijassa-1639	192	12	portion	portion	NOUN
ijassa-1639	192	13	of	of	ADP
ijassa-1639	192	14	successful	successful	ADJ
ijassa-1639	192	15	runs	run	NOUN
ijassa-1639	192	16	(	(	PUNCT
ijassa-1639	192	17	averaged	average	VERB
ijassa-1639	192	18	over	over	ADP
ijassa-1639	192	19	all	all	DET
ijassa-1639	192	20	test	test	NOUN
ijassa-1639	192	21	problems	problem	NOUN
ijassa-1639	192	22	)	)	PUNCT
ijassa-1639	192	23	,	,	PUNCT
ijassa-1639	192	24	while	while	SCONJ
ijassa-1639	192	25	πa(1	πa(1	NOUN
ijassa-1639	192	26	)	)	PUNCT
ijassa-1639	192	27	is	be	AUX
ijassa-1639	192	28	the	the	DET
ijassa-1639	192	29	quantity	quantity	NOUN
ijassa-1639	192	30	computed	compute	VERB
ijassa-1639	192	31	in	in	ADP
ijassa-1639	192	32	a	a	DET
ijassa-1639	192	33	similar	similar	ADJ
ijassa-1639	192	34	way	way	NOUN
ijassa-1639	192	35	but	but	CCONJ
ijassa-1639	192	36	using	use	VERB
ijassa-1639	192	37	the	the	DET
ijassa-1639	192	38	portions	portion	NOUN
ijassa-1639	192	39	of	of	ADP
ijassa-1639	192	40	successful	successful	ADJ
ijassa-1639	192	41	runs	run	NOUN
ijassa-1639	192	42	only	only	ADV
ijassa-1639	192	43	on	on	ADP
ijassa-1639	192	44	those	those	DET
ijassa-1639	192	45	problems	problem	NOUN
ijassa-1639	192	46	for	for	ADP
ijassa-1639	192	47	which	which	PRON
ijassa-1639	192	48	the	the	DET
ijassa-1639	192	49	average	average	ADJ
ijassa-1639	192	50	performance	performance	NOUN
ijassa-1639	192	51	of	of	ADP
ijassa-1639	192	52	the	the	DET
ijassa-1639	192	53	given	give	VERB
ijassa-1639	192	54	algorithm	algorithm	NOUN
ijassa-1639	192	55	over	over	ADP
ijassa-1639	192	56	successful	successful	ADJ
ijassa-1639	192	57	runs	run	NOUN
ijassa-1639	192	58	is	be	AUX
ijassa-1639	192	59	the	the	DET
ijassa-1639	192	60	best	good	ADJ
ijassa-1639	192	61	among	among	ADP
ijassa-1639	192	62	all	all	DET
ijassa-1639	192	63	algorithms	algorithm	NOUN
ijassa-1639	192	64	being	be	AUX
ijassa-1639	192	65	tested	test	VERB
ijassa-1639	192	66	.	.	PUNCT
ijassa-1639	193	1	in	in	ADP
ijassa-1639	193	2	case	case	NOUN
ijassa-1639	193	3	of	of	ADP
ijassa-1639	193	4	a	a	DET
ijassa-1639	193	5	single	single	ADJ
ijassa-1639	193	6	run	run	NOUN
ijassa-1639	193	7	for	for	ADP
ijassa-1639	193	8	each	each	DET
ijassa-1639	193	9	test	test	NOUN
ijassa-1639	193	10	problem	problem	NOUN
ijassa-1639	193	11	,	,	PUNCT
ijassa-1639	193	12	this	this	PRON
ijassa-1639	193	13	agrees	agree	VERB
ijassa-1639	193	14	with	with	ADP
ijassa-1639	193	15	the	the	DET
ijassa-1639	193	16	original	original	ADJ
ijassa-1639	193	17	proposal	proposal	NOUN
ijassa-1639	193	18	in	in	ADP
ijassa-1639	193	19	[	[	X
ijassa-1639	193	20	2	2	NUM
ijassa-1639	193	21	]	]	PUNCT
ijassa-1639	193	22	,	,	PUNCT
ijassa-1639	193	23	and	and	CCONJ
ijassa-1639	193	24	in	in	ADP
ijassa-1639	193	25	particular	particular	ADJ
ijassa-1639	193	26	,	,	PUNCT
ijassa-1639	193	27	copyright	copyright	NOUN
ijassa-1639	193	28	©	©	PROPN
ijassa-1639	193	29	2024	2024	NUM
ijassa-1639	193	30	assa	assa	NOUN
ijassa-1639	193	31	.	.	PUNCT
ijassa-1639	194	1	adv	adv	PROPN
ijassa-1639	194	2	syst	syst	PROPN
ijassa-1639	194	3	sci	sci	PROPN
ijassa-1639	194	4	appl	appl	PROPN
ijassa-1639	194	5	(	(	PUNCT
ijassa-1639	194	6	2024	2024	NUM
ijassa-1639	194	7	)	)	PUNCT
ijassa-1639	194	8	piecewise	piecewise	NOUN
ijassa-1639	194	9	levenberg	levenberg	PROPN
ijassa-1639	194	10	–	–	PUNCT
ijassa-1639	194	11	marquardt	marquardt	PROPN
ijassa-1639	194	12	method	method	NOUN
ijassa-1639	194	13	for	for	ADP
ijassa-1639	194	14	gneps	gneps	NOUN
ijassa-1639	194	15	27	27	NUM
ijassa-1639	194	16	table	table	NOUN
ijassa-1639	194	17	4.1	4.1	NUM
ijassa-1639	194	18	.	.	PUNCT
ijassa-1639	195	1	average	average	ADJ
ijassa-1639	195	2	elapsed	elapse	VERB
ijassa-1639	195	3	times	time	NOUN
ijassa-1639	195	4	(	(	PUNCT
ijassa-1639	195	5	seconds	second	NOUN
ijassa-1639	195	6	)	)	PUNCT
ijassa-1639	195	7	and	and	CCONJ
ijassa-1639	195	8	percentage	percentage	NOUN
ijassa-1639	195	9	of	of	ADP
ijassa-1639	195	10	tails	tail	NOUN
ijassa-1639	195	11	of	of	ADP
ijassa-1639	195	12	last	last	ADJ
ijassa-1639	195	13	full	full	ADJ
ijassa-1639	195	14	steps	step	NOUN
ijassa-1639	195	15	out	out	ADP
ijassa-1639	195	16	of	of	ADP
ijassa-1639	195	17	the	the	DET
ijassa-1639	195	18	average	average	ADJ
ijassa-1639	195	19	iteration	iteration	NOUN
ijassa-1639	195	20	counts	count	NOUN
ijassa-1639	195	21	,	,	PUNCT
ijassa-1639	195	22	over	over	ADP
ijassa-1639	195	23	successful	successful	ADJ
ijassa-1639	195	24	runs	run	NOUN
ijassa-1639	195	25	test	test	VERB
ijassa-1639	195	26	pwlm	pwlm	PROPN
ijassa-1639	195	27	pwlpn	pwlpn	PROPN
ijassa-1639	195	28	lm	lm	PROPN
ijassa-1639	195	29	-	-	PUNCT
ijassa-1639	195	30	had	have	VERB
ijassa-1639	195	31	lpn	lpn	NOUN
ijassa-1639	195	32	-	-	PUNCT
ijassa-1639	195	33	had	have	AUX
ijassa-1639	195	34	time	time	NOUN
ijassa-1639	195	35	tail	tail	NOUN
ijassa-1639	195	36	time	time	NOUN
ijassa-1639	195	37	tail	tail	NOUN
ijassa-1639	195	38	time	time	NOUN
ijassa-1639	195	39	tail	tail	NOUN
ijassa-1639	195	40	time	time	NOUN
ijassa-1639	195	41	tail	tail	NOUN
ijassa-1639	195	42	a1	a1	NOUN
ijassa-1639	195	43	0.080	0.080	NUM
ijassa-1639	195	44	100.0	100.0	NUM
ijassa-1639	195	45	0.068	0.068	NUM
ijassa-1639	195	46	100.0	100.0	NUM
ijassa-1639	195	47	0.016	0.016	NUM
ijassa-1639	195	48	76.3	76.3	NUM
ijassa-1639	195	49	0.057	0.057	NUM
ijassa-1639	195	50	100.0	100.0	NUM
ijassa-1639	195	51	a2	a2	PROPN
ijassa-1639	195	52	nan	nan	PROPN
ijassa-1639	195	53	nan	nan	PROPN
ijassa-1639	195	54	0.044	0.044	NUM
ijassa-1639	195	55	100.0	100.0	NUM
ijassa-1639	195	56	nan	nan	PROPN
ijassa-1639	195	57	nan	nan	PROPN
ijassa-1639	195	58	0.067	0.067	NUM
ijassa-1639	195	59	100.0	100.0	NUM
ijassa-1639	195	60	a3	a3	NOUN
ijassa-1639	195	61	0.003	0.003	NUM
ijassa-1639	195	62	100.0	100.0	NUM
ijassa-1639	195	63	0.043	0.043	NUM
ijassa-1639	195	64	100.0	100.0	NUM
ijassa-1639	195	65	0.006	0.006	NUM
ijassa-1639	195	66	100.0	100.0	NUM
ijassa-1639	195	67	0.066	0.066	NUM
ijassa-1639	195	68	100.0	100.0	NUM
ijassa-1639	195	69	a4	a4	NOUN
ijassa-1639	195	70	0.010	0.010	NUM
ijassa-1639	195	71	82.8	82.8	NUM
ijassa-1639	195	72	0.064	0.064	NUM
ijassa-1639	195	73	98.9	98.9	NUM
ijassa-1639	195	74	0.011	0.011	NUM
ijassa-1639	195	75	78.4	78.4	NUM
ijassa-1639	195	76	0.055	0.055	NUM
ijassa-1639	195	77	97.1	97.1	NUM
ijassa-1639	195	78	a5	a5	NOUN
ijassa-1639	195	79	0.005	0.005	NUM
ijassa-1639	195	80	100.0	100.0	NUM
ijassa-1639	195	81	0.042	0.042	NUM
ijassa-1639	195	82	100.0	100.0	NUM
ijassa-1639	195	83	0.009	0.009	NUM
ijassa-1639	195	84	100.0	100.0	NUM
ijassa-1639	195	85	0.053	0.053	NUM
ijassa-1639	195	86	100.0	100.0	NUM
ijassa-1639	195	87	a6	a6	NOUN
ijassa-1639	195	88	0.014	0.014	NUM
ijassa-1639	195	89	94.6	94.6	NUM
ijassa-1639	195	90	0.070	0.070	NUM
ijassa-1639	195	91	99.7	99.7	NUM
ijassa-1639	195	92	0.013	0.013	NUM
ijassa-1639	195	93	90.6	90.6	NUM
ijassa-1639	195	94	0.067	0.067	NUM
ijassa-1639	195	95	99.3	99.3	NUM
ijassa-1639	195	96	a7	a7	PROPN
ijassa-1639	195	97	0.022	0.022	NUM
ijassa-1639	195	98	100.0	100.0	NUM
ijassa-1639	195	99	0.092	0.092	NUM
ijassa-1639	195	100	100.0	100.0	NUM
ijassa-1639	195	101	0.018	0.018	NUM
ijassa-1639	195	102	86.5	86.5	NUM
ijassa-1639	195	103	0.077	0.077	NUM
ijassa-1639	195	104	100.0	100.0	NUM
ijassa-1639	195	105	a8	a8	PROPN
ijassa-1639	195	106	0.003	0.003	NUM
ijassa-1639	195	107	100.0	100.0	NUM
ijassa-1639	195	108	0.025	0.025	NUM
ijassa-1639	195	109	100.0	100.0	NUM
ijassa-1639	195	110	0.006	0.006	NUM
ijassa-1639	195	111	100.0	100.0	NUM
ijassa-1639	195	112	0.033	0.033	NUM
ijassa-1639	195	113	100.0	100.0	NUM
ijassa-1639	195	114	a9a	a9a	NOUN
ijassa-1639	195	115	0.064	0.064	NUM
ijassa-1639	195	116	75.7	75.7	NUM
ijassa-1639	195	117	2.508	2.508	NUM
ijassa-1639	195	118	18.0	18.0	NUM
ijassa-1639	195	119	0.055	0.055	NUM
ijassa-1639	195	120	97.7	97.7	NUM
ijassa-1639	195	121	0.277	0.277	NUM
ijassa-1639	195	122	70.8	70.8	NUM
ijassa-1639	195	123	a9b	a9b	PROPN
ijassa-1639	195	124	1.349	1.349	NUM
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ijassa-1639	195	126	0.612	0.612	NUM
ijassa-1639	195	127	59.9	59.9	NUM
ijassa-1639	195	128	0.173	0.173	NUM
ijassa-1639	195	129	100.0	100.0	NUM
ijassa-1639	195	130	0.737	0.737	NUM
ijassa-1639	195	131	77.3	77.3	NUM
ijassa-1639	195	132	a10a	a10a	PUNCT
ijassa-1639	196	1	0.031	0.031	NUM
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ijassa-1639	196	4	99.2	99.2	NUM
ijassa-1639	196	5	0.018	0.018	NUM
ijassa-1639	196	6	82.3	82.3	NUM
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ijassa-1639	196	8	98.1	98.1	NUM
ijassa-1639	196	9	a10b	a10b	DET
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ijassa-1639	196	11	75.6	75.6	NUM
ijassa-1639	196	12	0.466	0.466	NUM
ijassa-1639	196	13	99.7	99.7	NUM
ijassa-1639	196	14	0.309	0.309	NUM
ijassa-1639	196	15	87.3	87.3	NUM
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ijassa-1639	196	18	a10c	a10c	ADP
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ijassa-1639	196	20	10.2	10.2	NUM
ijassa-1639	196	21	1.612	1.612	NUM
ijassa-1639	196	22	84.3	84.3	NUM
ijassa-1639	196	23	nan	nan	PROPN
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ijassa-1639	196	25	4.097	4.097	NUM
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ijassa-1639	196	27	a10d	a10d	NUM
ijassa-1639	197	1	6.777	6.777	NUM
ijassa-1639	197	2	36.3	36.3	NUM
ijassa-1639	197	3	9.110	9.110	NUM
ijassa-1639	197	4	55.1	55.1	NUM
ijassa-1639	197	5	2.800	2.800	NUM
ijassa-1639	197	6	92.3	92.3	NUM
ijassa-1639	197	7	11.134	11.134	NUM
ijassa-1639	197	8	60.7	60.7	NUM
ijassa-1639	197	9	a10e	a10e	NUM
ijassa-1639	197	10	25.550	25.550	NUM
ijassa-1639	197	11	37.2	37.2	NUM
ijassa-1639	197	12	42.698	42.698	NUM
ijassa-1639	197	13	42.6	42.6	NUM
ijassa-1639	197	14	nan	nan	PROPN
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ijassa-1639	197	18	a11	a11	NOUN
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ijassa-1639	197	20	100.0	100.0	NUM
ijassa-1639	197	21	0.021	0.021	NUM
ijassa-1639	197	22	100.0	100.0	NUM
ijassa-1639	197	23	nan	nan	PROPN
ijassa-1639	197	24	nan	nan	PROPN
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ijassa-1639	197	26	100.0	100.0	NUM
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ijassa-1639	197	31	100.0	100.0	NUM
ijassa-1639	197	32	0.003	0.003	NUM
ijassa-1639	197	33	100.0	100.0	NUM
ijassa-1639	197	34	0.025	0.025	NUM
ijassa-1639	197	35	100.0	100.0	NUM
ijassa-1639	197	36	a13	a13	NOUN
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ijassa-1639	197	38	100.0	100.0	NUM
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ijassa-1639	197	40	100.0	100.0	NUM
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ijassa-1639	197	42	100.0	100.0	NUM
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ijassa-1639	197	44	100.0	100.0	NUM
ijassa-1639	197	45	a14	a14	PROPN
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ijassa-1639	197	47	100.0	100.0	NUM
ijassa-1639	197	48	0.040	0.040	NUM
ijassa-1639	197	49	98.9	98.9	NUM
ijassa-1639	197	50	0.012	0.012	NUM
ijassa-1639	197	51	81.8	81.8	NUM
ijassa-1639	197	52	0.049	0.049	NUM
ijassa-1639	197	53	100.0	100.0	NUM
ijassa-1639	197	54	a15	a15	NOUN
ijassa-1639	197	55	0.003	0.003	NUM
ijassa-1639	197	56	100.0	100.0	NUM
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ijassa-1639	197	58	100.0	100.0	NUM
ijassa-1639	197	59	0.004	0.004	NUM
ijassa-1639	197	60	100.0	100.0	NUM
ijassa-1639	197	61	0.037	0.037	NUM
ijassa-1639	197	62	100.0	100.0	NUM
ijassa-1639	197	63	a16a	a16a	PUNCT
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ijassa-1639	197	65	100.0	100.0	NUM
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ijassa-1639	197	67	100.0	100.0	NUM
ijassa-1639	197	68	0.004	0.004	NUM
ijassa-1639	197	69	100.0	100.0	NUM
ijassa-1639	197	70	0.033	0.033	NUM
ijassa-1639	197	71	97.9	97.9	NUM
ijassa-1639	197	72	a16b	a16b	NOUN
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ijassa-1639	197	76	100.0	100.0	NUM
ijassa-1639	197	77	0.004	0.004	NUM
ijassa-1639	197	78	100.0	100.0	NUM
ijassa-1639	197	79	0.030	0.030	NUM
ijassa-1639	197	80	100.0	100.0	NUM
ijassa-1639	197	81	a16c	a16c	PROPN
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ijassa-1639	197	83	100.0	100.0	NUM
ijassa-1639	197	84	0.031	0.031	NUM
ijassa-1639	197	85	100.0	100.0	NUM
ijassa-1639	197	86	0.005	0.005	NUM
ijassa-1639	197	87	100.0	100.0	NUM
ijassa-1639	197	88	0.039	0.039	NUM
ijassa-1639	197	89	84.0	84.0	NUM
ijassa-1639	197	90	a16d	a16d	NUM
ijassa-1639	197	91	0.007	0.007	NUM
ijassa-1639	197	92	100.0	100.0	NUM
ijassa-1639	197	93	0.032	0.032	NUM
ijassa-1639	197	94	100.0	100.0	NUM
ijassa-1639	197	95	0.007	0.007	NUM
ijassa-1639	197	96	100.0	100.0	NUM
ijassa-1639	197	97	0.037	0.037	NUM
ijassa-1639	197	98	100.0	100.0	NUM
ijassa-1639	197	99	a17	a17	NOUN
ijassa-1639	197	100	0.004	0.004	NUM
ijassa-1639	197	101	100.0	100.0	NUM
ijassa-1639	197	102	0.024	0.024	NUM
ijassa-1639	197	103	100.0	100.0	NUM
ijassa-1639	197	104	0.005	0.005	NUM
ijassa-1639	197	105	100.0	100.0	NUM
ijassa-1639	197	106	0.036	0.036	NUM
ijassa-1639	197	107	100.0	100.0	NUM
ijassa-1639	197	108	a18	a18	NOUN
ijassa-1639	197	109	0.007	0.007	NUM
ijassa-1639	197	110	100.0	100.0	NUM
ijassa-1639	197	111	0.050	0.050	NUM
ijassa-1639	197	112	100.0	100.0	NUM
ijassa-1639	197	113	0.011	0.011	NUM
ijassa-1639	197	114	94.5	94.5	NUM
ijassa-1639	197	115	0.053	0.053	NUM
ijassa-1639	197	116	100.0	100.0	NUM
ijassa-1639	197	117	harker	harker	NOUN
