id	sid	tid	token	lemma	pos
app01-6401	1	1	acta	acta	PROPN
app01-6401	1	2	polytechnica	polytechnica	PROPN
app01-6401	1	3	ctu	ctu	PROPN
app01-6401	1	4	proceedings	proceeding	NOUN
app01-6401	1	5	doi:10.14311	doi:10.14311	NOUN
app01-6401	1	6	/	/	PUNCT
app01-6401	1	7	app.2020.26.0117	app.2020.26.0117	SYM
app01-6401	1	8	acta	acta	PROPN
app01-6401	1	9	polytechnica	polytechnica	PROPN
app01-6401	1	10	ctu	ctu	NOUN
app01-6401	1	11	proceedings	proceeding	NOUN
app01-6401	1	12	26:117–125	26:117–125	NUM
app01-6401	1	13	,	,	PUNCT
app01-6401	1	14	2020	2020	NUM
app01-6401	1	15	©	©	PROPN
app01-6401	1	16	czech	czech	PROPN
app01-6401	1	17	technical	technical	PROPN
app01-6401	1	18	university	university	PROPN
app01-6401	1	19	in	in	ADP
app01-6401	1	20	prague	prague	PROPN
app01-6401	1	21	,	,	PUNCT
app01-6401	1	22	2020	2020	NUM
app01-6401	1	23	available	available	ADJ
app01-6401	1	24	online	online	ADV
app01-6401	1	25	at	at	ADP
app01-6401	1	26	https://ojs.cvut.cz/ojs/index.php/app	https://ojs.cvut.cz/ojs/index.php/app	NOUN
app01-6401	1	27	on	on	ADP
app01-6401	1	28	optimum	optimum	ADJ
app01-6401	1	29	design	design	NOUN
app01-6401	1	30	of	of	ADP
app01-6401	1	31	frame	frame	NOUN
app01-6401	1	32	structures	structure	NOUN
app01-6401	1	33	marek	marek	PROPN
app01-6401	1	34	tybureca,∗	tybureca,∗	PROPN
app01-6401	1	35	,	,	PUNCT
app01-6401	1	36	jan	jan	PROPN
app01-6401	1	37	zemana	zemana	PROPN
app01-6401	1	38	,	,	PUNCT
app01-6401	1	39	c	c	PROPN
app01-6401	1	40	,	,	PUNCT
app01-6401	1	41	martin	martin	PROPN
app01-6401	1	42	kružíkb	kružíkb	NOUN
app01-6401	1	43	,	,	PUNCT
app01-6401	1	44	c	c	X
app01-6401	1	45	,	,	PUNCT
app01-6401	1	46	didier	didier	PROPN
app01-6401	1	47	henriond	henriond	PROPN
app01-6401	1	48	,	,	PUNCT
app01-6401	1	49	e	e	PROPN
app01-6401	1	50	a	a	DET
app01-6401	1	51	czech	czech	PROPN
app01-6401	1	52	technical	technical	PROPN
app01-6401	1	53	university	university	PROPN
app01-6401	1	54	in	in	ADP
app01-6401	1	55	prague	prague	PROPN
app01-6401	1	56	,	,	PUNCT
app01-6401	1	57	faculty	faculty	NOUN
app01-6401	1	58	of	of	ADP
app01-6401	1	59	civil	civil	ADJ
app01-6401	1	60	engineering	engineering	NOUN
app01-6401	1	61	,	,	PUNCT
app01-6401	1	62	department	department	NOUN
app01-6401	1	63	of	of	ADP
app01-6401	1	64	mechanics	mechanic	NOUN
app01-6401	1	65	,	,	PUNCT
app01-6401	1	66	thákurova	thákurova	X
app01-6401	1	67	7	7	NUM
app01-6401	1	68	,	,	PUNCT
app01-6401	1	69	166	166	NUM
app01-6401	1	70	29	29	NUM
app01-6401	1	71	prague	prague	NOUN