ijassa-1639	197	118	0.003	0.003	NUM
ijassa-1639	197	119	100.0	100.0	NUM
ijassa-1639	197	120	0.023	0.023	NUM
ijassa-1639	197	121	100.0	100.0	NUM
ijassa-1639	197	122	0.006	0.006	NUM
ijassa-1639	197	123	100.0	100.0	NUM
ijassa-1639	197	124	0.036	0.036	NUM
ijassa-1639	197	125	100.0	100.0	NUM
ijassa-1639	197	126	heu	heu	PROPN
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ijassa-1639	197	128	100.0	100.0	NUM
ijassa-1639	197	129	0.053	0.053	NUM
ijassa-1639	197	130	100.0	100.0	NUM
ijassa-1639	197	131	0.011	0.011	NUM
ijassa-1639	197	132	100.0	100.0	NUM
ijassa-1639	197	133	0.057	0.057	NUM
ijassa-1639	197	134	100.0	100.0	NUM
ijassa-1639	197	135	lob	lob	NOUN
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ijassa-1639	197	137	37.6	37.6	NUM
ijassa-1639	198	1	nan	nan	PROPN
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ijassa-1639	199	5	ntf1	ntf1	VERB
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ijassa-1639	199	7	100.0	100.0	NUM
ijassa-1639	199	8	0.022	0.022	NUM
ijassa-1639	199	9	100.0	100.0	NUM
ijassa-1639	199	10	0.003	0.003	NUM
ijassa-1639	199	11	100.0	100.0	NUM
ijassa-1639	199	12	0.031	0.031	NUM
ijassa-1639	199	13	100.0	100.0	NUM
ijassa-1639	199	14	ntf2	ntf2	NOUN
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ijassa-1639	199	16	90.5	90.5	NUM
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ijassa-1639	199	18	99.4	99.4	NUM
ijassa-1639	199	19	0.006	0.006	NUM
ijassa-1639	199	20	94.8	94.8	NUM
ijassa-1639	199	21	0.034	0.034	NUM
ijassa-1639	199	22	100.0	100.0	NUM
ijassa-1639	199	23	spam	spam	NOUN
ijassa-1639	199	24	1380.005	1380.005	NUM
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ijassa-1639	199	27	95.9	95.9	NUM
ijassa-1639	200	1	nan	nan	PROPN
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ijassa-1639	200	5	tr1a	tr1a	PROPN
ijassa-1639	200	6	0.059	0.059	NUM
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ijassa-1639	200	8	0.111	0.111	NUM
ijassa-1639	200	9	90.4	90.4	NUM
ijassa-1639	200	10	0.050	0.050	NUM
ijassa-1639	200	11	94.4	94.4	NUM
ijassa-1639	200	12	0.071	0.071	NUM
ijassa-1639	200	13	96.7	96.7	NUM
ijassa-1639	200	14	tr1b	tr1b	PROPN
ijassa-1639	200	15	nan	nan	PROPN
ijassa-1639	200	16	nan	nan	PROPN
ijassa-1639	200	17	1.617	1.617	NUM
ijassa-1639	200	18	66.8	66.8	NUM
ijassa-1639	200	19	1.188	1.188	NUM
ijassa-1639	200	20	43.2	43.2	NUM
ijassa-1639	200	21	1.636	1.636	NUM
ijassa-1639	200	22	46.1	46.1	NUM
ijassa-1639	200	23	tr1c	tr1c	PROPN
ijassa-1639	200	24	3.878	3.878	NUM
ijassa-1639	200	25	26.2	26.2	NUM
ijassa-1639	200	26	2.245	2.245	NUM
ijassa-1639	200	27	71.4	71.4	NUM
ijassa-1639	200	28	2.231	2.231	NUM
ijassa-1639	200	29	39.7	39.7	NUM
ijassa-1639	200	30	1.365	1.365	NUM
ijassa-1639	200	31	62.6	62.6	NUM
ijassa-1639	200	32	copyright	copyright	NOUN
ijassa-1639	200	33	©	©	PROPN
ijassa-1639	200	34	2024	2024	NUM
ijassa-1639	200	35	assa	assa	NOUN
ijassa-1639	200	36	.	.	PUNCT
ijassa-1639	201	1	adv	adv	PROPN
ijassa-1639	201	2	syst	syst	PROPN
ijassa-1639	201	3	sci	sci	PROPN
ijassa-1639	201	4	appl	appl	PROPN
ijassa-1639	201	5	(	(	PUNCT
ijassa-1639	201	6	2024	2024	NUM
ijassa-1639	201	7	)	)	PUNCT
ijassa-1639	201	8	28	28	NUM
ijassa-1639	201	9	a.	a.	PROPN
ijassa-1639	201	10	f.	f.	PROPN
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ijassa-1639	201	12	,	,	PUNCT
ijassa-1639	201	13	e.	e.	PROPN
ijassa-1639	201	14	i.	i.	PROPN
ijassa-1639	201	15	uskov	uskov	PROPN
ijassa-1639	201	16	,	,	PUNCT
ijassa-1639	201	17	yan	yan	PROPN
ijassa-1639	201	18	zhibai	zhibai	PROPN
ijassa-1639	201	19	table	table	VERB
ijassa-1639	201	20	4.2	4.2	NUM
ijassa-1639	201	21	.	.	PUNCT
ijassa-1639	202	1	failures	failure	NOUN
ijassa-1639	202	2	test	test	VERB
ijassa-1639	202	3	pwlm	pwlm	PROPN
ijassa-1639	202	4	pwlpn	pwlpn	PROPN
ijassa-1639	202	5	lm	lm	PROPN
ijassa-1639	202	6	-	-	PUNCT
ijassa-1639	202	7	had	have	VERB
ijassa-1639	202	8	lpn	lpn	NOUN
ijassa-1639	202	9	-	-	PUNCT
ijassa-1639	202	10	had	have	AUX
ijassa-1639	202	11	a1	a1	NOUN
ijassa-1639	202	12	0	0	NUM
ijassa-1639	202	13	0	0	NUM
ijassa-1639	202	14	0	0	NUM
ijassa-1639	202	15	1	1	NUM
ijassa-1639	202	16	ss	ss	NOUN
ijassa-1639	202	17	a2	a2	PROPN
ijassa-1639	202	18	20	20	NUM
ijassa-1639	202	19	ss	ss	NOUN
ijassa-1639	202	20	0	0	NUM
ijassa-1639	202	21	20	20	NUM
ijassa-1639	202	22	(	(	PUNCT
ijassa-1639	202	23	13	13	NUM
ijassa-1639	202	24	sf	sf	PROPN
ijassa-1639	202	25	,	,	PUNCT
ijassa-1639	202	26	2	2	NUM
ijassa-1639	202	27	il	il	PROPN
ijassa-1639	202	28	,	,	PUNCT
ijassa-1639	202	29	5	5	NUM
ijassa-1639	202	30	ss	ss	NOUN
ijassa-1639	202	31	)	)	PUNCT
ijassa-1639	202	32	0	0	NUM
ijassa-1639	202	33	a3	a3	NOUN
ijassa-1639	202	34	0	0	NUM
ijassa-1639	202	35	12	12	NUM
ijassa-1639	202	36	sp	sp	ADP
ijassa-1639	202	37	1	1	NUM
ijassa-1639	202	38	sf	sf	NOUN
ijassa-1639	202	39	9	9	NUM
ijassa-1639	202	40	(	(	PUNCT
ijassa-1639	202	41	7	7	NUM
ijassa-1639	202	42	sp	sp	NOUN
ijassa-1639	202	43	,	,	PUNCT
ijassa-1639	202	44	2	2	NUM
ijassa-1639	202	45	ss	ss	NOUN
ijassa-1639	202	46	)	)	PUNCT
ijassa-1639	202	47	a4	a4	NOUN
ijassa-1639	202	48	4	4	NUM
ijassa-1639	202	49	(	(	PUNCT
ijassa-1639	202	50	1	1	NUM
ijassa-1639	202	51	sf	sf	PROPN
ijassa-1639	202	52	,	,	PUNCT
ijassa-1639	202	53	3	3	NUM
ijassa-1639	202	54	ss	ss	NOUN
ijassa-1639	202	55	)	)	PUNCT
ijassa-1639	202	56	0	0	NUM
ijassa-1639	202	57	4	4	NUM
ijassa-1639	202	58	sf	sf	NOUN
ijassa-1639	202	59	0	0	NUM
ijassa-1639	202	60	a5	a5	X
ijassa-1639	202	61	0	0	NUM
ijassa-1639	202	62	0	0	NUM
ijassa-1639	202	63	0	0	NUM
ijassa-1639	202	64	0	0	NUM
ijassa-1639	202	65	a6	a6	NOUN
ijassa-1639	202	66	2	2	NUM
ijassa-1639	202	67	ss	ss	NOUN
ijassa-1639	202	68	0	0	NUM
ijassa-1639	202	69	1	1	NUM
ijassa-1639	202	70	sf	sf	NOUN
ijassa-1639	202	71	0	0	NUM
ijassa-1639	202	72	a7	a7	PROPN
ijassa-1639	202	73	14	14	NUM
ijassa-1639	202	74	ss	ss	NOUN
ijassa-1639	202	75	8	8	NUM
ijassa-1639	202	76	sp	sp	ADP
ijassa-1639	202	77	0	0	NUM
ijassa-1639	202	78	0	0	NUM
ijassa-1639	202	79	a8	a8	NOUN
ijassa-1639	202	80	0	0	NUM
ijassa-1639	202	81	0	0	NUM
ijassa-1639	202	82	5	5	NUM
ijassa-1639	202	83	sf	sf	NOUN
ijassa-1639	202	84	0	0	NUM
ijassa-1639	202	85	a9a	a9a	NOUN
ijassa-1639	202	86	8	8	NUM
ijassa-1639	202	87	(	(	PUNCT
ijassa-1639	202	88	2	2	NUM
ijassa-1639	202	89	sf	sf	PROPN
ijassa-1639	202	90	,	,	PUNCT
ijassa-1639	202	91	6	6	NUM
ijassa-1639	202	92	ss	ss	NOUN
ijassa-1639	202	93	)	)	PUNCT
ijassa-1639	202	94	12	12	NUM
ijassa-1639	202	95	il	il	PROPN
ijassa-1639	202	96	0	0	NUM
ijassa-1639	202	97	0	0	NUM
ijassa-1639	202	98	a9b	a9b	PROPN
ijassa-1639	202	99	1	1	NUM
ijassa-1639	202	100	il	il	PROPN
ijassa-1639	202	101	0	0	NUM
ijassa-1639	202	102	0	0	NUM
ijassa-1639	202	103	0	0	PUNCT
ijassa-1639	203	1	a10a	a10a	NOUN
ijassa-1639	203	2	0	0	NUM
ijassa-1639	203	3	0	0	NUM
ijassa-1639	203	4	3	3	NUM
ijassa-1639	203	5	sf	sf	NOUN
ijassa-1639	203	6	0	0	NUM
ijassa-1639	203	7	a10b	a10b	SYM
ijassa-1639	203	8	0	0	NUM
ijassa-1639	203	9	0	0	NUM
ijassa-1639	203	10	2	2	NUM
ijassa-1639	203	11	(	(	PUNCT
ijassa-1639	203	12	1	1	NUM
ijassa-1639	203	13	sf	sf	PROPN
ijassa-1639	203	14	,	,	PUNCT
ijassa-1639	203	15	1	1	NUM
ijassa-1639	203	16	ss	ss	NOUN
ijassa-1639	203	17	)	)	PUNCT
ijassa-1639	203	18	0	0	PUNCT
ijassa-1639	204	1	a10c	a10c	X
ijassa-1639	204	2	0	0	NUM
ijassa-1639	204	3	0	0	NUM
ijassa-1639	204	4	20	20	NUM
ijassa-1639	204	5	(	(	PUNCT
ijassa-1639	204	6	2	2	NUM
ijassa-1639	204	7	sf	sf	PROPN
ijassa-1639	204	8	,	,	PUNCT
ijassa-1639	204	9	18	18	NUM
ijassa-1639	204	10	ss	ss	NOUN
ijassa-1639	204	11	)	)	PUNCT
ijassa-1639	204	12	0	0	PUNCT
ijassa-1639	205	1	a10d	a10d	NOUN
ijassa-1639	205	2	0	0	NUM
ijassa-1639	205	3	5	5	NUM
ijassa-1639	205	4	(	(	PUNCT
ijassa-1639	205	5	4	4	NUM
ijassa-1639	205	6	il	il	PROPN
ijassa-1639	205	7	,	,	PUNCT
ijassa-1639	205	8	1	1	NUM
ijassa-1639	205	9	sp	sp	NOUN
ijassa-1639	205	10	)	)	PUNCT
ijassa-1639	205	11	19	19	NUM
ijassa-1639	205	12	(	(	PUNCT
ijassa-1639	205	13	8	8	NUM
ijassa-1639	205	14	sf	sf	PROPN
ijassa-1639	205	15	,	,	PUNCT
ijassa-1639	205	16	11	11	NUM
ijassa-1639	205	17	ss	ss	NOUN
ijassa-1639	205	18	)	)	PUNCT
ijassa-1639	205	19	2	2	NUM
ijassa-1639	205	20	il	il	PROPN
ijassa-1639	205	21	a10e	a10e	PROPN
ijassa-1639	205	22	2	2	NUM
ijassa-1639	205	23	(	(	PUNCT
ijassa-1639	205	24	1	1	NUM
ijassa-1639	205	25	sf	sf	PROPN
ijassa-1639	205	26	,	,	PUNCT
ijassa-1639	205	27	1	1	NUM
ijassa-1639	205	28	ss	ss	NOUN
ijassa-1639	205	29	)	)	PUNCT
ijassa-1639	205	30	9	9	NUM
ijassa-1639	205	31	il	il	PROPN
ijassa-1639	205	32	20	20	NUM
ijassa-1639	205	33	(	(	PUNCT
ijassa-1639	205	34	13	13	NUM
ijassa-1639	205	35	sf	sf	PROPN
ijassa-1639	205	36	,	,	PUNCT
ijassa-1639	205	37	7	7	NUM
ijassa-1639	205	38	ss	ss	NOUN
ijassa-1639	205	39	)	)	PUNCT
ijassa-1639	205	40	0	0	NUM
ijassa-1639	206	1	a11	a11	PROPN
ijassa-1639	206	2	0	0	NUM
ijassa-1639	206	3	0	0	NUM
ijassa-1639	206	4	20	20	NUM
ijassa-1639	206	5	sf	sf	NOUN
ijassa-1639	206	6	0	0	NUM
ijassa-1639	206	7	a12	a12	NOUN
ijassa-1639	206	8	0	0	NUM
ijassa-1639	206	9	0	0	NUM
ijassa-1639	206	10	5	5	NUM
ijassa-1639	206	11	sf	sf	NOUN
ijassa-1639	206	12	0	0	NUM
ijassa-1639	206	13	a13	a13	PROPN
ijassa-1639	206	14	5	5	NUM
ijassa-1639	206	15	sf	sf	NOUN
ijassa-1639	206	16	0	0	NUM
ijassa-1639	206	17	0	0	NUM
ijassa-1639	206	18	0	0	NUM
ijassa-1639	206	19	a14	a14	NOUN
ijassa-1639	206	20	0	0	NUM
ijassa-1639	206	21	0	0	NUM
ijassa-1639	206	22	0	0	NUM
ijassa-1639	206	23	0	0	NUM
ijassa-1639	206	24	a15	a15	NOUN
ijassa-1639	206	25	0	0	NUM
ijassa-1639	206	26	0	0	NUM
ijassa-1639	206	27	2	2	NUM
ijassa-1639	206	28	sf	sf	NOUN
ijassa-1639	206	29	0	0	NUM
ijassa-1639	206	30	a16a	a16a	PUNCT
ijassa-1639	206	31	1	1	NUM
ijassa-1639	206	32	sf	sf	NOUN
ijassa-1639	206	33	0	0	NUM
ijassa-1639	206	34	2	2	NUM
ijassa-1639	206	35	sf	sf	NOUN
ijassa-1639	206	36	0	0	NUM
ijassa-1639	207	1	a16b	a16b	SYM
ijassa-1639	207	2	2	2	NUM
ijassa-1639	207	3	sf	sf	NOUN
ijassa-1639	207	4	0	0	NUM
ijassa-1639	207	5	2	2	NUM
ijassa-1639	207	6	sf	sf	NOUN
ijassa-1639	207	7	0	0	NUM
ijassa-1639	207	8	a16c	a16c	PROPN
ijassa-1639	207	9	1	1	NUM
ijassa-1639	207	10	sf	sf	NOUN
ijassa-1639	207	11	0	0	NUM
ijassa-1639	207	12	6	6	NUM
ijassa-1639	207	13	sf	sf	NOUN
ijassa-1639	207	14	0	0	PUNCT
ijassa-1639	207	15	a16d	a16d	NOUN
ijassa-1639	207	16	0	0	NUM
ijassa-1639	207	17	0	0	NUM
ijassa-1639	207	18	2	2	NUM
ijassa-1639	207	19	sf	sf	NOUN
ijassa-1639	207	20	0	0	NUM
ijassa-1639	207	21	a17	a17	NOUN
ijassa-1639	207	22	0	0	NUM
ijassa-1639	207	23	0	0	NUM
ijassa-1639	207	24	2	2	NUM
ijassa-1639	207	25	sf	sf	NOUN
ijassa-1639	207	26	0	0	NUM
ijassa-1639	207	27	a18	a18	NOUN
ijassa-1639	207	28	0	0	NUM
ijassa-1639	207	29	0	0	NUM
ijassa-1639	207	30	1	1	NUM
ijassa-1639	207	31	sf	sf	NOUN
ijassa-1639	207	32	0	0	NUM
ijassa-1639	207	33	harker	harker	NOUN
ijassa-1639	207	34	0	0	NUM
ijassa-1639	207	35	0	0	NUM
ijassa-1639	207	36	0	0	NUM
ijassa-1639	207	37	0	0	NUM
ijassa-1639	207	38	heu	heu	PROPN
ijassa-1639	207	39	15	15	NUM
ijassa-1639	207	40	ss	ss	NOUN
ijassa-1639	207	41	0	0	NUM
ijassa-1639	207	42	6	6	NUM
ijassa-1639	207	43	sf	sf	NOUN
ijassa-1639	207	44	0	0	NUM
ijassa-1639	207	45	lob	lob	NOUN
ijassa-1639	207	46	0	0	NUM
ijassa-1639	207	47	20	20	NUM
ijassa-1639	207	48	il	il	PROPN
ijassa-1639	207	49	20	20	NUM
ijassa-1639	207	50	ss	ss	NOUN
ijassa-1639	207	51	20	20	NUM
ijassa-1639	207	52	il	il	PROPN
ijassa-1639	207	53	ntf1	ntf1	NOUN
ijassa-1639	207	54	0	0	NUM
ijassa-1639	207	55	0	0	NUM
ijassa-1639	207	56	4	4	NUM
ijassa-1639	207	57	sf	sf	NOUN
ijassa-1639	207	58	0	0	NUM
ijassa-1639	207	59	ntf2	ntf2	NOUN
ijassa-1639	207	60	0	0	NUM
ijassa-1639	207	61	0	0	NUM
ijassa-1639	207	62	4	4	NUM
ijassa-1639	207	63	sf	sf	NOUN
ijassa-1639	207	64	0	0	NUM
ijassa-1639	207	65	spam	spam	NOUN
ijassa-1639	207	66	0	0	NUM
ijassa-1639	207	67	15	15	NUM
ijassa-1639	207	68	sf	sf	NOUN
ijassa-1639	207	69	20	20	NUM
ijassa-1639	207	70	sf	sf	NUM
ijassa-1639	207	71	17	17	NUM
ijassa-1639	207	72	(	(	PUNCT
ijassa-1639	207	73	14	14	NUM
ijassa-1639	207	74	sf	sf	PROPN
ijassa-1639	207	75	,	,	PUNCT
ijassa-1639	207	76	1	1	NUM
ijassa-1639	207	77	sp	sp	NOUN
ijassa-1639	207	78	,	,	PUNCT
ijassa-1639	207	79	2	2	NUM
ijassa-1639	207	80	ss	ss	NOUN
ijassa-1639	207	81	)	)	PUNCT
ijassa-1639	207	82	tr1a	tr1a	NOUN
ijassa-1639	207	83	16	16	NUM
ijassa-1639	207	84	(	(	PUNCT
ijassa-1639	207	85	9	9	NUM
ijassa-1639	207	86	sf	sf	PROPN
ijassa-1639	207	87	,	,	PUNCT
ijassa-1639	207	88	7	7	NUM
ijassa-1639	207	89	ss	ss	NOUN
ijassa-1639	207	90	)	)	PUNCT
ijassa-1639	207	91	2	2	NUM
ijassa-1639	207	92	sp	sp	ADP
ijassa-1639	207	93	1	1	NUM
ijassa-1639	207	94	sf	sf	NOUN
ijassa-1639	207	95	0	0	NUM
ijassa-1639	207	96	tr1b	tr1b	X
ijassa-1639	207	97	20	20	NUM
ijassa-1639	207	98	(	(	PUNCT
ijassa-1639	207	99	14	14	NUM
ijassa-1639	207	100	sf	sf	PROPN
ijassa-1639	207	101	,	,	PUNCT
ijassa-1639	207	102	1	1	NUM
ijassa-1639	207	103	il	il	PROPN
ijassa-1639	207	104	,	,	PUNCT
ijassa-1639	207	105	5	5	NUM
ijassa-1639	207	106	ss	ss	NOUN
ijassa-1639	207	107	)	)	PUNCT
ijassa-1639	207	108	1	1	NUM
ijassa-1639	207	109	sp	sp	ADP
ijassa-1639	207	110	12	12	NUM
ijassa-1639	207	111	(	(	PUNCT
ijassa-1639	207	112	9	9	NUM
ijassa-1639	207	113	sf	sf	PROPN
ijassa-1639	207	114	,	,	PUNCT
ijassa-1639	207	115	3	3	NUM
ijassa-1639	207	116	ss	ss	NOUN
ijassa-1639	207	117	)	)	PUNCT
ijassa-1639	207	118	0	0	PUNCT
ijassa-1639	208	1	tr1c	tr1c	NOUN
ijassa-1639	208	2	18	18	NUM
ijassa-1639	208	3	(	(	PUNCT
ijassa-1639	208	4	5	5	NUM
ijassa-1639	208	5	sf	sf	PROPN
ijassa-1639	208	6	,	,	PUNCT
ijassa-1639	208	7	3	3	NUM
ijassa-1639	208	8	il	il	PROPN
ijassa-1639	208	9	,	,	PUNCT
ijassa-1639	208	10	10	10	NUM
ijassa-1639	208	11	ss	ss	NOUN
ijassa-1639	208	12	)	)	PUNCT
ijassa-1639	208	13	4	4	NUM
ijassa-1639	208	14	(	(	PUNCT
ijassa-1639	208	15	3	3	NUM
ijassa-1639	208	16	il	il	PROPN
ijassa-1639	208	17	,	,	PUNCT
ijassa-1639	208	18	1	1	NUM
ijassa-1639	208	19	sp	sp	NOUN
ijassa-1639	208	20	)	)	PUNCT
ijassa-1639	208	21	11	11	NUM
ijassa-1639	208	22	(	(	PUNCT
ijassa-1639	208	23	5	5	NUM
ijassa-1639	208	24	sf	sf	PROPN
ijassa-1639	208	25	,	,	PUNCT
ijassa-1639	208	26	1	1	NUM
ijassa-1639	208	27	il	il	PROPN
ijassa-1639	208	28	,	,	PUNCT
ijassa-1639	208	29	5	5	NUM
ijassa-1639	208	30	ss	ss	NOUN
ijassa-1639	208	31	)	)	PUNCT
ijassa-1639	208	32	0	0	NUM
ijassa-1639	208	33	πa(t	πa(t	PUNCT
ijassa-1639	208	34	)	)	PUNCT
ijassa-1639	208	35	for	for	ADP
ijassa-1639	208	36	large	large	ADJ
ijassa-1639	208	37	t	t	PROPN
ijassa-1639	208	38	is	be	AUX
ijassa-1639	208	39	the	the	DET
ijassa-1639	208	40	portion	portion	NOUN
ijassa-1639	208	41	of	of	ADP
ijassa-1639	208	42	test	test	NOUN
ijassa-1639	208	43	problems	problem	NOUN
ijassa-1639	208	44	the	the	DET
ijassa-1639	208	45	runs	run	NOUN
ijassa-1639	208	46	of	of	ADP
ijassa-1639	208	47	algorithm	algorithm	NOUN
ijassa-1639	208	48	a	a	DET
ijassa-1639	208	49	on	on	ADP
ijassa-1639	208	50	which	which	PRON
ijassa-1639	208	51	are	be	AUX
ijassa-1639	208	52	successful	successful	ADJ
ijassa-1639	208	53	,	,	PUNCT
ijassa-1639	208	54	while	while	SCONJ
ijassa-1639	208	55	πa(1	πa(1	NOUN
ijassa-1639	208	56	)	)	PUNCT
ijassa-1639	208	57	is	be	AUX
ijassa-1639	208	58	the	the	DET
ijassa-1639	208	59	portion	portion	NOUN
ijassa-1639	208	60	of	of	ADP
ijassa-1639	208	61	problems	problem	NOUN
ijassa-1639	208	62	on	on	ADP
ijassa-1639	208	63	which	which	PRON
ijassa-1639	208	64	the	the	DET
ijassa-1639	208	65	runs	run	NOUN
ijassa-1639	208	66	of	of	ADP
ijassa-1639	208	67	algorithm	algorithm	NOUN
ijassa-1639	208	68	a	a	PRON
ijassa-1639	208	69	are	be	AUX
ijassa-1639	208	70	successful	successful	ADJ
ijassa-1639	208	71	and	and	CCONJ
ijassa-1639	208	72	its	its	PRON
ijassa-1639	208	73	efficiency	efficiency	NOUN
ijassa-1639	208	74	is	be	AUX
ijassa-1639	208	75	the	the	DET
ijassa-1639	208	76	best	good	ADJ
ijassa-1639	208	77	.	.	PUNCT
ijassa-1639	209	1	copyright	copyright	NOUN
ijassa-1639	209	2	©	©	PROPN
ijassa-1639	209	3	2024	2024	NUM
ijassa-1639	209	4	assa	assa	NOUN
ijassa-1639	209	5	.	.	PUNCT
ijassa-1639	210	1	adv	adv	PROPN
ijassa-1639	210	2	syst	syst	PROPN
ijassa-1639	210	3	sci	sci	PROPN
ijassa-1639	210	4	appl	appl	PROPN
ijassa-1639	210	5	(	(	PUNCT
ijassa-1639	210	6	2024	2024	NUM
ijassa-1639	210	7	)	)	PUNCT
ijassa-1639	210	8	piecewise	piecewise	NOUN
ijassa-1639	210	9	levenberg	levenberg	PROPN
ijassa-1639	210	10	–	–	PUNCT
ijassa-1639	210	11	marquardt	marquardt	PROPN
ijassa-1639	210	12	method	method	NOUN
ijassa-1639	210	13	for	for	ADP
ijassa-1639	210	14	gneps	gneps	NOUN
ijassa-1639	210	15	29	29	NUM
ijassa-1639	210	16	figure	figure	NOUN
ijassa-1639	210	17	4.1	4.1	NUM
ijassa-1639	210	18	presents	present	VERB
ijassa-1639	210	19	the	the	DET
ijassa-1639	210	20	comparison	comparison	NOUN
ijassa-1639	210	21	for	for	ADP
ijassa-1639	210	22	three	three	NUM
ijassa-1639	210	23	different	different	ADJ
ijassa-1639	210	24	values	value	NOUN
ijassa-1639	210	25	of	of	ADP
ijassa-1639	210	26	σ̄.	σ̄.	PUNCT
ijassa-1639	210	27	figure	figure	NOUN
ijassa-1639	210	28	4.1a	4.1a	NOUN
ijassa-1639	210	29	demonstrates	demonstrate	VERB
ijassa-1639	210	30	the	the	DET
ijassa-1639	210	31	advantages	advantage	NOUN
ijassa-1639	210	32	of	of	ADP
ijassa-1639	210	33	running	run	VERB
ijassa-1639	210	34	pwlm	pwlm	NOUN
ijassa-1639	210	35	with	with	ADP
ijassa-1639	210	36	σ̄	σ̄	PROPN
ijassa-1639	210	37	=	=	SYM
ijassa-1639	210	38	10−10	10−10	NUM
ijassa-1639	210	39	,	,	PUNCT
ijassa-1639	210	40	by	by	ADP
ijassa-1639	210	41	iteration	iteration	NOUN
ijassa-1639	210	42	count	count	NOUN
ijassa-1639	210	43	,	,	PUNCT
ijassa-1639	210	44	while	while	SCONJ
ijassa-1639	210	45	robustness	robustness	NOUN
ijassa-1639	210	46	of	of	ADP
ijassa-1639	210	47	all	all	DET
ijassa-1639	210	48	compared	compare	VERB
ijassa-1639	210	49	variants	variant	NOUN
ijassa-1639	210	50	is	be	AUX
ijassa-1639	210	51	nearly	nearly	ADV
ijassa-1639	210	52	the	the	DET
ijassa-1639	210	53	same	same	ADJ
ijassa-1639	210	54	.	.	PUNCT
ijassa-1639	211	1	in	in	ADP
ijassa-1639	211	2	figure	figure	NOUN
ijassa-1639	211	3	4.1b	4.1b	PROPN
ijassa-1639	211	4	,	,	PUNCT
ijassa-1639	211	5	the	the	DET
ijassa-1639	211	6	comparison	comparison	NOUN
ijassa-1639	211	7	by	by	ADP
ijassa-1639	211	8	iteration	iteration	NOUN
ijassa-1639	211	9	count	count	NOUN
ijassa-1639	211	10	is	be	AUX
ijassa-1639	211	11	similar	similar	ADJ
ijassa-1639	211	12	,	,	PUNCT
ijassa-1639	211	13	while	while	SCONJ
ijassa-1639	211	14	robustness	robustness	NOUN
ijassa-1639	211	15	for	for	ADP
ijassa-1639	211	16	this	this	DET
ijassa-1639	211	17	choice	choice	NOUN
ijassa-1639	211	18	of	of	ADP
ijassa-1639	211	19	σ̄	σ̄	PRON
ijassa-1639	211	20	is	be	AUX
ijassa-1639	211	21	only	only	ADV
ijassa-1639	211	22	slightly	slightly	ADV
ijassa-1639	211	23	lower	low	ADJ
ijassa-1639	211	24	than	than	ADP
ijassa-1639	211	25	for	for	ADP
ijassa-1639	211	26	the	the	DET
ijassa-1639	211	27	value	value	NOUN
ijassa-1639	211	28	σ̄	σ̄	X
ijassa-1639	211	29	=	=	SYM
ijassa-1639	211	30	10−8	10−8	NUM
ijassa-1639	211	31	.	.	PUNCT
ijassa-1639	212	1	that	that	PRON
ijassa-1639	212	2	is	be	AUX
ijassa-1639	212	3	why	why	SCONJ
ijassa-1639	212	4	σ̄	σ̄	PRON
ijassa-1639	212	5	=	=	SYM
ijassa-1639	212	6	10−10	10−10	PROPN
ijassa-1639	212	7	was	be	AUX
ijassa-1639	212	8	adopted	adopt	VERB
ijassa-1639	212	9	in	in	ADP
ijassa-1639	212	10	further	further	ADJ
ijassa-1639	212	11	experiments	experiment	NOUN
ijassa-1639	212	12	.	.	PUNCT
ijassa-1639	213	1	at	at	ADP
ijassa-1639	213	2	this	this	DET
ijassa-1639	213	3	point	point	NOUN
ijassa-1639	213	4	we	we	PRON
ijassa-1639	213	5	mention	mention	VERB
ijassa-1639	213	6	that	that	SCONJ
ijassa-1639	213	7	we	we	PRON
ijassa-1639	213	8	have	have	AUX
ijassa-1639	213	9	also	also	ADV
ijassa-1639	213	10	experimented	experiment	VERB
ijassa-1639	213	11	with	with	ADP
ijassa-1639	213	12	different	different	ADJ
ijassa-1639	213	13	values	value	NOUN
ijassa-1639	213	14	of	of	ADP
ijassa-1639	213	15	the	the	DET
ijassa-1639	213	16	exponent	exponent	ADJ
ijassa-1639	213	17	θ	θ	PROPN
ijassa-1639	213	18	in	in	ADP
ijassa-1639	213	19	the	the	DET
ijassa-1639	213	20	regularization	regularization	NOUN
ijassa-1639	213	21	parameter	parameter	NOUN
ijassa-1639	213	22	employed	employ	VERB
ijassa-1639	213	23	by	by	ADP
ijassa-1639	213	24	pwlm	pwlm	PROPN
ijassa-1639	213	25	.	.	PUNCT
ijassa-1639	214	1	specifically	specifically	ADV
ijassa-1639	214	2	,	,	PUNCT
ijassa-1639	214	3	we	we	PRON
ijassa-1639	214	4	tried	try	VERB
ijassa-1639	214	5	θ	θ	PROPN
ijassa-1639	214	6	=	=	SYM
ijassa-1639	214	7	1.5	1.5	NUM
ijassa-1639	214	8	and	and	CCONJ
ijassa-1639	214	9	θ	θ	NOUN
ijassa-1639	214	10	=	=	SYM
ijassa-1639	214	11	1	1	NUM
ijassa-1639	214	12	,	,	PUNCT
ijassa-1639	214	13	along	along	ADP
ijassa-1639	214	14	with	with	ADP
ijassa-1639	214	15	the	the	DET
ijassa-1639	214	16	basic	basic	ADJ
ijassa-1639	214	17	choice	choice	NOUN
ijassa-1639	214	18	θ	θ	NOUN
ijassa-1639	214	19	=	=	SYM
ijassa-1639	214	20	2	2	NUM
ijassa-1639	214	21	,	,	PUNCT
ijassa-1639	214	22	but	but	CCONJ
ijassa-1639	214	23	much	much	ADJ
ijassa-1639	214	24	difference	difference	NOUN
ijassa-1639	214	25	in	in	ADP
ijassa-1639	214	26	performance	performance	NOUN
ijassa-1639	214	27	was	be	AUX
ijassa-1639	214	28	detected	detect	VERB
ijassa-1639	214	29	neither	neither	CCONJ
ijassa-1639	214	30	by	by	ADP
ijassa-1639	214	31	iteration	iteration	NOUN
ijassa-1639	214	32	counts	count	NOUN
ijassa-1639	214	33	not	not	PART
ijassa-1639	214	34	by	by	ADP
ijassa-1639	214	35	evaluations	evaluation	NOUN
ijassa-1639	214	36	of	of	ADP
ijassa-1639	214	37	φ	φ	PROPN
ijassa-1639	214	38	.	.	PUNCT
ijassa-1639	215	1	the	the	DET
ijassa-1639	215	2	variant	variant	NOUN
ijassa-1639	215	3	with	with	ADP
ijassa-1639	215	4	θ	θ	PROPN
ijassa-1639	215	5	=	=	SYM
ijassa-1639	215	6	1	1	NUM
ijassa-1639	215	7	seriously	seriously	ADV
ijassa-1639	215	8	outperforms	outperform	VERB
ijassa-1639	215	9	the	the	DET
ijassa-1639	215	10	alternatives	alternative	NOUN
ijassa-1639	215	11	by	by	ADP
ijassa-1639	215	12	the	the	DET
ijassa-1639	215	13	elapsed	elapse	VERB
ijassa-1639	215	14	time	time	NOUN
ijassa-1639	215	15	,	,	PUNCT
ijassa-1639	215	16	and	and	CCONJ
ijassa-1639	215	17	especially	especially	ADV
ijassa-1639	215	18	the	the	DET
ijassa-1639	215	19	variant	variant	NOUN
ijassa-1639	215	20	with	with	ADP
ijassa-1639	215	21	θ	θ	PROPN
ijassa-1639	215	22	=	=	SYM
ijassa-1639	215	23	2	2	X
ijassa-1639	215	24	.	.	PUNCT
ijassa-1639	216	1	this	this	DET
ijassa-1639	216	2	phenomenon	phenomenon	NOUN
ijassa-1639	216	3	is	be	AUX
ijassa-1639	216	4	explained	explain	VERB
ijassa-1639	216	5	by	by	ADP
ijassa-1639	216	6	the	the	DET
ijassa-1639	216	7	difference	difference	NOUN
ijassa-1639	216	8	in	in	ADP
ijassa-1639	216	9	solution	solution	NOUN
ijassa-1639	216	10	times	time	NOUN
ijassa-1639	216	11	for	for	ADP
ijassa-1639	216	12	pwlm	pwlm	PROPN
ijassa-1639	216	13	subproblems	subproblem	NOUN
ijassa-1639	216	14	formed	form	VERB
ijassa-1639	216	15	with	with	ADP
ijassa-1639	216	16	different	different	ADJ
ijassa-1639	216	17	θ	θ	PROPN
ijassa-1639	216	18	,	,	PUNCT
ijassa-1639	216	19	which	which	PRON
ijassa-1639	216	20	shows	show	VERB
ijassa-1639	216	21	up	up	ADP
ijassa-1639	216	22	mostly	mostly	ADV
ijassa-1639	216	23	for	for	ADP
ijassa-1639	216	24	relatively	relatively	ADV
ijassa-1639	216	25	small	small	ADJ
ijassa-1639	216	26	problems	problem	NOUN
ijassa-1639	216	27	.	.	PUNCT
ijassa-1639	217	1	for	for	ADP
ijassa-1639	217	2	large	large	ADJ
ijassa-1639	217	3	problems	problem	NOUN
ijassa-1639	217	4	(	(	PUNCT
ijassa-1639	217	5	as	as	SCONJ
ijassa-1639	217	6	selected	select	VERB
ijassa-1639	217	7	below	below	ADV
ijassa-1639	217	8	)	)	PUNCT
ijassa-1639	217	9	,	,	PUNCT
ijassa-1639	217	10	the	the	DET
ijassa-1639	217	11	difference	difference	NOUN
ijassa-1639	217	12	in	in	ADP
ijassa-1639	217	13	behavior	behavior	NOUN
ijassa-1639	217	14	is	be	AUX
ijassa-1639	217	15	negligible	negligible	ADJ
ijassa-1639	217	16	,	,	PUNCT
ijassa-1639	217	17	by	by	ADP
ijassa-1639	217	18	all	all	DET
ijassa-1639	217	19	the	the	DET
ijassa-1639	217	20	criteria	criterion	NOUN
ijassa-1639	217	21	,	,	PUNCT
ijassa-1639	217	22	including	include	VERB
ijassa-1639	217	23	times	time	NOUN
ijassa-1639	217	24	,	,	PUNCT
ijassa-1639	217	25	and	and	CCONJ
ijassa-1639	217	26	we	we	PRON
ijassa-1639	217	27	kept	keep	VERB
ijassa-1639	217	28	θ	θ	NOUN
ijassa-1639	217	29	=	=	SYM
ijassa-1639	217	30	2	2	NUM
ijassa-1639	217	31	for	for	ADP
ijassa-1639	217	32	the	the	DET
ijassa-1639	217	33	rest	rest	NOUN
ijassa-1639	217	34	of	of	ADP
ijassa-1639	217	35	the	the	DET
ijassa-1639	217	36	experiments	experiment	NOUN
ijassa-1639	217	37	.	.	PUNCT
ijassa-1639	218	1	in	in	ADP
ijassa-1639	218	2	figure	figure	NOUN
ijassa-1639	218	3	4.2a	4.2a	NUM
ijassa-1639	218	4	,	,	PUNCT
ijassa-1639	218	5	we	we	PRON
ijassa-1639	218	6	compare	compare	VERB
ijassa-1639	218	7	the	the	DET
ijassa-1639	218	8	specified	specified	ADJ
ijassa-1639	218	9	versions	version	NOUN
ijassa-1639	218	10	of	of	ADP
ijassa-1639	218	11	pwlm	pwlm	PROPN
ijassa-1639	218	12	and	and	CCONJ
ijassa-1639	218	13	lm	lm	NOUN
ijassa-1639	218	14	-	-	PUNCT
ijassa-1639	218	15	had	have	VERB
ijassa-1639	218	16	with	with	ADP
ijassa-1639	218	17	each	each	DET
ijassa-1639	218	18	other	other	ADJ
ijassa-1639	218	19	,	,	PUNCT
ijassa-1639	218	20	and	and	CCONJ
ijassa-1639	218	21	with	with	ADP
ijassa-1639	218	22	pwlpn	pwlpn	NOUN
ijassa-1639	218	23	and	and	CCONJ
ijassa-1639	218	24	lpn	lpn	PROPN
ijassa-1639	218	25	-	-	PUNCT
ijassa-1639	218	26	had	have	VERB
ijassa-1639	218	27	,	,	PUNCT
ijassa-1639	218	28	with	with	ADP
ijassa-1639	218	29	average	average	ADJ
ijassa-1639	218	30	counts	count	NOUN
ijassa-1639	218	31	of	of	ADP
ijassa-1639	218	32	iterations	iteration	NOUN
ijassa-1639	218	33	and	and	CCONJ
ijassa-1639	218	34	evaluations	evaluation	NOUN
ijassa-1639	218	35	of	of	ADP
ijassa-1639	218	36	φ	φ	PROPN
ijassa-1639	218	37	adopted	adopt	VERB
ijassa-1639	218	38	as	as	ADP
ijassa-1639	218	39	efficiency	efficiency	NOUN
ijassa-1639	218	40	measures	measure	NOUN
ijassa-1639	218	41	.	.	PUNCT
ijassa-1639	219	1	pwlm	pwlm	PROPN
ijassa-1639	219	2	demonstrates	demonstrate	VERB
ijassa-1639	219	3	robustness	robustness	NOUN
ijassa-1639	219	4	somehow	somehow	ADV
ijassa-1639	219	5	lower	low	ADJ
ijassa-1639	219	6	than	than	ADP
ijassa-1639	219	7	that	that	PRON
ijassa-1639	219	8	of	of	ADP
ijassa-1639	219	9	lp	lp	PROPN
ijassa-1639	219	10	-	-	PUNCT
ijassa-1639	219	11	newton	newton	NOUN
ijassa-1639	219	12	-	-	PUNCT
ijassa-1639	219	13	based	base	VERB
ijassa-1639	219	14	methods	method	NOUN
ijassa-1639	219	15	(	(	PUNCT
ijassa-1639	219	16	thus	thus	ADV
ijassa-1639	219	17	providing	provide	VERB
ijassa-1639	219	18	an	an	DET
ijassa-1639	219	19	extra	extra	ADJ
ijassa-1639	219	20	evidence	evidence	NOUN
ijassa-1639	219	21	of	of	ADP
ijassa-1639	219	22	the	the	DET
ijassa-1639	219	23	use	use	NOUN
ijassa-1639	219	24	of	of	ADP
ijassa-1639	219	25	the	the	DET
ijassa-1639	219	26	latter	latter	ADJ