app01-6401	1	72	6	6	NUM
app01-6401	1	73	,	,	PUNCT
app01-6401	1	74	czech	czech	PROPN
app01-6401	1	75	republic	republic	PROPN
app01-6401	1	76	b	b	PROPN
app01-6401	1	77	czech	czech	PROPN
app01-6401	1	78	technical	technical	PROPN
app01-6401	1	79	university	university	PROPN
app01-6401	1	80	in	in	ADP
app01-6401	1	81	prague	prague	PROPN
app01-6401	1	82	,	,	PUNCT
app01-6401	1	83	faculty	faculty	NOUN
app01-6401	1	84	of	of	ADP
app01-6401	1	85	civil	civil	ADJ
app01-6401	1	86	engineering	engineering	NOUN
app01-6401	1	87	,	,	PUNCT
app01-6401	1	88	departement	departement	NOUN
app01-6401	1	89	of	of	ADP
app01-6401	1	90	physics	physics	NOUN
app01-6401	1	91	,	,	PUNCT
app01-6401	1	92	thákurova	thákurova	PROPN
app01-6401	1	93	7	7	NUM
app01-6401	1	94	,	,	PUNCT
app01-6401	1	95	166	166	NUM
app01-6401	1	96	29	29	NUM
app01-6401	1	97	prague	prague	NOUN
app01-6401	1	98	6	6	NUM
app01-6401	1	99	,	,	PUNCT
app01-6401	1	100	czech	czech	PROPN
app01-6401	1	101	republic	republic	NOUN
app01-6401	1	102	c	c	PROPN
app01-6401	1	103	czech	czech	PROPN
app01-6401	1	104	academy	academy	PROPN
app01-6401	1	105	of	of	ADP
app01-6401	1	106	sciences	sciences	PROPN
app01-6401	1	107	,	,	PUNCT
app01-6401	1	108	institute	institute	NOUN
app01-6401	1	109	of	of	ADP
app01-6401	1	110	information	information	NOUN
app01-6401	1	111	theory	theory	NOUN
app01-6401	1	112	and	and	CCONJ
app01-6401	1	113	automation	automation	NOUN
app01-6401	1	114	,	,	PUNCT
app01-6401	1	115	department	department	NOUN
app01-6401	1	116	of	of	ADP
app01-6401	1	117	decision	decision	NOUN
app01-6401	1	118	-	-	PUNCT
app01-6401	1	119	making	make	VERB
app01-6401	1	120	theory	theory	NOUN
app01-6401	1	121	,	,	PUNCT
app01-6401	1	122	pod	pod	PROPN
app01-6401	1	123	vodárenskou	vodárenskou	PROPN
app01-6401	1	124	věží	věží	VERB
app01-6401	1	125	4	4	NUM
app01-6401	1	126	,	,	PUNCT
app01-6401	1	127	182	182	NUM
app01-6401	1	128	08	08	NUM
app01-6401	1	129	prague	prague	NOUN
app01-6401	1	130	8	8	NUM
app01-6401	1	131	,	,	PUNCT
app01-6401	1	132	czech	czech	PROPN
app01-6401	1	133	republic	republic	PROPN
app01-6401	2	1	d	d	PROPN
app01-6401	2	2	university	university	PROPN
app01-6401	2	3	of	of	ADP
app01-6401	2	4	toulouse	toulouse	NOUN
app01-6401	2	5	,	,	PUNCT
app01-6401	2	6	laas	laas	NOUN
app01-6401	2	7	-	-	PUNCT
app01-6401	2	8	cnrs	cnrs	NOUN
app01-6401	2	9	,	,	PUNCT
app01-6401	2	10	7	7	NUM
app01-6401	2	11	avenue	avenue	PROPN
app01-6401	2	12	du	du	PROPN
app01-6401	2	13	colonel	colonel	PROPN
app01-6401	2	14	roche	roche	PROPN