ijassa-1639	219	27	)	)	PUNCT
ijassa-1639	219	28	,	,	PUNCT
ijassa-1639	219	29	but	but	CCONJ
ijassa-1639	219	30	definitely	definitely	ADV
ijassa-1639	219	31	higher	high	ADJ
ijassa-1639	219	32	than	than	ADP
ijassa-1639	219	33	that	that	PRON
ijassa-1639	219	34	of	of	ADP
ijassa-1639	219	35	lm	lm	VERB
ijassa-1639	219	36	-	-	PUNCT
ijassa-1639	219	37	had	have	AUX
ijassa-1639	219	38	.	.	PUNCT
ijassa-1639	220	1	moreover	moreover	ADV
ijassa-1639	220	2	,	,	PUNCT
ijassa-1639	220	3	the	the	DET
ijassa-1639	220	4	performance	performance	NOUN
ijassa-1639	220	5	of	of	ADP
ijassa-1639	220	6	pwlpn	pwlpn	NOUN
ijassa-1639	220	7	and	and	CCONJ
ijassa-1639	220	8	lpn	lpn	NOUN
ijassa-1639	220	9	-	-	PUNCT
ijassa-1639	220	10	had	have	VERB
ijassa-1639	220	11	is	be	AUX
ijassa-1639	220	12	quite	quite	ADV
ijassa-1639	220	13	similar	similar	ADJ
ijassa-1639	220	14	,	,	PUNCT
ijassa-1639	220	15	while	while	SCONJ
ijassa-1639	220	16	pwlm	pwlm	NOUN
ijassa-1639	220	17	by	by	ADP
ijassa-1639	220	18	far	far	ADJ
ijassa-1639	220	19	outperforms	outperform	NOUN
ijassa-1639	220	20	all	all	DET
ijassa-1639	220	21	the	the	DET
ijassa-1639	220	22	alternatives	alternative	NOUN
ijassa-1639	220	23	by	by	ADP
ijassa-1639	220	24	efficiency	efficiency	NOUN
ijassa-1639	220	25	.	.	PUNCT
ijassa-1639	221	1	furthermore	furthermore	ADV
ijassa-1639	221	2	,	,	PUNCT
ijassa-1639	221	3	in	in	ADP
ijassa-1639	221	4	figure	figure	NOUN
ijassa-1639	221	5	4.3	4.3	NUM
ijassa-1639	221	6	,	,	PUNCT
ijassa-1639	221	7	we	we	PRON
ijassa-1639	221	8	provide	provide	VERB
ijassa-1639	221	9	the	the	DET
ijassa-1639	221	10	results	result	NOUN
ijassa-1639	221	11	of	of	ADP
ijassa-1639	221	12	comparison	comparison	NOUN
ijassa-1639	221	13	by	by	ADP
ijassa-1639	221	14	average	average	ADJ
ijassa-1639	221	15	elapsed	elapse	VERB
ijassa-1639	221	16	time	time	NOUN
ijassa-1639	221	17	as	as	ADP
ijassa-1639	221	18	a	a	DET
ijassa-1639	221	19	measure	measure	NOUN
ijassa-1639	221	20	of	of	ADP
ijassa-1639	221	21	efficiency	efficiency	NOUN
ijassa-1639	221	22	.	.	PUNCT
ijassa-1639	222	1	figure	figure	VERB
ijassa-1639	222	2	4.3a	4.3a	NUM
ijassa-1639	222	3	is	be	AUX
ijassa-1639	222	4	for	for	ADP
ijassa-1639	222	5	the	the	DET
ijassa-1639	222	6	entire	entire	ADJ
ijassa-1639	222	7	set	set	NOUN
ijassa-1639	222	8	of	of	ADP
ijassa-1639	222	9	test	test	NOUN
ijassa-1639	222	10	problems	problem	NOUN
ijassa-1639	222	11	,	,	PUNCT
ijassa-1639	222	12	while	while	SCONJ
ijassa-1639	222	13	in	in	ADP
ijassa-1639	222	14	figure	figure	NOUN
ijassa-1639	222	15	4.3b	4.3b	NOUN
ijassa-1639	222	16	,	,	PUNCT
ijassa-1639	222	17	only	only	ADV
ijassa-1639	222	18	selected	select	VERB
ijassa-1639	222	19	large	large	ADJ
ijassa-1639	222	20	problems	problem	NOUN
ijassa-1639	222	21	were	be	AUX
ijassa-1639	222	22	left	leave	VERB
ijassa-1639	222	23	for	for	ADP
ijassa-1639	222	24	comparison	comparison	NOUN
ijassa-1639	222	25	,	,	PUNCT
ijassa-1639	222	26	namely	namely	ADV
ijassa-1639	222	27	,	,	PUNCT
ijassa-1639	222	28	those	those	PRON
ijassa-1639	222	29	with	with	ADP
ijassa-1639	222	30	more	more	ADJ
ijassa-1639	222	31	that	that	SCONJ
ijassa-1639	222	32	100	100	NUM
ijassa-1639	222	33	variables	variable	NOUN
ijassa-1639	222	34	and/or	and/or	CCONJ
ijassa-1639	222	35	constraints	constraint	VERB
ijassa-1639	222	36	:	:	PUNCT
ijassa-1639	222	37	a9b	a9b	X
ijassa-1639	222	38	,	,	PUNCT
ijassa-1639	222	39	a10b	a10b	PROPN
ijassa-1639	222	40	,	,	PUNCT
ijassa-1639	222	41	a10c	a10c	ADP
ijassa-1639	222	42	,	,	PUNCT
ijassa-1639	222	43	a10d	a10d	NOUN
ijassa-1639	222	44	,	,	PUNCT
ijassa-1639	222	45	a10e	a10e	PROPN
ijassa-1639	222	46	,	,	PUNCT
ijassa-1639	222	47	spam	spam	NOUN
ijassa-1639	222	48	,	,	PUNCT
ijassa-1639	222	49	tr1b	tr1b	PROPN
ijassa-1639	222	50	,	,	PUNCT
ijassa-1639	222	51	tr1c	tr1c	PROPN
ijassa-1639	222	52	.	.	PROPN
ijassa-1639	223	1	pwlm	pwlm	PROPN
ijassa-1639	223	2	outperforms	outperform	VERB
ijassa-1639	223	3	both	both	CCONJ
ijassa-1639	223	4	pwlpn	pwlpn	NOUN
ijassa-1639	223	5	and	and	CCONJ
ijassa-1639	223	6	lpn	lpn	NOUN
ijassa-1639	223	7	-	-	PUNCT
ijassa-1639	223	8	had	have	AUX
ijassa-1639	223	9	by	by	ADP
ijassa-1639	223	10	efficiency	efficiency	NOUN
ijassa-1639	223	11	on	on	ADP
ijassa-1639	223	12	the	the	DET
ijassa-1639	223	13	full	full	ADJ
ijassa-1639	223	14	test	test	NOUN
ijassa-1639	223	15	set	set	NOUN
ijassa-1639	223	16	,	,	PUNCT
ijassa-1639	223	17	although	although	SCONJ
ijassa-1639	223	18	it	it	PRON
ijassa-1639	223	19	is	be	AUX
ijassa-1639	223	20	somewhat	somewhat	ADV
ijassa-1639	223	21	less	less	ADV
ijassa-1639	223	22	robust	robust	ADJ
ijassa-1639	223	23	.	.	PUNCT
ijassa-1639	224	1	the	the	DET
ijassa-1639	224	2	picture	picture	NOUN
ijassa-1639	224	3	with	with	ADP
ijassa-1639	224	4	robustness	robustness	NOUN
ijassa-1639	224	5	remains	remain	VERB
ijassa-1639	224	6	the	the	DET
ijassa-1639	224	7	same	same	ADJ
ijassa-1639	224	8	for	for	ADP
ijassa-1639	224	9	large	large	ADJ
ijassa-1639	224	10	problems	problem	NOUN
ijassa-1639	224	11	(	(	PUNCT
ijassa-1639	224	12	and	and	CCONJ
ijassa-1639	224	13	robustness	robustness	NOUN
ijassa-1639	224	14	of	of	ADP
ijassa-1639	224	15	lm	lm	NOUN
ijassa-1639	224	16	-	-	PUNCT
ijassa-1639	224	17	had	have	AUX
ijassa-1639	224	18	appears	appear	VERB
ijassa-1639	224	19	very	very	ADV
ijassa-1639	224	20	low	low	ADJ
ijassa-1639	224	21	in	in	ADP
ijassa-1639	224	22	this	this	DET
ijassa-1639	224	23	case	case	NOUN
ijassa-1639	224	24	)	)	PUNCT
ijassa-1639	224	25	,	,	PUNCT
ijassa-1639	224	26	but	but	CCONJ
ijassa-1639	224	27	now	now	ADV
ijassa-1639	224	28	the	the	DET
ijassa-1639	224	29	performance	performance	NOUN
ijassa-1639	224	30	of	of	ADP
ijassa-1639	224	31	pwlpn	pwlpn	NOUN
ijassa-1639	224	32	and	and	CCONJ
ijassa-1639	224	33	lpn	lpn	NOUN
ijassa-1639	224	34	-	-	PUNCT
ijassa-1639	224	35	had	have	AUX
ijassa-1639	224	36	is	be	AUX
ijassa-1639	224	37	much	much	ADV
ijassa-1639	224	38	improved	improve	VERB
ijassa-1639	224	39	by	by	ADP
ijassa-1639	224	40	efficiency	efficiency	NOUN
ijassa-1639	224	41	as	as	ADV
ijassa-1639	224	42	well	well	ADV
ijassa-1639	224	43	,	,	PUNCT
ijassa-1639	224	44	apparently	apparently	ADV
ijassa-1639	224	45	because	because	SCONJ
ijassa-1639	224	46	large	large	ADJ
ijassa-1639	224	47	linear	linear	ADJ
ijassa-1639	224	48	programming	programming	NOUN
ijassa-1639	224	49	subproblems	subproblem	NOUN
ijassa-1639	224	50	are	be	AUX
ijassa-1639	224	51	solved	solve	VERB
ijassa-1639	224	52	faster	fast	ADV
ijassa-1639	224	53	than	than	ADP
ijassa-1639	224	54	the	the	DET
ijassa-1639	224	55	quadratic	quadratic	ADJ
ijassa-1639	224	56	programming	programming	NOUN
ijassa-1639	224	57	subproblems	subproblem	NOUN
ijassa-1639	224	58	.	.	PUNCT
ijassa-1639	225	1	the	the	DET
ijassa-1639	225	2	detailed	detailed	ADJ
ijassa-1639	225	3	information	information	NOUN
ijassa-1639	225	4	on	on	ADP
ijassa-1639	225	5	average	average	ADJ
ijassa-1639	225	6	times	time	NOUN
ijassa-1639	225	7	is	be	AUX
ijassa-1639	225	8	collected	collect	VERB
ijassa-1639	225	9	in	in	ADP
ijassa-1639	225	10	table	table	NOUN
ijassa-1639	225	11	4.1	4.1	NUM
ijassa-1639	225	12	,	,	PUNCT
ijassa-1639	225	13	where	where	SCONJ
ijassa-1639	225	14	the	the	DET
ijassa-1639	225	15	identifiers	identifier	NOUN
ijassa-1639	225	16	of	of	ADP
ijassa-1639	225	17	large	large	ADJ
ijassa-1639	225	18	problems	problem	NOUN
ijassa-1639	225	19	are	be	AUX
ijassa-1639	225	20	boldfaced	boldface	VERB
ijassa-1639	225	21	.	.	PUNCT
ijassa-1639	226	1	in	in	ADP
ijassa-1639	226	2	addition	addition	NOUN
ijassa-1639	226	3	,	,	PUNCT
ijassa-1639	226	4	in	in	ADP
ijassa-1639	226	5	that	that	DET
ijassa-1639	226	6	table	table	NOUN
ijassa-1639	226	7	,	,	PUNCT
ijassa-1639	226	8	we	we	PRON
ijassa-1639	226	9	also	also	ADV
ijassa-1639	226	10	report	report	VERB
ijassa-1639	226	11	on	on	ADP
ijassa-1639	226	12	the	the	DET
ijassa-1639	226	13	percentage	percentage	NOUN
ijassa-1639	226	14	of	of	ADP
ijassa-1639	226	15	tails	tail	NOUN
ijassa-1639	226	16	of	of	ADP
ijassa-1639	226	17	last	last	ADJ
ijassa-1639	226	18	full	full	ADJ
ijassa-1639	226	19	(	(	PUNCT
ijassa-1639	226	20	with	with	ADP
ijassa-1639	226	21	αk	αk	NOUN
ijassa-1639	226	22	=	=	SYM
ijassa-1639	226	23	1	1	X
ijassa-1639	226	24	)	)	PUNCT
ijassa-1639	226	25	steps	step	NOUN
ijassa-1639	226	26	of	of	ADP
ijassa-1639	226	27	the	the	DET
ijassa-1639	226	28	algorithms	algorithm	NOUN
ijassa-1639	226	29	in	in	ADP
ijassa-1639	226	30	question	question	NOUN
ijassa-1639	226	31	before	before	ADP
ijassa-1639	226	32	successful	successful	ADJ
ijassa-1639	226	33	termination	termination	NOUN
ijassa-1639	226	34	,	,	PUNCT
ijassa-1639	226	35	out	out	ADP
ijassa-1639	226	36	of	of	ADP
ijassa-1639	226	37	the	the	DET
ijassa-1639	226	38	average	average	ADJ
ijassa-1639	226	39	iteration	iteration	NOUN
ijassa-1639	226	40	counts	count	NOUN
ijassa-1639	226	41	.	.	PUNCT
ijassa-1639	227	1	the	the	DET
ijassa-1639	227	2	issue	issue	NOUN
ijassa-1639	227	3	of	of	ADP
ijassa-1639	227	4	ultimate	ultimate	ADJ
ijassa-1639	227	5	acceptance	acceptance	NOUN
ijassa-1639	227	6	of	of	ADP
ijassa-1639	227	7	the	the	DET
ijassa-1639	227	8	full	full	ADJ
ijassa-1639	227	9	step	step	NOUN
ijassa-1639	227	10	is	be	AUX
ijassa-1639	227	11	crucial	crucial	ADJ
ijassa-1639	227	12	for	for	ADP
ijassa-1639	227	13	superlinear	superlinear	ADJ
ijassa-1639	227	14	convergence	convergence	NOUN
ijassa-1639	227	15	guaranties	guaranty	NOUN
ijassa-1639	227	16	,	,	PUNCT
ijassa-1639	227	17	like	like	ADP
ijassa-1639	227	18	those	those	PRON
ijassa-1639	227	19	established	establish	VERB
ijassa-1639	227	20	for	for	ADP
ijassa-1639	227	21	algorithm	algorithm	NOUN
ijassa-1639	227	22	3.1	3.1	NUM
ijassa-1639	227	23	in	in	ADP
ijassa-1639	227	24	theorem	theorem	NOUN
ijassa-1639	227	25	3.2	3.2	NUM
ijassa-1639	227	26	.	.	PUNCT
ijassa-1639	228	1	in	in	ADP
ijassa-1639	228	2	our	our	PRON
ijassa-1639	228	3	experiments	experiment	NOUN
ijassa-1639	228	4	,	,	PUNCT
ijassa-1639	228	5	the	the	DET
ijassa-1639	228	6	only	only	ADJ
ijassa-1639	228	7	cases	case	NOUN
ijassa-1639	228	8	where	where	SCONJ
ijassa-1639	228	9	the	the	DET
ijassa-1639	228	10	last	last	ADJ
ijassa-1639	228	11	step	step	NOUN
ijassa-1639	228	12	was	be	AUX
ijassa-1639	228	13	not	not	PART
ijassa-1639	228	14	full	full	ADJ
ijassa-1639	228	15	were	be	AUX
ijassa-1639	228	16	encountered	encounter	VERB
ijassa-1639	228	17	only	only	ADV
ijassa-1639	228	18	for	for	ADP
ijassa-1639	228	19	lm	lm	VERB
ijassa-1639	228	20	-	-	PUNCT
ijassa-1639	228	21	had	have	AUX
ijassa-1639	228	22	,	,	PUNCT
ijassa-1639	228	23	in	in	ADP
ijassa-1639	228	24	5	5	NUM
ijassa-1639	228	25	runs	run	NOUN
ijassa-1639	228	26	out	out	ADP
ijassa-1639	228	27	of	of	ADP
ijassa-1639	228	28	16	16	NUM
ijassa-1639	228	29	successful	successful	ADJ
ijassa-1639	228	30	for	for	ADP
ijassa-1639	228	31	ntf2	ntf2	NOUN
ijassa-1639	228	32	,	,	PUNCT
ijassa-1639	228	33	and	and	CCONJ
ijassa-1639	228	34	for	for	ADP
ijassa-1639	228	35	lpn	lpn	NOUN
ijassa-1639	228	36	-	-	PUNCT
ijassa-1639	228	37	had	have	AUX
ijassa-1639	228	38	,	,	PUNCT
ijassa-1639	228	39	in	in	ADP
ijassa-1639	228	40	1	1	NUM
ijassa-1639	228	41	run	run	VERB
ijassa-1639	228	42	out	out	ADP
ijassa-1639	228	43	of	of	ADP
ijassa-1639	228	44	20	20	NUM
ijassa-1639	228	45	successful	successful	ADJ
ijassa-1639	228	46	for	for	ADP
ijassa-1639	228	47	a16c	a16c	NOUN
ijassa-1639	228	48	.	.	PUNCT
ijassa-1639	229	1	the	the	DET
ijassa-1639	229	2	largest	large	ADJ
ijassa-1639	229	3	problem	problem	NOUN
ijassa-1639	229	4	in	in	ADP
ijassa-1639	229	5	the	the	DET
ijassa-1639	229	6	test	test	NOUN
ijassa-1639	229	7	set	set	NOUN
ijassa-1639	229	8	is	be	AUX
ijassa-1639	229	9	spam	spam	NOUN
ijassa-1639	229	10	,	,	PUNCT
ijassa-1639	229	11	in	in	ADP
ijassa-1639	229	12	which	which	PRON
ijassa-1639	229	13	n	n	NOUN
ijassa-1639	229	14	=	=	SYM
ijassa-1639	229	15	101	101	NUM
ijassa-1639	229	16	,	,	PUNCT
ijassa-1639	229	17	n	n	NOUN
ijassa-1639	229	18	=	=	SYM
ijassa-1639	229	19	2020	2020	NUM
ijassa-1639	229	20	,	,	PUNCT
ijassa-1639	229	21	m	m	VERB
ijassa-1639	229	22	=	=	NOUN
ijassa-1639	229	23	4040	4040	NUM
ijassa-1639	229	24	.	.	PUNCT
ijassa-1639	230	1	it	it	PRON
ijassa-1639	230	2	is	be	AUX
ijassa-1639	230	3	successfully	successfully	ADV
ijassa-1639	230	4	solved	solve	VERB
ijassa-1639	230	5	by	by	ADP
ijassa-1639	230	6	pwlm	pwlm	NOUN
ijassa-1639	230	7	,	,	PUNCT
ijassa-1639	230	8	and	and	CCONJ
ijassa-1639	230	9	in	in	ADP
ijassa-1639	230	10	a	a	DET
ijassa-1639	230	11	modest	modest	ADJ
ijassa-1639	230	12	number	number	NOUN
ijassa-1639	230	13	of	of	ADP
ijassa-1639	230	14	iterations	iteration	NOUN
ijassa-1639	230	15	,	,	PUNCT
ijassa-1639	230	16	while	while	SCONJ
ijassa-1639	230	17	all	all	DET
ijassa-1639	230	18	the	the	DET
ijassa-1639	230	19	other	other	ADJ
ijassa-1639	230	20	algorithms	algorithm	NOUN
ijassa-1639	230	21	involved	involve	VERB
ijassa-1639	230	22	typically	typically	ADV
ijassa-1639	230	23	fail	fail	VERB
ijassa-1639	230	24	on	on	ADP
ijassa-1639	230	25	it	it	PRON
ijassa-1639	230	26	.	.	PUNCT
ijassa-1639	231	1	many	many	ADJ
ijassa-1639	231	2	failures	failure	NOUN
ijassa-1639	231	3	are	be	AUX
ijassa-1639	231	4	caused	cause	VERB
ijassa-1639	231	5	by	by	ADP
ijassa-1639	231	6	inability	inability	NOUN
ijassa-1639	231	7	of	of	ADP
ijassa-1639	231	8	quadprog	quadprog	NOUN
ijassa-1639	231	9	or	or	CCONJ
ijassa-1639	231	10	linprog	linprog	VERB
ijassa-1639	231	11	to	to	PART
ijassa-1639	231	12	solve	solve	VERB
ijassa-1639	231	13	the	the	DET
ijassa-1639	231	14	corresponding	corresponding	ADJ
ijassa-1639	231	15	subproblems	subproblem	NOUN
ijassa-1639	231	16	;	;	PUNCT
ijassa-1639	231	17	for	for	ADP
ijassa-1639	231	18	example	example	NOUN
ijassa-1639	231	19	,	,	PUNCT
ijassa-1639	231	20	this	this	PRON
ijassa-1639	231	21	is	be	AUX
ijassa-1639	231	22	the	the	DET
ijassa-1639	231	23	case	case	NOUN
ijassa-1639	231	24	for	for	ADP
ijassa-1639	231	25	pwlpn	pwlpn	NOUN
ijassa-1639	231	26	,	,	PUNCT
ijassa-1639	231	27	lm	lm	NOUN
ijassa-1639	231	28	-	-	PUNCT
ijassa-1639	231	29	had	have	VERB
ijassa-1639	231	30	,	,	PUNCT
ijassa-1639	231	31	and	and	CCONJ
ijassa-1639	231	32	lpn	lpn	NOUN
ijassa-1639	231	33	-	-	PUNCT
ijassa-1639	231	34	had	have	VERB
ijassa-1639	231	35	,	,	PUNCT
ijassa-1639	231	36	when	when	SCONJ
ijassa-1639	231	37	run	run	VERB
ijassa-1639	231	38	for	for	ADP
ijassa-1639	231	39	spam	spam	NOUN
ijassa-1639	231	40	.	.	PUNCT
ijassa-1639	232	1	lm	lm	VERB
ijassa-1639	232	2	-	-	PUNCT
ijassa-1639	232	3	had	have	AUX
ijassa-1639	232	4	also	also	ADV
ijassa-1639	232	5	systematically	systematically	ADV
ijassa-1639	232	6	fails	fail	VERB
ijassa-1639	232	7	for	for	ADP
ijassa-1639	232	8	the	the	DET
ijassa-1639	232	9	specified	specify	VERB
ijassa-1639	232	10	reason	reason	NOUN
ijassa-1639	232	11	for	for	ADP
ijassa-1639	232	12	problems	problem	NOUN
ijassa-1639	232	13	a2	a2	PROPN
ijassa-1639	232	14	,	,	PUNCT
ijassa-1639	232	15	a10d	a10d	NOUN
ijassa-1639	232	16	,	,	PUNCT
ijassa-1639	232	17	a10e	a10e	PROPN
ijassa-1639	232	18	,	,	PUNCT
ijassa-1639	232	19	a11	a11	PROPN
ijassa-1639	232	20	,	,	PUNCT
ijassa-1639	232	21	tr1c	tr1c	PROPN
ijassa-1639	232	22	.	.	NOUN
ijassa-1639	232	23	typical	typical	ADJ
ijassa-1639	232	24	failures	failure	NOUN
ijassa-1639	232	25	of	of	ADP
ijassa-1639	232	26	other	other	ADJ
ijassa-1639	232	27	kind	kind	NOUN
ijassa-1639	232	28	are	be	AUX
ijassa-1639	232	29	caused	cause	VERB
ijassa-1639	232	30	by	by	ADP
ijassa-1639	232	31	the	the	DET
ijassa-1639	232	32	stepzize	stepzize	PROPN
ijassa-1639	232	33	parameter	parameter	NOUN
ijassa-1639	232	34	becoming	become	VERB
ijassa-1639	232	35	too	too	ADV
ijassa-1639	232	36	small	small	ADJ
ijassa-1639	232	37	.	.	PUNCT
ijassa-1639	233	1	problem	problem	NOUN
ijassa-1639	233	2	a2	a2	PROPN
ijassa-1639	233	3	is	be	AUX
ijassa-1639	233	4	also	also	ADV
ijassa-1639	233	5	troublesome	troublesome	ADJ
ijassa-1639	233	6	for	for	ADP
ijassa-1639	233	7	pwlm	pwlm	NOUN
ijassa-1639	233	8	in	in	ADP
ijassa-1639	233	9	a	a	DET
ijassa-1639	233	10	different	different	ADJ
ijassa-1639	233	11	way	way	NOUN
ijassa-1639	233	12	,	,	PUNCT
ijassa-1639	233	13	with	with	ADP
ijassa-1639	233	14	all	all	DET
ijassa-1639	233	15	runs	run	NOUN
ijassa-1639	233	16	ending	end	VERB
ijassa-1639	233	17	up	up	ADP
ijassa-1639	233	18	with	with	ADP
ijassa-1639	233	19	failures	failure	NOUN
ijassa-1639	233	20	because	because	SCONJ
ijassa-1639	233	21	of	of	ADP
ijassa-1639	233	22	a	a	DET
ijassa-1639	233	23	too	too	ADV
ijassa-1639	233	24	small	small	ADJ
ijassa-1639	233	25	stepsize	stepsize	NOUN
ijassa-1639	233	26	generated	generate	VERB
ijassa-1639	233	27	,	,	PUNCT
ijassa-1639	233	28	but	but	CCONJ
ijassa-1639	233	29	that	that	PRON
ijassa-1639	233	30	was	be	AUX
ijassa-1639	233	31	actually	actually	ADV
ijassa-1639	233	32	caused	cause	VERB
ijassa-1639	233	33	by	by	ADP
ijassa-1639	233	34	convergence	convergence	NOUN
ijassa-1639	233	35	to	to	ADP
ijassa-1639	233	36	stationary	stationary	ADJ
ijassa-1639	233	37	points	point	NOUN
ijassa-1639	233	38	for	for	ADP
ijassa-1639	233	39	an	an	DET
ijassa-1639	233	40	active	active	ADJ
ijassa-1639	233	41	smooth	smooth	ADJ
ijassa-1639	233	42	selection	selection	NOUN
ijassa-1639	233	43	being	be	AUX
ijassa-1639	233	44	used	use	VERB
ijassa-1639	233	45	,	,	PUNCT
ijassa-1639	233	46	that	that	PRON
ijassa-1639	233	47	are	be	AUX
ijassa-1639	233	48	not	not	PART
ijassa-1639	233	49	solutions	solution	NOUN
ijassa-1639	233	50	.	.	PUNCT
ijassa-1639	234	1	observe	observe	VERB
ijassa-1639	234	2	that	that	SCONJ
ijassa-1639	234	3	such	such	ADJ
ijassa-1639	234	4	scenario	scenario	NOUN
ijassa-1639	234	5	is	be	AUX
ijassa-1639	234	6	of	of	ADP
ijassa-1639	234	7	course	course	NOUN
ijassa-1639	234	8	not	not	PART
ijassa-1639	234	9	ruled	rule	VERB
ijassa-1639	234	10	out	out	ADP
ijassa-1639	234	11	by	by	ADP
ijassa-1639	234	12	theorem	theorem	ADJ
ijassa-1639	234	13	3.1	3.1	NUM
ijassa-1639	234	14	.	.	PUNCT
ijassa-1639	234	15	information	information	NOUN
ijassa-1639	234	16	about	about	ADP
ijassa-1639	234	17	failures	failure	NOUN
ijassa-1639	234	18	and	and	CCONJ
ijassa-1639	234	19	their	their	PRON
ijassa-1639	234	20	reasons	reason	NOUN
ijassa-1639	234	21	is	be	AUX
ijassa-1639	234	22	summarized	summarize	VERB
ijassa-1639	234	23	in	in	ADP
ijassa-1639	234	24	table	table	NOUN
ijassa-1639	234	25	4.2	4.2	NUM
ijassa-1639	234	26	making	making	NOUN
ijassa-1639	234	27	use	use	NOUN
ijassa-1639	234	28	of	of	ADP
ijassa-1639	234	29	the	the	DET
ijassa-1639	234	30	following	follow	VERB
ijassa-1639	234	31	abbreviations	abbreviation	NOUN
ijassa-1639	234	32	for	for	ADP
ijassa-1639	234	33	failures	failure	NOUN
ijassa-1639	234	34	’	'	PUNCT
ijassa-1639	234	35	reasons	reason	NOUN
ijassa-1639	234	36	:	:	PUNCT
ijassa-1639	234	37	•	•	NUM
ijassa-1639	234	38	sf	sf	NOUN
ijassa-1639	234	39	:	:	PUNCT
ijassa-1639	234	40	solving	solve	VERB
ijassa-1639	234	41	subproblem	subproblem	NOUN
ijassa-1639	234	42	failed	fail	VERB
ijassa-1639	234	43	.	.	PUNCT
ijassa-1639	235	1	•	•	NUM
ijassa-1639	235	2	il	il	PROPN
ijassa-1639	235	3	:	:	PUNCT
ijassa-1639	235	4	failure	failure	NOUN
ijassa-1639	235	5	by	by	ADP
ijassa-1639	235	6	iteration	iteration	NOUN
ijassa-1639	235	7	limit	limit	NOUN
ijassa-1639	235	8	.	.	PUNCT
ijassa-1639	236	1	•	•	X
ijassa-1639	236	2	sp	sp	NOUN
ijassa-1639	236	3	:	:	PUNCT
ijassa-1639	236	4	stationary	stationary	ADJ
ijassa-1639	236	5	point	point	NOUN
ijassa-1639	236	6	that	that	PRON
ijassa-1639	236	7	is	be	AUX
ijassa-1639	236	8	not	not	PART
ijassa-1639	236	9	a	a	DET
ijassa-1639	236	10	solution	solution	NOUN
ijassa-1639	236	11	.	.	PUNCT
ijassa-1639	237	1	copyright	copyright	NOUN
ijassa-1639	237	2	©	©	PROPN
ijassa-1639	237	3	2024	2024	NUM
ijassa-1639	237	4	assa	assa	NOUN
ijassa-1639	237	5	.	.	PUNCT
ijassa-1639	238	1	adv	adv	PROPN
ijassa-1639	238	2	syst	syst	PROPN
ijassa-1639	238	3	sci	sci	PROPN
ijassa-1639	238	4	appl	appl	PROPN
ijassa-1639	238	5	(	(	PUNCT
ijassa-1639	238	6	2024	2024	NUM
ijassa-1639	238	7	)	)	PUNCT
ijassa-1639	238	8	30	30	NUM
ijassa-1639	238	9	a.	a.	NOUN
ijassa-1639	238	10	f.	f.	PROPN
ijassa-1639	238	11	izmailov	izmailov	PROPN
ijassa-1639	238	12	,	,	PUNCT
ijassa-1639	238	13	e.	e.	PROPN
ijassa-1639	238	14	i.	i.	PROPN
ijassa-1639	238	15	uskov	uskov	PROPN
ijassa-1639	238	16	,	,	PUNCT
ijassa-1639	238	17	yan	yan	PROPN
ijassa-1639	238	18	zhibai	zhibai	PROPN
ijassa-1639	238	19	•	•	PROPN
ijassa-1639	238	20	ss	ss	PROPN
ijassa-1639	238	21	:	:	PUNCT
ijassa-1639	238	22	stepsize	stepsize	VERB
ijassa-1639	238	23	too	too	ADV
ijassa-1639	238	24	small	small	ADJ
ijassa-1639	238	25	.	.	PUNCT
ijassa-1639	239	1	at	at	ADP
ijassa-1639	239	2	the	the	DET
ijassa-1639	239	3	end	end	NOUN
ijassa-1639	239	4	,	,	PUNCT
ijassa-1639	239	5	we	we	PRON
ijassa-1639	239	6	briefly	briefly	ADV
ijassa-1639	239	7	mention	mention	VERB
ijassa-1639	239	8	some	some	DET
ijassa-1639	239	9	possibilities	possibility	NOUN
ijassa-1639	239	10	to	to	PART
ijassa-1639	239	11	further	far	ADV
ijassa-1639	239	12	improve	improve	VERB
ijassa-1639	239	13	the	the	DET
ijassa-1639	239	14	performance	performance	NOUN
ijassa-1639	239	15	of	of	ADP
ijassa-1639	239	16	pwlm	pwlm	PROPN
ijassa-1639	239	17	for	for	ADP
ijassa-1639	239	18	gnep	gnep	NOUN
ijassa-1639	239	19	.	.	PUNCT
ijassa-1639	240	1	tuning	tune	VERB
ijassa-1639	240	2	σ̄	σ̄	PRON
ijassa-1639	240	3	for	for	ADP
ijassa-1639	240	4	each	each	DET
ijassa-1639	240	5	problem	problem	NOUN
ijassa-1639	240	6	sometimes	sometimes	ADV
ijassa-1639	240	7	gives	give	VERB
ijassa-1639	240	8	some	some	DET
ijassa-1639	240	9	positive	positive	ADJ
ijassa-1639	240	10	effect	effect	NOUN
ijassa-1639	240	11	.	.	PUNCT
ijassa-1639	241	1	moreover	moreover	ADV
ijassa-1639	241	2	,	,	PUNCT
ijassa-1639	241	3	alternative	alternative	ADJ
ijassa-1639	241	4	rules	rule	NOUN
ijassa-1639	241	5	for	for	ADP
ijassa-1639	241	6	σ	σ	PROPN
ijassa-1639	241	7	(	(	PUNCT
ijassa-1639	241	8	·	·	PUNCT
ijassa-1639	241	9	)	)	PUNCT
ijassa-1639	241	10	might	might	AUX
ijassa-1639	241	11	be	be	AUX
ijassa-1639	241	12	tried	try	VERB
ijassa-1639	241	13	,	,	PUNCT
ijassa-1639	241	14	such	such	ADJ
ijassa-1639	241	15	as	as	ADP
ijassa-1639	241	16	σ(u	σ(u	NOUN
ijassa-1639	241	17	)	)	PUNCT
ijassa-1639	242	1	=	=	VERB
ijassa-1639	242	2	σ̄∥φ(u)∥θ/(1	σ̄∥φ(u)∥θ/(1	NOUN
ijassa-1639	242	3	+	+	CCONJ
ijassa-1639	242	4	∥φ(u)∥θ	∥φ(u)∥θ	NOUN
ijassa-1639	242	5	)	)	PUNCT
ijassa-1639	242	6	,	,	PUNCT
ijassa-1639	242	7	or	or	CCONJ
ijassa-1639	242	8	σ(u	σ(u	NOUN
ijassa-1639	242	9	)	)	PUNCT
ijassa-1639	242	10	=	=	PUNCT
ijassa-1639	242	11	σ̄∥(φ′(u))⊤φ(u)∥θ	σ̄∥(φ′(u))⊤φ(u)∥θ	NOUN
ijassa-1639	242	12	as	as	SCONJ
ijassa-1639	242	13	proposed	propose	VERB
ijassa-1639	242	14	in	in	ADP
ijassa-1639	242	15	[	[	X
ijassa-1639	242	16	12	12	NUM
ijassa-1639	242	17	]	]	PUNCT
ijassa-1639	242	18	,	,	PUNCT
ijassa-1639	242	19	perhaps	perhaps	ADV
ijassa-1639	242	20	involving	involve	VERB
ijassa-1639	242	21	some	some	DET
ijassa-1639	242	22	extra	extra	ADJ
ijassa-1639	242	23	parameters	parameter	NOUN
ijassa-1639	242	24	,	,	PUNCT
ijassa-1639	242	25	or	or	CCONJ
ijassa-1639	242	26	some	some	DET
ijassa-1639	242	27	combinations	combination	NOUN
ijassa-1639	242	28	of	of	ADP
ijassa-1639	242	29	these	these	DET
ijassa-1639	242	30	rules	rule	NOUN
ijassa-1639	242	31	.	.	PUNCT
ijassa-1639	243	1	the	the	DET
ijassa-1639	243	2	cases	case	NOUN
ijassa-1639	243	3	when	when	SCONJ
ijassa-1639	243	4	a	a	DET
ijassa-1639	243	5	short	short	ADJ
ijassa-1639	243	6	step	step	NOUN
ijassa-1639	243	7	is	be	AUX
ijassa-1639	243	8	generated	generate	VERB
ijassa-1639	243	9	can	can	AUX
ijassa-1639	243	10	be	be	AUX
ijassa-1639	243	11	handled	handle	VERB
ijassa-1639	243	12	in	in	ADP
ijassa-1639	243	13	a	a	DET
ijassa-1639	243	14	more	more	ADV
ijassa-1639	243	15	sophisticated	sophisticated	ADJ
ijassa-1639	243	16	way	way	NOUN
ijassa-1639	243	17	rather	rather	ADV
ijassa-1639	243	18	than	than	ADP
ijassa-1639	243	19	just	just	ADV
ijassa-1639	243	20	declaring	declare	VERB
ijassa-1639	243	21	failure	failure	NOUN
ijassa-1639	243	22	,	,	PUNCT
ijassa-1639	243	23	like	like	ADP
ijassa-1639	243	24	trying	try	VERB
ijassa-1639	243	25	some	some	DET
ijassa-1639	243	26	safeguarding	safeguard	VERB
ijassa-1639	243	27	steps	step	NOUN
ijassa-1639	243	28	in	in	ADP
ijassa-1639	243	29	such	such	ADJ
ijassa-1639	243	30	cases	case	NOUN
ijassa-1639	243	31	.	.	PUNCT
ijassa-1639	244	1	finally	finally	ADV
ijassa-1639	244	2	,	,	PUNCT
ijassa-1639	244	3	the	the	DET
ijassa-1639	244	4	use	use	NOUN
ijassa-1639	244	5	of	of	ADP
ijassa-1639	244	6	more	more	ADV
ijassa-1639	244	7	advanced	advanced	ADJ
ijassa-1639	244	8	qp	qp	NOUN
ijassa-1639	244	9	-	-	PUNCT
ijassa-1639	244	10	solvers	solver	NOUN
ijassa-1639	244	11	for	for	ADP
ijassa-1639	244	12	subproblems	subproblem	NOUN
ijassa-1639	244	13	should	should	AUX
ijassa-1639	244	14	certainly	certainly	ADV
ijassa-1639	244	15	be	be	AUX
ijassa-1639	244	16	helpful	helpful	ADJ
ijassa-1639	244	17	,	,	PUNCT
ijassa-1639	244	18	e.g.	e.g.	ADV
ijassa-1639	244	19	,	,	PUNCT
ijassa-1639	244	20	those	those	PRON
ijassa-1639	244	21	applying	apply	VERB
ijassa-1639	244	22	some	some	DET
ijassa-1639	244	23	pre	pre	ADJ
ijassa-1639	244	24	-	-	ADJ
ijassa-1639	244	25	processing	processing	ADJ
ijassa-1639	244	26	/	/	SYM
ijassa-1639	244	27	scaling	scaling	NOUN
ijassa-1639	244	28	.	.	PUNCT
ijassa-1639	245	1	all	all	PRON
ijassa-1639	245	2	that	that	PRON
ijassa-1639	245	3	will	will	AUX
ijassa-1639	245	4	be	be	AUX
ijassa-1639	245	5	the	the	DET
ijassa-1639	245	6	subject	subject	NOUN
ijassa-1639	245	7	of	of	ADP
ijassa-1639	245	8	future	future	ADJ
ijassa-1639	245	9	research	research	NOUN
ijassa-1639	245	10	.	.	PUNCT
ijassa-1639	246	1	acknowledgements	acknowledgement	NOUN
ijassa-1639	246	2	the	the	DET
ijassa-1639	246	3	authors	author	NOUN
ijassa-1639	246	4	thank	thank	VERB
ijassa-1639	246	5	axel	axel	PROPN
ijassa-1639	246	6	dreves	dreve	NOUN
ijassa-1639	246	7	and	and	CCONJ
ijassa-1639	246	8	markus	marku	NOUN
ijassa-1639	246	9	herrich	herrich	PRON
ijassa-1639	246	10	for	for	ADP
ijassa-1639	246	11	their	their	PRON
ijassa-1639	246	12	assistance	assistance	NOUN
ijassa-1639	246	13	with	with	ADP
ijassa-1639	246	14	a	a	DET
ijassa-1639	246	15	matlab	matlab	NOUN
ijassa-1639	246	16	implementation	implementation	NOUN
ijassa-1639	246	17	of	of	ADP
ijassa-1639	246	18	the	the	DET
ijassa-1639	246	19	gnep	gnep	PROPN
ijassa-1639	246	20	test	test	NOUN
ijassa-1639	246	21	collection	collection	NOUN
ijassa-1639	246	22	and	and	CCONJ
ijassa-1639	246	23	of	of	ADP
ijassa-1639	246	24	the	the	DET
ijassa-1639	246	25	lp	lp	PROPN
ijassa-1639	246	26	-	-	PUNCT
ijassa-1639	246	27	newton	newton	PROPN
ijassa-1639	246	28	method	method	NOUN
ijassa-1639	246	29	,	,	PUNCT
ijassa-1639	246	30	used	use	VERB
ijassa-1639	246	31	in	in	ADP
ijassa-1639	246	32	section	section	NOUN
ijassa-1639	246	33	4	4	NUM
ijassa-1639	246	34	of	of	ADP
ijassa-1639	246	35	this	this	DET