app01-6401	2	15	,	,	PUNCT
app01-6401	2	16	31400	31400	NUM
app01-6401	2	17	toulouse	toulouse	NOUN
app01-6401	2	18	,	,	PUNCT
app01-6401	2	19	france	france	PROPN
app01-6401	2	20	e	e	PROPN
app01-6401	2	21	czech	czech	PROPN
app01-6401	2	22	technical	technical	PROPN
app01-6401	2	23	university	university	PROPN
app01-6401	2	24	in	in	ADP
app01-6401	2	25	prague	prague	PROPN
app01-6401	2	26	,	,	PUNCT
app01-6401	2	27	faculty	faculty	NOUN
app01-6401	2	28	of	of	ADP
app01-6401	2	29	electrical	electrical	ADJ
app01-6401	2	30	engineering	engineering	NOUN
app01-6401	2	31	,	,	PUNCT
app01-6401	2	32	department	department	NOUN
app01-6401	2	33	of	of	ADP
app01-6401	2	34	control	control	PROPN
app01-6401	2	35	engineering	engineering	PROPN
app01-6401	2	36	,	,	PUNCT
app01-6401	2	37	karlovo	karlovo	PROPN
app01-6401	2	38	náměstí	náměstí	NOUN
app01-6401	2	39	13	13	NUM
app01-6401	2	40	,	,	PUNCT
app01-6401	2	41	121	121	NUM
app01-6401	2	42	35	35	NUM
app01-6401	2	43	prague	prague	NOUN
app01-6401	2	44	2	2	NUM
app01-6401	2	45	,	,	PUNCT
app01-6401	2	46	czech	czech	PROPN
app01-6401	2	47	republic	republic	NOUN
app01-6401	2	48	∗	∗	NOUN
app01-6401	2	49	corresponding	correspond	VERB
app01-6401	2	50	author	author	NOUN
app01-6401	2	51	:	:	PUNCT
app01-6401	2	52	marek.tyburec@fsv.cvut.cz	marek.tyburec@fsv.cvut.cz	NUM
app01-6401	2	53	abstract	abstract	NOUN
app01-6401	2	54	.	.	PUNCT
app01-6401	3	1	optimization	optimization	NOUN
app01-6401	3	2	of	of	ADP
app01-6401	3	3	frame	frame	NOUN
app01-6401	3	4	structures	structure	NOUN
app01-6401	3	5	is	be	AUX
app01-6401	3	6	formulated	formulate	VERB
app01-6401	3	7	as	as	ADP
app01-6401	3	8	a	a	DET
app01-6401	3	9	non	non	ADJ
app01-6401	3	10	-	-	ADJ
app01-6401	3	11	convex	convex	ADJ
app01-6401	3	12	optimization	optimization	NOUN
app01-6401	3	13	problem	problem	NOUN
app01-6401	3	14	,	,	PUNCT
app01-6401	3	15	which	which	PRON
app01-6401	3	16	is	be	AUX
app01-6401	3	17	currently	currently	ADV
app01-6401	3	18	solved	solve	VERB
app01-6401	3	19	to	to	ADP
app01-6401	3	20	local	local	ADJ
app01-6401	3	21	optimality	optimality	NOUN
app01-6401	3	22	.	.	PUNCT
app01-6401	4	1	in	in	ADP
app01-6401	4	2	this	this	DET
app01-6401	4	3	contribution	contribution	NOUN
app01-6401	4	4	,	,	PUNCT
app01-6401	4	5	we	we	PRON
app01-6401	4	6	investigate	investigate	VERB
app01-6401	4	7	four	four	NUM
app01-6401	4	8	optimization	optimization	NOUN
app01-6401	4	9	approaches	approach	NOUN
app01-6401	4	10	:	:	PUNCT
app01-6401	4	11	(	(	PUNCT
app01-6401	4	12	i	i	NOUN