ijassa-1639	246	36	work	work	NOUN
ijassa-1639	246	37	.	.	PUNCT
ijassa-1639	247	1	this	this	DET
ijassa-1639	247	2	work	work	NOUN
ijassa-1639	247	3	was	be	AUX
ijassa-1639	247	4	funded	fund	VERB
ijassa-1639	247	5	by	by	ADP
ijassa-1639	247	6	the	the	DET
ijassa-1639	247	7	russian	russian	PROPN
ijassa-1639	247	8	science	science	PROPN
ijassa-1639	247	9	foundation	foundation	PROPN
ijassa-1639	247	10	grant	grant	VERB
ijassa-1639	247	11	24	24	NUM
ijassa-1639	247	12	-	-	PUNCT
ijassa-1639	247	13	21	21	NUM
ijassa-1639	247	14	-	-	PUNCT
ijassa-1639	247	15	00015	00015	NUM
ijassa-1639	247	16	(	(	PUNCT
ijassa-1639	247	17	https://rscf.ru/en/project/24-21-00015/	https://rscf.ru/en/project/24-21-00015/	NUM
ijassa-1639	247	18	)	)	PUNCT
ijassa-1639	247	19	.	.	PUNCT
ijassa-1639	248	1	references	reference	NOUN
ijassa-1639	248	2	1	1	NUM
ijassa-1639	248	3	.	.	PUNCT
ijassa-1639	249	1	behling	behling	NOUN
ijassa-1639	249	2	,	,	PUNCT
ijassa-1639	249	3	r.	r.	PROPN
ijassa-1639	249	4	&	&	CCONJ
ijassa-1639	249	5	fischer	fischer	PROPN
ijassa-1639	249	6	,	,	PUNCT
ijassa-1639	249	7	a.	a.	NOUN
ijassa-1639	249	8	(	(	PUNCT
ijassa-1639	249	9	2012	2012	NUM
ijassa-1639	249	10	)	)	PUNCT
ijassa-1639	249	11	a	a	DET
ijassa-1639	249	12	unified	unified	ADJ
ijassa-1639	249	13	local	local	ADJ
ijassa-1639	249	14	convergence	convergence	NOUN
ijassa-1639	249	15	analysis	analysis	NOUN
ijassa-1639	249	16	of	of	ADP
ijassa-1639	249	17	inexact	inexact	ADJ
ijassa-1639	249	18	constrained	constrain	VERB
ijassa-1639	249	19	levenberg	levenberg	PROPN
ijassa-1639	249	20	–	–	PUNCT
ijassa-1639	249	21	marquardt	marquardt	PROPN
ijassa-1639	249	22	methods	method	NOUN
ijassa-1639	249	23	,	,	PUNCT
ijassa-1639	249	24	optim	optim	ADJ
ijassa-1639	249	25	.	.	PUNCT
ijassa-1639	250	1	lett	lett	PROPN
ijassa-1639	250	2	.	.	PROPN
ijassa-1639	250	3	,	,	PUNCT
ijassa-1639	250	4	6	6	NUM
ijassa-1639	250	5	,	,	PUNCT
ijassa-1639	250	6	927–940	927–940	NUM
ijassa-1639	250	7	.	.	NOUN
ijassa-1639	251	1	2	2	NUM
ijassa-1639	251	2	.	.	X
ijassa-1639	251	3	dolan	dolan	PROPN
ijassa-1639	251	4	,	,	PUNCT
ijassa-1639	251	5	e.d	e.d	PROPN
ijassa-1639	251	6	.	.	PROPN
ijassa-1639	251	7	&	&	CCONJ
ijassa-1639	251	8	more	more	ADJ
ijassa-1639	251	9	,	,	PUNCT
ijassa-1639	251	10	j.j	j.j	PROPN
ijassa-1639	251	11	.	.	PROPN
ijassa-1639	251	12	(	(	PUNCT
ijassa-1639	251	13	2002	2002	NUM
ijassa-1639	251	14	)	)	PUNCT
ijassa-1639	251	15	benchmarking	benchmarke	VERB
ijassa-1639	251	16	optimization	optimization	NOUN
ijassa-1639	251	17	software	software	NOUN
ijassa-1639	251	18	with	with	ADP
ijassa-1639	251	19	performance	performance	NOUN
ijassa-1639	251	20	profiles	profile	NOUN
ijassa-1639	251	21	,	,	PUNCT
ijassa-1639	251	22	math	math	NOUN
ijassa-1639	251	23	.	.	PUNCT
ijassa-1639	252	1	program	program	PROPN
ijassa-1639	252	2	.	.	PUNCT
ijassa-1639	252	3	,	,	PUNCT
ijassa-1639	252	4	91	91	NUM
ijassa-1639	252	5	,	,	PUNCT
ijassa-1639	252	6	201–213	201–213	NUM
ijassa-1639	252	7	.	.	NOUN
ijassa-1639	253	1	3	3	X
ijassa-1639	253	2	.	.	X
ijassa-1639	253	3	dorovskikh	dorovskikh	PROPN
ijassa-1639	253	4	,	,	PUNCT
ijassa-1639	253	5	d.i	d.i	PROPN
ijassa-1639	253	6	.	.	PROPN
ijassa-1639	253	7	,	,	PUNCT
ijassa-1639	253	8	izmailov	izmailov	PROPN
ijassa-1639	253	9	,	,	PUNCT
ijassa-1639	253	10	a.f	a.f	PROPN
ijassa-1639	253	11	.	.	PROPN
ijassa-1639	253	12	&	&	CCONJ
ijassa-1639	253	13	uskov	uskov	PROPN
ijassa-1639	253	14	,	,	PUNCT
ijassa-1639	253	15	e.i	e.i	PROPN
ijassa-1639	253	16	.	.	PROPN
ijassa-1639	253	17	(	(	PUNCT
ijassa-1639	253	18	2024	2024	NUM
ijassa-1639	253	19	)	)	PUNCT
ijassa-1639	253	20	globalizing	globalize	VERB
ijassa-1639	253	21	convergence	convergence	NOUN
ijassa-1639	253	22	of	of	ADP
ijassa-1639	253	23	piecewise	piecewise	PROPN
ijassa-1639	253	24	newton	newton	PROPN
ijassa-1639	253	25	methods	method	NOUN
ijassa-1639	253	26	,	,	PUNCT
ijassa-1639	253	27	russian	russian	ADJ
ijassa-1639	253	28	universities	university	NOUN
ijassa-1639	253	29	reports	report	VERB
ijassa-1639	253	30	.	.	PUNCT
ijassa-1639	254	1	mathematics	mathematic	NOUN
ijassa-1639	254	2	,	,	PUNCT
ijassa-1639	254	3	29	29	NUM
ijassa-1639	254	4	,	,	PUNCT
ijassa-1639	254	5	149–163	149–163	NUM
ijassa-1639	254	6	.	.	NOUN
ijassa-1639	254	7	4	4	NUM
ijassa-1639	254	8	.	.	NUM
ijassa-1639	254	9	dreves	dreve	NOUN
ijassa-1639	254	10	,	,	PUNCT
ijassa-1639	254	11	a.	a.	PROPN
ijassa-1639	254	12	,	,	PUNCT
ijassa-1639	254	13	facchinei	facchinei	PROPN
ijassa-1639	254	14	,	,	PUNCT
ijassa-1639	254	15	f.	f.	PROPN
ijassa-1639	254	16	,	,	PUNCT
ijassa-1639	254	17	fischer	fischer	PROPN
ijassa-1639	254	18	,	,	PUNCT
ijassa-1639	254	19	a.	a.	PROPN
ijassa-1639	254	20	&	&	CCONJ
ijassa-1639	254	21	herrich	herrich	PROPN
ijassa-1639	254	22	,	,	PUNCT
ijassa-1639	254	23	m.	m.	NOUN
ijassa-1639	254	24	(	(	PUNCT
ijassa-1639	254	25	2014	2014	NUM
ijassa-1639	254	26	)	)	PUNCT
ijassa-1639	254	27	a	a	DET
ijassa-1639	254	28	new	new	ADJ
ijassa-1639	254	29	error	error	NOUN
ijassa-1639	254	30	bound	bind	VERB
ijassa-1639	254	31	result	result	NOUN
ijassa-1639	254	32	for	for	ADP
ijassa-1639	254	33	generalized	generalized	ADJ
ijassa-1639	254	34	nash	nash	PROPN
ijassa-1639	254	35	equilibrium	equilibrium	NOUN
ijassa-1639	254	36	problems	problem	NOUN
ijassa-1639	254	37	and	and	CCONJ
ijassa-1639	254	38	its	its	PRON
ijassa-1639	254	39	algorithmic	algorithmic	ADJ
ijassa-1639	254	40	application	application	NOUN
ijassa-1639	254	41	,	,	PUNCT
ijassa-1639	254	42	comput	comput	NOUN
ijassa-1639	254	43	.	.	PUNCT
ijassa-1639	255	1	optim	optim	PROPN
ijassa-1639	255	2	.	.	PUNCT
ijassa-1639	256	1	appl	appl	PROPN
ijassa-1639	256	2	.	.	PROPN
ijassa-1639	256	3	,	,	PUNCT
ijassa-1639	256	4	59	59	NUM
ijassa-1639	256	5	,	,	PUNCT
ijassa-1639	256	6	63–84	63–84	NOUN
ijassa-1639	256	7	.	.	PUNCT
ijassa-1639	257	1	5	5	X
ijassa-1639	257	2	.	.	NUM
ijassa-1639	257	3	dreves	dreve	NOUN
ijassa-1639	257	4	,	,	PUNCT
ijassa-1639	257	5	a.	a.	PROPN
ijassa-1639	257	6	,	,	PUNCT
ijassa-1639	257	7	facchinei	facchinei	PROPN
ijassa-1639	257	8	,	,	PUNCT
ijassa-1639	257	9	f.	f.	PROPN
ijassa-1639	257	10	,	,	PUNCT
ijassa-1639	257	11	kanzow	kanzow	PROPN
ijassa-1639	257	12	,	,	PUNCT
ijassa-1639	257	13	c.	c.	PROPN
ijassa-1639	257	14	&	&	CCONJ
ijassa-1639	257	15	sagratella	sagratella	PROPN
ijassa-1639	257	16	,	,	PUNCT
ijassa-1639	257	17	s.	s.	PROPN
ijassa-1639	257	18	(	(	PUNCT
ijassa-1639	257	19	2011	2011	NUM
ijassa-1639	257	20	)	)	PUNCT
ijassa-1639	257	21	on	on	ADP
ijassa-1639	257	22	the	the	DET
ijassa-1639	257	23	solution	solution	NOUN
ijassa-1639	257	24	of	of	ADP
ijassa-1639	257	25	the	the	DET
ijassa-1639	257	26	kkt	kkt	PROPN
ijassa-1639	257	27	conditions	condition	NOUN
ijassa-1639	257	28	of	of	ADP
ijassa-1639	257	29	generalized	generalized	ADJ
ijassa-1639	257	30	nash	nash	PROPN
ijassa-1639	257	31	equilibrium	equilibrium	NOUN
ijassa-1639	257	32	problems	problem	NOUN
ijassa-1639	257	33	,	,	PUNCT
ijassa-1639	257	34	siam	siam	PROPN
ijassa-1639	257	35	j.	j.	PROPN
ijassa-1639	257	36	optim	optim	PROPN
ijassa-1639	257	37	.	.	PROPN
ijassa-1639	257	38	,	,	PUNCT
ijassa-1639	257	39	21	21	NUM
ijassa-1639	257	40	,	,	PUNCT
ijassa-1639	257	41	1082	1082	NUM
ijassa-1639	257	42	–	–	PUNCT
ijassa-1639	257	43	1108	1108	NUM
ijassa-1639	257	44	.	.	PUNCT
ijassa-1639	258	1	6	6	NUM
ijassa-1639	258	2	.	.	X
ijassa-1639	258	3	facchinei	facchinei	PROPN
ijassa-1639	258	4	,	,	PUNCT
ijassa-1639	258	5	f.	f.	PROPN
ijassa-1639	258	6	,	,	PUNCT
ijassa-1639	258	7	fischer	fischer	PROPN
ijassa-1639	258	8	,	,	PUNCT
ijassa-1639	258	9	a.	a.	PROPN
ijassa-1639	258	10	&	&	CCONJ
ijassa-1639	258	11	herrich	herrich	PROPN
ijassa-1639	258	12	,	,	PUNCT
ijassa-1639	258	13	m.	m.	NOUN
ijassa-1639	258	14	(	(	PUNCT
ijassa-1639	258	15	2013	2013	NUM
ijassa-1639	258	16	)	)	PUNCT
ijassa-1639	258	17	a	a	DET
ijassa-1639	258	18	family	family	NOUN
ijassa-1639	258	19	of	of	ADP
ijassa-1639	258	20	newton	newton	PROPN
ijassa-1639	258	21	methods	method	NOUN
ijassa-1639	258	22	for	for	ADP
ijassa-1639	258	23	nonsmooth	nonsmooth	ADJ
ijassa-1639	258	24	constrained	constrain	VERB
ijassa-1639	258	25	systems	system	NOUN
ijassa-1639	258	26	with	with	ADP
ijassa-1639	258	27	nonisolated	nonisolated	ADJ
ijassa-1639	258	28	solutions	solution	NOUN
ijassa-1639	258	29	,	,	PUNCT
ijassa-1639	258	30	math	math	NOUN
ijassa-1639	258	31	.	.	PUNCT
ijassa-1639	259	1	methods	method	NOUN
ijassa-1639	259	2	oper	oper	PROPN
ijassa-1639	259	3	.	.	PUNCT
ijassa-1639	260	1	res	res	PROPN
ijassa-1639	260	2	.	.	PROPN
ijassa-1639	260	3	,	,	PUNCT
ijassa-1639	260	4	77	77	NUM
ijassa-1639	260	5	,	,	PUNCT
ijassa-1639	260	6	433–443	433–443	NUM
ijassa-1639	260	7	.	.	PUNCT
ijassa-1639	261	1	7	7	X
ijassa-1639	261	2	.	.	X
ijassa-1639	261	3	facchinei	facchinei	PROPN
ijassa-1639	261	4	,	,	PUNCT
ijassa-1639	261	5	f.	f.	PROPN
ijassa-1639	261	6	,	,	PUNCT
ijassa-1639	261	7	fischer	fischer	PROPN
ijassa-1639	261	8	,	,	PUNCT
ijassa-1639	261	9	a.	a.	PROPN
ijassa-1639	261	10	&	&	CCONJ
ijassa-1639	261	11	herrich	herrich	PROPN
ijassa-1639	261	12	,	,	PUNCT
ijassa-1639	261	13	m.	m.	NOUN
ijassa-1639	261	14	(	(	PUNCT
ijassa-1639	261	15	2014	2014	NUM
ijassa-1639	261	16	)	)	PUNCT
ijassa-1639	261	17	an	an	DET
ijassa-1639	261	18	lp	lp	PROPN
ijassa-1639	261	19	-	-	PUNCT
ijassa-1639	261	20	newton	newton	PROPN
ijassa-1639	261	21	method	method	NOUN
ijassa-1639	261	22	:	:	PUNCT
ijassa-1639	261	23	nonsmooth	nonsmooth	PROPN
ijassa-1639	261	24	equations	equation	NOUN
ijassa-1639	261	25	,	,	PUNCT
ijassa-1639	261	26	kkt	kkt	PROPN
ijassa-1639	261	27	systems	systems	PROPN
ijassa-1639	261	28	,	,	PUNCT
ijassa-1639	261	29	and	and	CCONJ
ijassa-1639	261	30	nonisolated	nonisolated	ADJ
ijassa-1639	261	31	solutions	solution	NOUN
ijassa-1639	261	32	,	,	PUNCT
ijassa-1639	261	33	math	math	NOUN
ijassa-1639	261	34	.	.	PUNCT
ijassa-1639	261	35	program	program	PROPN
ijassa-1639	261	36	.	.	PUNCT
ijassa-1639	262	1	,	,	PUNCT
ijassa-1639	262	2	146	146	NUM
ijassa-1639	262	3	,	,	PUNCT
ijassa-1639	262	4	1–36	1–36	PROPN
ijassa-1639	262	5	.	.	NOUN
ijassa-1639	262	6	8	8	NUM
ijassa-1639	262	7	.	.	X
ijassa-1639	263	1	facchinei	facchinei	PROPN
ijassa-1639	263	2	,	,	PUNCT
ijassa-1639	263	3	f.	f.	PROPN
ijassa-1639	263	4	,	,	PUNCT
ijassa-1639	263	5	fischer	fischer	PROPN
ijassa-1639	263	6	,	,	PUNCT
ijassa-1639	263	7	a.	a.	PROPN
ijassa-1639	263	8	&	&	CCONJ
ijassa-1639	263	9	piccialli	piccialli	PROPN
ijassa-1639	263	10	,	,	PUNCT
ijassa-1639	263	11	v.	v.	PROPN
ijassa-1639	263	12	(	(	PUNCT
ijassa-1639	263	13	2007	2007	NUM
ijassa-1639	263	14	)	)	PUNCT
ijassa-1639	263	15	on	on	ADP
ijassa-1639	263	16	generalized	generalized	ADJ
ijassa-1639	263	17	nash	nash	NOUN
ijassa-1639	263	18	games	game	NOUN
ijassa-1639	263	19	and	and	CCONJ
ijassa-1639	263	20	variational	variational	ADJ
ijassa-1639	263	21	inequalities	inequality	NOUN
ijassa-1639	263	22	,	,	PUNCT
ijassa-1639	264	1	oper	oper	PROPN
ijassa-1639	264	2	.	.	PUNCT
ijassa-1639	264	3	res	res	PROPN
ijassa-1639	264	4	.	.	PUNCT
ijassa-1639	265	1	lett	lett	PROPN
ijassa-1639	265	2	.	.	PROPN
ijassa-1639	265	3	,	,	PUNCT
ijassa-1639	265	4	35	35	NUM
ijassa-1639	265	5	,	,	PUNCT
ijassa-1639	265	6	159–164	159–164	NUM
ijassa-1639	265	7	.	.	PUNCT
ijassa-1639	266	1	9	9	NUM
ijassa-1639	266	2	.	.	X
ijassa-1639	266	3	facchinei	facchinei	PROPN
ijassa-1639	266	4	,	,	PUNCT
ijassa-1639	266	5	f.	f.	PROPN
ijassa-1639	266	6	,	,	PUNCT
ijassa-1639	266	7	fischer	fischer	PROPN
ijassa-1639	266	8	,	,	PUNCT
ijassa-1639	266	9	a.	a.	PROPN
ijassa-1639	266	10	&	&	CCONJ
ijassa-1639	266	11	piccialli	piccialli	PROPN
ijassa-1639	266	12	,	,	PUNCT
ijassa-1639	266	13	v.	v.	PROPN
ijassa-1639	266	14	(	(	PUNCT
ijassa-1639	266	15	2009	2009	NUM
ijassa-1639	266	16	)	)	PUNCT
ijassa-1639	266	17	generalized	generalize	VERB
ijassa-1639	266	18	nash	nash	PROPN
ijassa-1639	266	19	equilibrium	equilibrium	NOUN
ijassa-1639	266	20	problems	problem	NOUN
ijassa-1639	266	21	and	and	CCONJ
ijassa-1639	266	22	newton	newton	PROPN
ijassa-1639	266	23	methods	method	NOUN
ijassa-1639	266	24	,	,	PUNCT
ijassa-1639	266	25	math	math	NOUN
ijassa-1639	266	26	.	.	PUNCT
ijassa-1639	266	27	program	program	PROPN
ijassa-1639	266	28	.	.	PUNCT
ijassa-1639	266	29	,	,	PUNCT
ijassa-1639	266	30	117	117	NUM
ijassa-1639	266	31	,	,	PUNCT
ijassa-1639	266	32	163–194	163–194	NUM
ijassa-1639	266	33	.	.	NOUN
ijassa-1639	267	1	10	10	NUM
ijassa-1639	267	2	.	.	PUNCT
ijassa-1639	268	1	facchinei	facchinei	PROPN
ijassa-1639	268	2	,	,	PUNCT
ijassa-1639	268	3	f.	f.	PROPN
ijassa-1639	268	4	&	&	CCONJ
ijassa-1639	268	5	kanzow	kanzow	PROPN
ijassa-1639	268	6	,	,	PUNCT
ijassa-1639	268	7	c.	c.	PROPN
ijassa-1639	268	8	(	(	PUNCT
ijassa-1639	268	9	2010	2010	NUM
ijassa-1639	268	10	)	)	PUNCT
ijassa-1639	268	11	generalized	generalize	VERB
ijassa-1639	268	12	nash	nash	PROPN
ijassa-1639	268	13	equilibrium	equilibrium	NOUN
ijassa-1639	268	14	problems	problem	NOUN
ijassa-1639	268	15	,	,	PUNCT
ijassa-1639	269	1	ann	ann	PROPN
ijassa-1639	269	2	.	.	PUNCT
ijassa-1639	269	3	oper	oper	PROPN
ijassa-1639	269	4	.	.	PUNCT
ijassa-1639	269	5	res	res	PROPN
ijassa-1639	269	6	.	.	PROPN
ijassa-1639	269	7	,	,	PUNCT
ijassa-1639	269	8	175	175	NUM
ijassa-1639	269	9	,	,	PUNCT
ijassa-1639	269	10	177–211	177–211	NUM
ijassa-1639	269	11	.	.	PUNCT
ijassa-1639	270	1	11	11	NUM
ijassa-1639	270	2	.	.	PUNCT
ijassa-1639	271	1	facchinei	facchinei	PROPN
ijassa-1639	271	2	,	,	PUNCT
ijassa-1639	271	3	f.	f.	PROPN
ijassa-1639	271	4	&	&	CCONJ
ijassa-1639	271	5	kanzow	kanzow	PROPN
ijassa-1639	271	6	,	,	PUNCT
ijassa-1639	271	7	c.	c.	PROPN
ijassa-1639	271	8	(	(	PUNCT
ijassa-1639	271	9	2010	2010	NUM
ijassa-1639	271	10	)	)	PUNCT
ijassa-1639	271	11	penalty	penalty	NOUN
ijassa-1639	271	12	methods	method	NOUN
ijassa-1639	271	13	for	for	ADP
ijassa-1639	271	14	the	the	DET
ijassa-1639	271	15	solution	solution	NOUN
ijassa-1639	271	16	of	of	ADP
ijassa-1639	271	17	generalized	generalized	ADJ
ijassa-1639	271	18	nash	nash	PROPN
ijassa-1639	271	19	equilibrium	equilibrium	NOUN
ijassa-1639	271	20	problems	problem	NOUN
ijassa-1639	271	21	,	,	PUNCT
ijassa-1639	271	22	siam	siam	PROPN
ijassa-1639	271	23	j.	j.	PROPN
ijassa-1639	271	24	optim	optim	PROPN
ijassa-1639	271	25	.	.	PROPN
ijassa-1639	271	26	,	,	PUNCT
ijassa-1639	271	27	20	20	NUM
ijassa-1639	271	28	,	,	PUNCT
ijassa-1639	271	29	2228–2253	2228–2253	NUM
ijassa-1639	271	30	.	.	PUNCT
ijassa-1639	272	1	12	12	NUM
ijassa-1639	272	2	.	.	PUNCT
ijassa-1639	273	1	fischer	fischer	PROPN
ijassa-1639	273	2	,	,	PUNCT
ijassa-1639	273	3	a.	a.	NOUN
ijassa-1639	273	4	(	(	PUNCT
ijassa-1639	273	5	2002	2002	NUM
ijassa-1639	273	6	)	)	PUNCT
ijassa-1639	273	7	local	local	ADJ
ijassa-1639	273	8	behavior	behavior	NOUN
ijassa-1639	273	9	of	of	ADP
ijassa-1639	273	10	an	an	DET
ijassa-1639	273	11	iterative	iterative	NOUN
ijassa-1639	273	12	framework	framework	NOUN
ijassa-1639	273	13	for	for	ADP
ijassa-1639	273	14	generalized	generalized	ADJ
ijassa-1639	273	15	equations	equation	NOUN
ijassa-1639	273	16	with	with	ADP
ijassa-1639	273	17	nonisolated	nonisolated	ADJ
ijassa-1639	273	18	solutions	solution	NOUN
ijassa-1639	273	19	,	,	PUNCT
ijassa-1639	273	20	math	math	NOUN
ijassa-1639	273	21	.	.	PUNCT
ijassa-1639	274	1	program	program	PROPN
ijassa-1639	274	2	.	.	PUNCT
ijassa-1639	275	1	,	,	PUNCT
ijassa-1639	275	2	94	94	NUM
ijassa-1639	275	3	,	,	PUNCT
ijassa-1639	275	4	91–124	91–124	NUM
ijassa-1639	275	5	.	.	NOUN
ijassa-1639	276	1	13	13	NUM
ijassa-1639	276	2	.	.	PUNCT
ijassa-1639	277	1	fischer	fischer	PROPN
ijassa-1639	277	2	,	,	PUNCT
ijassa-1639	277	3	a.	a.	PROPN
ijassa-1639	277	4	,	,	PUNCT
ijassa-1639	277	5	herrich	herrich	NOUN
ijassa-1639	277	6	,	,	PUNCT
ijassa-1639	277	7	m.	m.	NOUN
ijassa-1639	277	8	,	,	PUNCT
ijassa-1639	277	9	izmailov	izmailov	PROPN
ijassa-1639	277	10	,	,	PUNCT
ijassa-1639	277	11	a.f	a.f	PROPN
ijassa-1639	277	12	.	.	PROPN
ijassa-1639	277	13	&	&	CCONJ
ijassa-1639	277	14	solodov	solodov	PROPN
ijassa-1639	277	15	,	,	PUNCT
ijassa-1639	277	16	m.v	m.v	PROPN
ijassa-1639	277	17	.	.	PROPN
ijassa-1639	278	1	(	(	PUNCT
ijassa-1639	278	2	2016	2016	NUM
ijassa-1639	278	3	)	)	PUNCT
ijassa-1639	278	4	a	a	DET
ijassa-1639	278	5	globally	globally	ADV
ijassa-1639	278	6	convergent	convergent	ADJ
ijassa-1639	278	7	lp	lp	PROPN
ijassa-1639	278	8	-	-	PUNCT
ijassa-1639	278	9	newton	newton	PROPN
ijassa-1639	278	10	method	method	NOUN
ijassa-1639	278	11	,	,	PUNCT
ijassa-1639	278	12	siam	siam	PROPN
ijassa-1639	278	13	j.	j.	PROPN
ijassa-1639	278	14	optim	optim	PROPN
ijassa-1639	278	15	.	.	PROPN
ijassa-1639	278	16	,	,	PUNCT
ijassa-1639	278	17	26	26	NUM
ijassa-1639	278	18	,	,	PUNCT
ijassa-1639	278	19	2012–2033	2012–2033	NUM
ijassa-1639	278	20	.	.	PUNCT
ijassa-1639	279	1	copyright	copyright	NOUN
ijassa-1639	279	2	©	©	PROPN
ijassa-1639	279	3	2024	2024	NUM
ijassa-1639	279	4	assa	assa	NOUN
ijassa-1639	279	5	.	.	PUNCT
ijassa-1639	280	1	adv	adv	PROPN
ijassa-1639	280	2	syst	syst	PROPN
ijassa-1639	280	3	sci	sci	PROPN
ijassa-1639	280	4	appl	appl	PROPN
ijassa-1639	280	5	(	(	PUNCT
ijassa-1639	280	6	2024	2024	NUM
ijassa-1639	280	7	)	)	PUNCT
ijassa-1639	280	8	https://rscf.ru/en/project/24-21-00015/	https://rscf.ru/en/project/24-21-00015/	PRON
ijassa-1639	280	9	piecewise	piecewise	PROPN
ijassa-1639	280	10	levenberg	levenberg	PROPN
ijassa-1639	280	11	–	–	PUNCT
ijassa-1639	280	12	marquardt	marquardt	PROPN
ijassa-1639	280	13	method	method	NOUN
ijassa-1639	280	14	for	for	ADP
ijassa-1639	280	15	gneps	gneps	NOUN
ijassa-1639	280	16	31	31	NUM
ijassa-1639	280	17	14	14	NUM
ijassa-1639	280	18	.	.	PUNCT
ijassa-1639	281	1	fischer	fischer	PROPN
ijassa-1639	281	2	,	,	PUNCT
ijassa-1639	281	3	a.	a.	PROPN
ijassa-1639	281	4	,	,	PUNCT
ijassa-1639	281	5	herrich	herrich	NOUN
ijassa-1639	281	6	,	,	PUNCT
ijassa-1639	281	7	m.	m.	NOUN
ijassa-1639	281	8	,	,	PUNCT
ijassa-1639	281	9	izmailov	izmailov	PROPN
ijassa-1639	281	10	,	,	PUNCT
ijassa-1639	281	11	a.f	a.f	PROPN
ijassa-1639	281	12	.	.	PROPN
ijassa-1639	281	13	&	&	CCONJ
ijassa-1639	281	14	solodov	solodov	PROPN
ijassa-1639	281	15	,	,	PUNCT
ijassa-1639	281	16	m.v	m.v	PROPN
ijassa-1639	281	17	.	.	PROPN
ijassa-1639	282	1	(	(	PUNCT
ijassa-1639	282	2	2016	2016	NUM
ijassa-1639	282	3	)	)	PUNCT
ijassa-1639	282	4	convergence	convergence	NOUN
ijassa-1639	282	5	conditions	condition	NOUN
ijassa-1639	282	6	for	for	ADP
ijassa-1639	282	7	newton	newton	NOUN
ijassa-1639	282	8	-	-	PUNCT
ijassa-1639	282	9	type	type	NOUN
ijassa-1639	282	10	methods	method	NOUN
ijassa-1639	282	11	applied	apply	VERB
ijassa-1639	282	12	to	to	ADP
ijassa-1639	282	13	complementarity	complementarity	NOUN
ijassa-1639	282	14	systems	system	NOUN
ijassa-1639	282	15	with	with	ADP
ijassa-1639	282	16	nonisolated	nonisolated	ADJ
ijassa-1639	282	17	solutions	solution	NOUN
ijassa-1639	282	18	,	,	PUNCT
ijassa-1639	282	19	comput	comput	NOUN
ijassa-1639	282	20	.	.	PUNCT
ijassa-1639	283	1	optim	optim	PROPN
ijassa-1639	283	2	.	.	PUNCT
ijassa-1639	284	1	appl	appl	PROPN
ijassa-1639	284	2	.	.	PROPN
ijassa-1639	284	3	,	,	PUNCT
ijassa-1639	284	4	63	63	NUM
ijassa-1639	284	5	,	,	PUNCT
ijassa-1639	284	6	425–459	425–459	NUM
ijassa-1639	284	7	.	.	PUNCT
ijassa-1639	285	1	15	15	NUM
ijassa-1639	285	2	.	.	PUNCT
ijassa-1639	286	1	fischer	fischer	PROPN
ijassa-1639	286	2	,	,	PUNCT
ijassa-1639	286	3	a.	a.	PROPN
ijassa-1639	286	4	,	,	PUNCT
ijassa-1639	286	5	herrich	herrich	NOUN
ijassa-1639	286	6	,	,	PUNCT
ijassa-1639	286	7	m.	m.	NOUN
ijassa-1639	286	8	&	&	CCONJ
ijassa-1639	286	9	schönefeld	schönefeld	PROPN
ijassa-1639	286	10	,	,	PUNCT
ijassa-1639	286	11	k.	k.	PROPN
ijassa-1639	286	12	(	(	PUNCT
ijassa-1639	286	13	2014	2014	NUM
ijassa-1639	286	14	)	)	PUNCT
ijassa-1639	286	15	generalized	generalize	VERB
ijassa-1639	286	16	nash	nash	PROPN
ijassa-1639	286	17	equilibrium	equilibrium	NOUN
ijassa-1639	286	18	problems	problem	NOUN
ijassa-1639	286	19	–	–	PUNCT
ijassa-1639	286	20	recent	recent	ADJ
ijassa-1639	286	21	advances	advance	NOUN
ijassa-1639	286	22	and	and	CCONJ
ijassa-1639	286	23	challenges	challenge	NOUN
ijassa-1639	286	24	,	,	PUNCT
ijassa-1639	286	25	pesquisa	pesquisa	PROPN
ijassa-1639	286	26	operacional	operacional	ADJ
ijassa-1639	286	27	,	,	PUNCT
ijassa-1639	286	28	34	34	NUM
ijassa-1639	286	29	,	,	PUNCT
ijassa-1639	286	30	521–558	521–558	NUM
ijassa-1639	286	31	.	.	NOUN
ijassa-1639	286	32	16	16	NUM
ijassa-1639	286	33	.	.	PUNCT
ijassa-1639	287	1	fischer	fischer	PROPN
ijassa-1639	287	2	,	,	PUNCT
ijassa-1639	287	3	a.	a.	PROPN
ijassa-1639	287	4	,	,	PUNCT
ijassa-1639	287	5	izmailov	izmailov	PROPN
ijassa-1639	287	6	,	,	PUNCT
ijassa-1639	287	7	a.f	a.f	PROPN
ijassa-1639	287	8	.	.	PROPN
ijassa-1639	287	9	&	&	CCONJ
ijassa-1639	287	10	jelitte	jelitte	PROPN
ijassa-1639	287	11	,	,	PUNCT
ijassa-1639	287	12	m.	m.	NOUN
ijassa-1639	287	13	(	(	PUNCT
ijassa-1639	287	14	2021	2021	NUM
ijassa-1639	287	15	)	)	PUNCT
ijassa-1639	287	16	newton	newton	NOUN
ijassa-1639	287	17	-	-	PUNCT
ijassa-1639	287	18	type	type	NOUN
ijassa-1639	287	19	methods	method	NOUN
ijassa-1639	287	20	near	near	ADP
ijassa-1639	287	21	critical	critical	ADJ
ijassa-1639	287	22	solutions	solution	NOUN
ijassa-1639	287	23	of	of	ADP
ijassa-1639	287	24	piecewise	piecewise	NOUN
ijassa-1639	287	25	smooth	smooth	ADJ
ijassa-1639	287	26	nonlinear	nonlinear	ADJ
ijassa-1639	287	27	equations	equation	NOUN
ijassa-1639	287	28	,	,	PUNCT
ijassa-1639	287	29	comput	comput	NOUN
ijassa-1639	287	30	.	.	PUNCT
ijassa-1639	288	1	optim	optim	PROPN
ijassa-1639	288	2	.	.	PUNCT
ijassa-1639	289	1	appl	appl	PROPN
ijassa-1639	289	2	.	.	PROPN
ijassa-1639	289	3	,	,	PUNCT
ijassa-1639	289	4	80	80	NUM
ijassa-1639	289	5	,	,	PUNCT
ijassa-1639	289	6	587	587	NUM
ijassa-1639	289	7	–	–	PUNCT
ijassa-1639	289	8	615	615	NUM
ijassa-1639	289	9	.	.	PUNCT
ijassa-1639	289	10	17	17	NUM
ijassa-1639	289	11	.	.	PUNCT
ijassa-1639	290	1	fischer	fischer	PROPN
ijassa-1639	290	2	,	,	PUNCT
ijassa-1639	290	3	a.	a.	PROPN
ijassa-1639	290	4	,	,	PUNCT
ijassa-1639	290	5	izmailov	izmailov	PROPN
ijassa-1639	290	6	,	,	PUNCT
ijassa-1639	290	7	a.f	a.f	PROPN
ijassa-1639	290	8	.	.	PROPN
ijassa-1639	290	9	&	&	CCONJ
ijassa-1639	290	10	solodov	solodov	PROPN
ijassa-1639	290	11	,	,	PUNCT
ijassa-1639	290	12	m.v	m.v	PROPN
ijassa-1639	290	13	.	.	PROPN
ijassa-1639	290	14	(	(	PUNCT
ijassa-1639	290	15	2023	2023	NUM
ijassa-1639	290	16	)	)	PUNCT
ijassa-1639	290	17	the	the	DET
ijassa-1639	290	18	levenberg	levenberg	PROPN
ijassa-1639	290	19	–	–	PUNCT
ijassa-1639	290	20	marquardt	marquardt	PROPN
ijassa-1639	290	21	method	method	NOUN
ijassa-1639	290	22	:	:	PUNCT
ijassa-1639	290	23	an	an	DET
ijassa-1639	290	24	overview	overview	NOUN
ijassa-1639	290	25	of	of	ADP
ijassa-1639	290	26	modern	modern	ADJ
ijassa-1639	290	27	convergence	convergence	NOUN
ijassa-1639	290	28	theories	theory	NOUN
ijassa-1639	290	29	and	and	CCONJ
ijassa-1639	290	30	more	more	ADJ
ijassa-1639	290	31	,	,	PUNCT
ijassa-1639	290	32	comput	comput	ADJ
ijassa-1639	290	33	.	.	PUNCT
ijassa-1639	291	1	optim	optim	PROPN
ijassa-1639	291	2	.	.	PUNCT
ijassa-1639	292	1	appl	appl	PROPN
ijassa-1639	292	2	.	.	PROPN
ijassa-1639	292	3	,	,	PUNCT
ijassa-1639	292	4	2024	2024	NUM
ijassa-1639	292	5	.	.	PUNCT
ijassa-1639	293	1	18	18	NUM
ijassa-1639	293	2	.	.	PUNCT
ijassa-1639	293	3	fischer	fischer	PROPN
ijassa-1639	293	4	,	,	PUNCT
ijassa-1639	293	5	a.	a.	PROPN
ijassa-1639	293	6	&	&	CCONJ
ijassa-1639	293	7	shukla	shukla	PROPN
ijassa-1639	293	8	,	,	PUNCT
ijassa-1639	293	9	p.k	p.k	PROPN
ijassa-1639	293	10	.	.	PROPN
ijassa-1639	293	11	(	(	PUNCT
ijassa-1639	293	12	2008	2008	NUM
ijassa-1639	293	13	)	)	PUNCT
ijassa-1639	293	14	a	a	DET
ijassa-1639	293	15	levenberg	levenberg	PROPN
ijassa-1639	293	16	–	–	PUNCT
ijassa-1639	293	17	marquardt	marquardt	PROPN
ijassa-1639	293	18	algorithm	algorithm	NOUN
ijassa-1639	293	19	for	for	ADP
ijassa-1639	293	20	unconstrained	unconstrained	ADJ
ijassa-1639	293	21	multicriteria	multicriteria	PROPN
ijassa-1639	293	22	optimization	optimization	PROPN
ijassa-1639	293	23	,	,	PUNCT
ijassa-1639	293	24	oper	oper	PROPN
ijassa-1639	293	25	.	.	PUNCT
ijassa-1639	293	26	res	res	PROPN
ijassa-1639	293	27	.	.	PUNCT
ijassa-1639	294	1	lett	lett	PROPN
ijassa-1639	294	2	.	.	PROPN
ijassa-1639	294	3	,	,	PUNCT
ijassa-1639	294	4	36	36	NUM
ijassa-1639	294	5	,	,	PUNCT
ijassa-1639	294	6	643–646	643–646	NUM
ijassa-1639	294	7	.	.	PUNCT
ijassa-1639	295	1	19	19	NUM
ijassa-1639	295	2	.	.	PUNCT
ijassa-1639	296	1	fukushima	fukushima	PROPN
ijassa-1639	296	2	,	,	PUNCT
ijassa-1639	296	3	m.	m.	NOUN
ijassa-1639	296	4	&	&	CCONJ
ijassa-1639	296	5	pang	pang	PROPN
ijassa-1639	296	6	,	,	PUNCT
ijassa-1639	296	7	j.-s	j.-s	PROPN
ijassa-1639	296	8	.	.	PUNCT
ijassa-1639	297	1	(	(	PUNCT
ijassa-1639	297	2	2005	2005	NUM
ijassa-1639	297	3	)	)	PUNCT
ijassa-1639	297	4	quasi	quasi	ADJ
ijassa-1639	297	5	-	-	ADJ
ijassa-1639	297	6	variational	variational	ADJ
ijassa-1639	297	7	inequalities	inequality	NOUN
ijassa-1639	297	8	,	,	PUNCT
ijassa-1639	297	9	generalized	generalized	ADJ
ijassa-1639	297	10	nash	nash	NOUN
ijassa-1639	297	11	equilibria	equilibrium	NOUN
ijassa-1639	297	12	,	,	PUNCT
ijassa-1639	297	13	and	and	CCONJ
ijassa-1639	297	14	multi	multi	ADJ
ijassa-1639	297	15	-	-	ADJ
ijassa-1639	297	16	leader	leader	ADJ
ijassa-1639	297	17	-	-	PUNCT
ijassa-1639	297	18	follower	follower	NOUN
ijassa-1639	297	19	games	game	NOUN
ijassa-1639	297	20	,	,	PUNCT
ijassa-1639	297	21	comput	comput	NOUN
ijassa-1639	297	22	.	.	PUNCT
ijassa-1639	298	1	manag	manag	PROPN
ijassa-1639	298	2	.	.	PUNCT
ijassa-1639	299	1	science	science	NOUN
ijassa-1639	299	2	,	,	PUNCT
ijassa-1639	299	3	2	2	NUM
ijassa-1639	299	4	,	,	PUNCT
ijassa-1639	299	5	21–56	21–56	NUM
ijassa-1639	299	6	.	.	NOUN
ijassa-1639	299	7	20	20	NUM
ijassa-1639	299	8	.	.	PUNCT
ijassa-1639	300	1	harker	harker	PROPN
ijassa-1639	300	2	,	,	PUNCT
ijassa-1639	300	3	p.t	p.t	PROPN
ijassa-1639	300	4	.	.	PROPN
ijassa-1639	300	5	(	(	PUNCT
ijassa-1639	300	6	1991	1991	NUM
ijassa-1639	300	7	)	)	PUNCT
ijassa-1639	300	8	generalized	generalize	VERB
ijassa-1639	300	9	nash	nash	NOUN
ijassa-1639	300	10	games	game	NOUN
ijassa-1639	300	11	and	and	CCONJ
ijassa-1639	300	12	quasi	quasi	ADJ
ijassa-1639	300	13	-	-	ADJ
ijassa-1639	300	14	variational	variational	ADJ
ijassa-1639	300	15	inequalities	inequality	NOUN
ijassa-1639	300	16	,	,	PUNCT
ijassa-1639	300	17	eur	eur	PROPN
ijassa-1639	300	18	.	.	PUNCT
ijassa-1639	301	1	j.	j.	PROPN
ijassa-1639	301	2	oper	oper	PROPN
ijassa-1639	301	3	.	.	PUNCT
ijassa-1639	302	1	res	res	PROPN
ijassa-1639	302	2	.	.	PROPN
ijassa-1639	302	3	,	,	PUNCT
ijassa-1639	302	4	54	54	NUM
ijassa-1639	302	5	,	,	PUNCT
ijassa-1639	302	6	81–94	81–94	NUM
ijassa-1639	302	7	.	.	PUNCT
ijassa-1639	303	1	21	21	NUM
ijassa-1639	303	2	.	.	PUNCT
ijassa-1639	303	3	von	von	PROPN
ijassa-1639	303	4	heusinger	heusinger	PROPN
ijassa-1639	303	5	,	,	PUNCT
ijassa-1639	303	6	a.	a.	PROPN
ijassa-1639	303	7	,	,	PUNCT
ijassa-1639	303	8	kanzow	kanzow	NOUN
ijassa-1639	303	9	,	,	PUNCT
ijassa-1639	303	10	c.	c.	PROPN
ijassa-1639	303	11	&	&	CCONJ
ijassa-1639	303	12	fukushima	fukushima	PROPN
ijassa-1639	303	13	,	,	PUNCT
ijassa-1639	303	14	m.	m.	NOUN
ijassa-1639	303	15	(	(	PUNCT
ijassa-1639	303	16	2012	2012	NUM
ijassa-1639	303	17	)	)	PUNCT
ijassa-1639	303	18	newton	newton	PROPN
ijassa-1639	303	19	’s	’s	PART
ijassa-1639	303	20	method	method	NOUN
ijassa-1639	303	21	for	for	ADP
ijassa-1639	303	22	computing	compute	VERB
ijassa-1639	303	23	a	a	DET
ijassa-1639	303	24	normalized	normalize	VERB
ijassa-1639	303	25	equilibrium	equilibrium	NOUN
ijassa-1639	303	26	in	in	ADP
ijassa-1639	303	27	the	the	DET
ijassa-1639	303	28	generalized	generalize	VERB
ijassa-1639	303	29	nash	nash	ADJ
ijassa-1639	303	30	game	game	NOUN
ijassa-1639	303	31	through	through	ADP
ijassa-1639	303	32	fixed	fix	VERB
ijassa-1639	303	33	point	point	NOUN
ijassa-1639	303	34	formulation	formulation	NOUN
ijassa-1639	303	35	,	,	PUNCT
ijassa-1639	303	36	math	math	NOUN
ijassa-1639	303	37	.	.	PUNCT
ijassa-1639	304	1	program	program	PROPN
ijassa-1639	304	2	.	.	PUNCT
ijassa-1639	305	1	,	,	PUNCT
ijassa-1639	305	2	132	132	NUM
ijassa-1639	305	3	,	,	PUNCT
ijassa-1639	305	4	99–123	99–123	NUM
ijassa-1639	305	5	.	.	PUNCT
ijassa-1639	306	1	22	22	NUM
ijassa-1639	306	2	.	.	PUNCT
ijassa-1639	307	1	izmailov	izmailov	PROPN
ijassa-1639	307	2	,	,	PUNCT
ijassa-1639	307	3	a.f	a.f	PROPN
ijassa-1639	307	4	.	.	PROPN
ijassa-1639	307	5	&	&	CCONJ
ijassa-1639	307	6	solodov	solodov	PROPN
ijassa-1639	307	7	,	,	PUNCT
ijassa-1639	307	8	m.v	m.v	PROPN
ijassa-1639	307	9	.	.	PROPN
ijassa-1639	307	10	(	(	PUNCT
ijassa-1639	307	11	2014	2014	NUM
ijassa-1639	307	12	)	)	PUNCT
ijassa-1639	307	13	on	on	ADP
ijassa-1639	307	14	error	error	NOUN
ijassa-1639	307	15	bounds	bound	NOUN
ijassa-1639	307	16	and	and	CCONJ
ijassa-1639	307	17	newton	newton	NOUN
ijassa-1639	307	18	-	-	PUNCT
ijassa-1639	307	19	type	type	NOUN
ijassa-1639	307	20	methods	method	NOUN
ijassa-1639	307	21	for	for	ADP
ijassa-1639	307	22	generalized	generalized	ADJ
ijassa-1639	307	23	nash	nash	PROPN
ijassa-1639	307	24	equilibrium	equilibrium	NOUN
ijassa-1639	307	25	problems	problem	NOUN
ijassa-1639	307	26	,	,	PUNCT
ijassa-1639	307	27	comput	comput	NOUN
ijassa-1639	307	28	.	.	PUNCT
ijassa-1639	308	1	optim	optim	PROPN
ijassa-1639	308	2	.	.	PUNCT
ijassa-1639	309	1	appl	appl	PROPN
ijassa-1639	309	2	.	.	PROPN
ijassa-1639	309	3	,	,	PUNCT
ijassa-1639	309	4	59	59	NUM
ijassa-1639	309	5	,	,	PUNCT
ijassa-1639	309	6	201–218	201–218	NUM
ijassa-1639	309	7	.	.	NOUN
ijassa-1639	309	8	23	23	NUM
ijassa-1639	309	9	.	.	PUNCT
ijassa-1639	310	1	izmailov	izmailov	PROPN
ijassa-1639	310	2	,	,	PUNCT
ijassa-1639	310	3	a.f	a.f	PROPN
ijassa-1639	310	4	.	.	PROPN
ijassa-1639	310	5	,	,	PUNCT
ijassa-1639	310	6	solodov	solodov	PROPN
ijassa-1639	310	7	,	,	PUNCT
ijassa-1639	310	8	m.v	m.v	PROPN
ijassa-1639	310	9	.	.	PROPN
ijassa-1639	310	10	&	&	CCONJ
ijassa-1639	310	11	uskov	uskov	PROPN
ijassa-1639	310	12	,	,	PUNCT
ijassa-1639	310	13	e.i	e.i	PROPN
ijassa-1639	310	14	.	.	PROPN
ijassa-1639	310	15	(	(	PUNCT
ijassa-1639	310	16	2015	2015	NUM
ijassa-1639	310	17	)	)	PUNCT
ijassa-1639	310	18	combining	combine	VERB
ijassa-1639	310	19	stabilized	stabilize	VERB
ijassa-1639	310	20	sqp	sqp	NOUN
ijassa-1639	310	21	with	with	ADP
ijassa-1639	310	22	the	the	DET
ijassa-1639	310	23	augmented	augment	VERB
ijassa-1639	310	24	lagrangian	lagrangian	ADJ
ijassa-1639	310	25	algorithm	algorithm	NOUN
ijassa-1639	310	26	,	,	PUNCT
ijassa-1639	310	27	comput	comput	NOUN
ijassa-1639	310	28	.	.	PUNCT
ijassa-1639	311	1	optim	optim	PROPN
ijassa-1639	311	2	.	.	PUNCT
ijassa-1639	312	1	appl	appl	PROPN
ijassa-1639	312	2	.	.	PROPN
ijassa-1639	312	3	,	,	PUNCT
ijassa-1639	312	4	62	62	NUM
ijassa-1639	312	5	,	,	PUNCT
ijassa-1639	312	6	405–429	405–429	NUM
ijassa-1639	312	7	.	.	NOUN
ijassa-1639	312	8	24	24	NUM
ijassa-1639	312	9	.	.	PUNCT
ijassa-1639	313	1	izmailov	izmailov	PROPN
ijassa-1639	313	2	,	,	PUNCT
ijassa-1639	313	3	a.f	a.f	PROPN
ijassa-1639	313	4	.	.	PROPN
ijassa-1639	313	5	,	,	PUNCT
ijassa-1639	313	6	uskov	uskov	PROPN
ijassa-1639	313	7	,	,	PUNCT
ijassa-1639	313	8	e.i	e.i	PROPN
ijassa-1639	313	9	.	.	PROPN
ijassa-1639	313	10	&	&	CCONJ
ijassa-1639	313	11	yan	yan	PROPN
ijassa-1639	313	12	zhibai	zhibai	PROPN
ijassa-1639	313	13	(	(	PUNCT
ijassa-1639	313	14	2024	2024	NUM
ijassa-1639	313	15	)	)	PUNCT
ijassa-1639	313	16	globalization	globalization	NOUN
ijassa-1639	313	17	of	of	ADP
ijassa-1639	313	18	convergence	convergence	NOUN
ijassa-1639	313	19	of	of	ADP
ijassa-1639	313	20	the	the	DET
ijassa-1639	313	21	constrained	constrain	VERB
ijassa-1639	313	22	piecewise	piecewise	NOUN
ijassa-1639	313	23	levenberg	levenberg	PROPN
ijassa-1639	313	24	–	–	PUNCT
ijassa-1639	313	25	marquardt	marquardt	PROPN
ijassa-1639	313	26	method	method	NOUN
ijassa-1639	313	27	,	,	PUNCT
ijassa-1639	313	28	submitted	submit	VERB
ijassa-1639	313	29	.	.	PUNCT
ijassa-1639	314	1	25	25	NUM
ijassa-1639	314	2	.	.	X
ijassa-1639	314	3	izmailov	izmailov	PROPN
ijassa-1639	314	4	,	,	PUNCT
ijassa-1639	314	5	a.f	a.f	PROPN
ijassa-1639	314	6	.	.	PROPN
ijassa-1639	314	7	,	,	PUNCT
ijassa-1639	314	8	uskov	uskov	PROPN
ijassa-1639	314	9	,	,	PUNCT
ijassa-1639	314	10	e.i	e.i	PROPN
ijassa-1639	314	11	.	.	PROPN
ijassa-1639	314	12	&	&	CCONJ
ijassa-1639	314	13	yan	yan	PROPN
ijassa-1639	314	14	zhibai	zhibai	PROPN
ijassa-1639	314	15	(	(	PUNCT
ijassa-1639	314	16	2024	2024	NUM
ijassa-1639	314	17	)	)	PUNCT
ijassa-1639	314	18	the	the	DET
ijassa-1639	314	19	piecewise	piecewise	NOUN
ijassa-1639	314	20	levenberg	levenberg	PROPN
ijassa-1639	314	21	–	–	PUNCT
ijassa-1639	314	22	marquardt	marquardt	PROPN
ijassa-1639	314	23	method	method	NOUN
ijassa-1639	314	24	,	,	PUNCT
ijassa-1639	314	25	adv	adv	PROPN
ijassa-1639	314	26	.	.	PUNCT
ijassa-1639	314	27	syst	syst	PROPN
ijassa-1639	314	28	.	.	PUNCT
ijassa-1639	315	1	sci	sci	PROPN
ijassa-1639	315	2	.	.	PUNCT
ijassa-1639	315	3	appl	appl	PROPN
ijassa-1639	315	4	.	.	PROPN
ijassa-1639	315	5	,	,	PUNCT
ijassa-1639	315	6	24	24	NUM
ijassa-1639	315	7	,	,	PUNCT
ijassa-1639	315	8	29–39	29–39	NUM
ijassa-1639	315	9	.	.	PUNCT
ijassa-1639	316	1	26	26	NUM
ijassa-1639	316	2	.	.	PUNCT
ijassa-1639	317	1	kanzow	kanzow	PROPN
ijassa-1639	317	2	,	,	PUNCT
ijassa-1639	317	3	c.	c.	PROPN
ijassa-1639	317	4	,	,	PUNCT
ijassa-1639	317	5	yamashita	yamashita	PROPN
ijassa-1639	317	6	,	,	PUNCT
ijassa-1639	317	7	n.	n.	PROPN
ijassa-1639	317	8	&	&	CCONJ
ijassa-1639	317	9	fukushima	fukushima	PROPN
ijassa-1639	317	10	,	,	PUNCT
ijassa-1639	317	11	m.	m.	NOUN
ijassa-1639	317	12	(	(	PUNCT
ijassa-1639	317	13	2004	2004	NUM
ijassa-1639	317	14	)	)	PUNCT
ijassa-1639	317	15	levenberg	levenberg	PROPN
ijassa-1639	317	16	–	–	PUNCT
ijassa-1639	317	17	marquardt	marquardt	PROPN
ijassa-1639	317	18	methods	method	NOUN
ijassa-1639	317	19	with	with	ADP
ijassa-1639	317	20	strong	strong	ADJ
ijassa-1639	317	21	local	local	ADJ
ijassa-1639	317	22	convergence	convergence	NOUN
ijassa-1639	317	23	properties	property	NOUN
ijassa-1639	317	24	for	for	ADP
ijassa-1639	317	25	solving	solve	VERB
ijassa-1639	317	26	nonlinear	nonlinear	ADJ
ijassa-1639	317	27	equations	equation	NOUN
ijassa-1639	317	28	with	with	ADP
ijassa-1639	317	29	convex	convex	NOUN
ijassa-1639	317	30	constraints	constraint	NOUN
ijassa-1639	317	31	,	,	PUNCT
ijassa-1639	317	32	j.	j.	PROPN
ijassa-1639	317	33	comput	comput	PROPN
ijassa-1639	317	34	.	.	PUNCT
ijassa-1639	318	1	appl	appl	PROPN
ijassa-1639	318	2	.	.	PROPN
ijassa-1639	318	3	math	math	PROPN
ijassa-1639	318	4	.	.	PUNCT
ijassa-1639	318	5	,	,	PUNCT
ijassa-1639	318	6	172	172	NUM
ijassa-1639	318	7	,	,	PUNCT
ijassa-1639	318	8	375–397	375–397	NUM
ijassa-1639	318	9	.	.	PUNCT
ijassa-1639	319	1	27	27	NUM
ijassa-1639	319	2	.	.	X
ijassa-1639	320	1	kubotam	kubotam	PROPN
ijassa-1639	320	2	,	,	PUNCT
ijassa-1639	320	3	k.	k.	PROPN
ijassa-1639	320	4	&	&	CCONJ
ijassa-1639	320	5	fukushima	fukushima	PROPN
ijassa-1639	320	6	,	,	PUNCT
ijassa-1639	320	7	m.	m.	NOUN
ijassa-1639	320	8	(	(	PUNCT
ijassa-1639	320	9	2010	2010	NUM
ijassa-1639	320	10	)	)	PUNCT
ijassa-1639	320	11	gap	gap	NOUN
ijassa-1639	320	12	function	function	NOUN
ijassa-1639	320	13	approach	approach	NOUN
ijassa-1639	320	14	to	to	ADP
ijassa-1639	320	15	the	the	DET
ijassa-1639	320	16	generalized	generalize	VERB
ijassa-1639	320	17	nash	nash	PROPN
ijassa-1639	320	18	equilibrium	equilibrium	NOUN
ijassa-1639	320	19	problem	problem	NOUN
ijassa-1639	320	20	,	,	PUNCT
ijassa-1639	320	21	j.	j.	PROPN
ijassa-1639	320	22	optim	optim	PROPN
ijassa-1639	320	23	.	.	PUNCT
ijassa-1639	321	1	theory	theory	NOUN
ijassa-1639	321	2	appl	appl	PROPN
ijassa-1639	321	3	.	.	PROPN
ijassa-1639	321	4	,	,	PUNCT
ijassa-1639	321	5	144	144	NUM
ijassa-1639	321	6	,	,	PUNCT
ijassa-1639	321	7	511–531	511–531	NUM
ijassa-1639	321	8	.	.	PUNCT
ijassa-1639	322	1	28	28	NUM
ijassa-1639	322	2	.	.	PUNCT
ijassa-1639	323	1	kulkarni	kulkarni	PROPN
ijassa-1639	323	2	,	,	PUNCT
ijassa-1639	323	3	a.a	a.a	PROPN
ijassa-1639	323	4	.	.	PROPN
ijassa-1639	323	5	&	&	CCONJ
ijassa-1639	323	6	shanbhag	shanbhag	PROPN
ijassa-1639	323	7	,	,	PUNCT
ijassa-1639	323	8	u.v	u.v	PROPN
ijassa-1639	323	9	.	.	PROPN
ijassa-1639	323	10	(	(	PUNCT
ijassa-1639	323	11	2012	2012	NUM
ijassa-1639	323	12	)	)	PUNCT
ijassa-1639	323	13	revisiting	revisit	VERB
ijassa-1639	323	14	generalized	generalize	VERB
ijassa-1639	323	15	nash	nash	NOUN
ijassa-1639	323	16	games	game	NOUN
ijassa-1639	323	17	and	and	CCONJ
ijassa-1639	323	18	variational	variational	ADJ
ijassa-1639	323	19	inequalities	inequality	NOUN
ijassa-1639	323	20	,	,	PUNCT
ijassa-1639	323	21	j.	j.	PROPN
ijassa-1639	323	22	optim	optim	PROPN
ijassa-1639	323	23	.	.	PUNCT
ijassa-1639	323	24	theory	theory	NOUN
ijassa-1639	323	25	appl	appl	PROPN
ijassa-1639	323	26	.	.	PROPN
ijassa-1639	323	27	,	,	PUNCT
ijassa-1639	323	28	154	154	NUM
ijassa-1639	323	29	,	,	PUNCT
ijassa-1639	323	30	175–186	175–186	NUM
ijassa-1639	323	31	.	.	NOUN
ijassa-1639	323	32	29	29	NUM
ijassa-1639	323	33	.	.	PUNCT
ijassa-1639	324	1	nabetani	nabetani	PROPN
ijassa-1639	324	2	,	,	PUNCT
ijassa-1639	324	3	k.	k.	PROPN
ijassa-1639	324	4	,	,	PUNCT
ijassa-1639	324	5	tseng	tseng	PROPN
ijassa-1639	324	6	,	,	PUNCT
ijassa-1639	324	7	p.	p.	PROPN
ijassa-1639	324	8	&	&	CCONJ
ijassa-1639	324	9	fukushima	fukushima	PROPN
ijassa-1639	324	10	,	,	PUNCT
ijassa-1639	324	11	m.	m.	NOUN
ijassa-1639	324	12	(	(	PUNCT
ijassa-1639	324	13	2011	2011	NUM
ijassa-1639	324	14	)	)	PUNCT
ijassa-1639	324	15	parametrized	parametrized	ADJ
ijassa-1639	324	16	variational	variational	ADJ
ijassa-1639	324	17	inequality	inequality	NOUN
ijassa-1639	324	18	approaches	approach	NOUN
ijassa-1639	324	19	to	to	ADP
ijassa-1639	324	20	generalized	generalize	VERB
ijassa-1639	324	21	nash	nash	PROPN
ijassa-1639	324	22	equilibrium	equilibrium	NOUN
ijassa-1639	324	23	problems	problem	NOUN
ijassa-1639	324	24	with	with	ADP
ijassa-1639	324	25	shared	share	VERB
ijassa-1639	324	26	constraints	constraint	NOUN
ijassa-1639	324	27	,	,	PUNCT
ijassa-1639	324	28	comput	comput	NOUN
ijassa-1639	324	29	.	.	PUNCT
ijassa-1639	325	1	optim	optim	PROPN
ijassa-1639	325	2	.	.	PUNCT
ijassa-1639	326	1	appl	appl	PROPN
ijassa-1639	326	2	.	.	PROPN
ijassa-1639	326	3	,	,	PUNCT
ijassa-1639	326	4	48	48	NUM
ijassa-1639	326	5	,	,	PUNCT
ijassa-1639	326	6	423–452	423–452	NUM
ijassa-1639	326	7	.	.	PUNCT
ijassa-1639	326	8	30	30	NUM
ijassa-1639	326	9	.	.	PUNCT
ijassa-1639	327	1	rosen	rosen	PROPN
ijassa-1639	327	2	,	,	PUNCT
ijassa-1639	327	3	j.b	j.b	PROPN
ijassa-1639	327	4	.	.	PUNCT
ijassa-1639	327	5	(	(	PUNCT
ijassa-1639	327	6	1965	1965	NUM
ijassa-1639	327	7	)	)	PUNCT
ijassa-1639	327	8	existence	existence	NOUN
ijassa-1639	327	9	and	and	CCONJ
ijassa-1639	327	10	uniqueness	uniqueness	NOUN
ijassa-1639	327	11	of	of	ADP
ijassa-1639	327	12	equilibrium	equilibrium	NOUN
ijassa-1639	327	13	points	point	NOUN
ijassa-1639	327	14	for	for	ADP
ijassa-1639	327	15	concave	concave	ADJ
ijassa-1639	327	16	n	n	PRON
ijassa-1639	327	17	person	person	NOUN
ijassa-1639	327	18	games	game	NOUN
ijassa-1639	327	19	,	,	PUNCT
ijassa-1639	327	20	econometrica	econometrica	PROPN
ijassa-1639	327	21	,	,	PUNCT
ijassa-1639	327	22	33	33	NUM
ijassa-1639	327	23	,	,	PUNCT
ijassa-1639	327	24	52–534	52–534	NUM
ijassa-1639	327	25	.	.	PUNCT
ijassa-1639	328	1	copyright	copyright	NOUN
ijassa-1639	328	2	©	©	PROPN
ijassa-1639	328	3	2024	2024	NUM
ijassa-1639	328	4	assa	assa	NOUN
ijassa-1639	328	5	.	.	PUNCT
ijassa-1639	329	1	adv	adv	PROPN
ijassa-1639	329	2	syst	syst	PROPN
ijassa-1639	329	3	sci	sci	PROPN
ijassa-1639	329	4	appl	appl	PROPN
ijassa-1639	329	5	(	(	PUNCT
ijassa-1639	329	6	2024	2024	NUM
ijassa-1639	329	7	)	)	PUNCT
ijassa-1639	329	8	introduction	introduction	NOUN
ijassa-1639	329	9	generalized	generalize	VERB
ijassa-1639	329	10	nash	nash	PROPN
ijassa-1639	329	11	equilibrium	equilibrium	NOUN
ijassa-1639	329	12	problem	problem	NOUN
ijassa-1639	329	13	and	and	CCONJ
ijassa-1639	329	14	related	relate	VERB
ijassa-1639	329	15	constrained	constrain	VERB
ijassa-1639	329	16	equations	equation	NOUN
ijassa-1639	329	17	piecewise	piecewise	VERB
ijassa-1639	329	18	levenberg	levenberg	PROPN
ijassa-1639	329	19	–	–	PUNCT
ijassa-1639	329	20	marquardt	marquardt	PROPN
ijassa-1639	329	21	method	method	PROPN
ijassa-1639	329	22	numerical	numerical	ADJ
ijassa-1639	329	23	results	result	NOUN