app01-6401	4	13	)	)	PUNCT
app01-6401	4	14	general	general	ADJ
app01-6401	4	15	non	non	ADJ
app01-6401	4	16	-	-	ADJ
app01-6401	4	17	linear	linear	ADJ
app01-6401	4	18	optimization	optimization	NOUN
app01-6401	4	19	,	,	PUNCT
app01-6401	4	20	(	(	PUNCT
app01-6401	4	21	ii	ii	NOUN
app01-6401	4	22	)	)	PUNCT
app01-6401	4	23	optimality	optimality	NOUN
app01-6401	4	24	criteria	criterion	NOUN
app01-6401	4	25	method	method	NOUN
app01-6401	4	26	,	,	PUNCT
app01-6401	4	27	(	(	PUNCT
app01-6401	4	28	iii	iii	X
app01-6401	4	29	)	)	PUNCT
app01-6401	4	30	non	non	ADJ
app01-6401	4	31	-	-	ADJ
app01-6401	4	32	linear	linear	ADJ
app01-6401	4	33	semidefinite	semidefinite	NOUN
app01-6401	4	34	programming	programming	NOUN
app01-6401	4	35	,	,	PUNCT
app01-6401	4	36	and	and	CCONJ
app01-6401	4	37	(	(	PUNCT
app01-6401	4	38	iv	iv	X
app01-6401	4	39	)	)	PUNCT
app01-6401	4	40	polynomial	polynomial	ADJ
app01-6401	4	41	optimization	optimization	NOUN
app01-6401	4	42	.	.	PUNCT
app01-6401	5	1	we	we	PRON
app01-6401	5	2	show	show	VERB
app01-6401	5	3	that	that	SCONJ
app01-6401	5	4	polynomial	polynomial	ADJ
app01-6401	5	5	optimization	optimization	NOUN
app01-6401	5	6	solves	solve	VERB
app01-6401	5	7	the	the	DET
app01-6401	5	8	frame	frame	NOUN
app01-6401	5	9	structure	structure	NOUN
app01-6401	5	10	optimization	optimization	NOUN
app01-6401	5	11	to	to	ADP
app01-6401	5	12	global	global	ADJ
app01-6401	5	13	optimality	optimality	NOUN
app01-6401	5	14	by	by	ADP
app01-6401	5	15	building	build	VERB
app01-6401	5	16	the	the	DET
app01-6401	5	17	(	(	PUNCT
app01-6401	5	18	moment	moment	NOUN
app01-6401	5	19	-	-	PUNCT
app01-6401	5	20	sums	sum	NOUN
app01-6401	5	21	-	-	PUNCT
app01-6401	5	22	of	of	ADP
app01-6401	5	23	-	-	PUNCT
app01-6401	5	24	squares	square	NOUN
app01-6401	5	25	)	)	PUNCT
app01-6401	5	26	hierarchy	hierarchy	NOUN
app01-6401	5	27	of	of	ADP
app01-6401	5	28	convex	convex	ADJ
app01-6401	5	29	linear	linear	ADJ
app01-6401	5	30	semidefinite	semidefinite	NOUN
app01-6401	5	31	programming	programming	NOUN
app01-6401	5	32	problems	problem	NOUN
app01-6401	5	33	,	,	PUNCT
app01-6401	5	34	and	and	CCONJ
app01-6401	5	35	it	it	PRON
app01-6401	5	36	also	also	ADV
app01-6401	5	37	provides	provide	VERB
app01-6401	5	38	guaranteed	guarantee	VERB
app01-6401	5	39	lower	low	ADJ
app01-6401	5	40	and	and	CCONJ
app01-6401	5	41	upper	upper	ADJ
app01-6401	5	42	bounds	bound	NOUN
app01-6401	5	43	on	on	ADP
app01-6401	5	44	optimal	optimal	ADJ
app01-6401	5	45	design	design	NOUN
app01-6401	5	46	.	.	PUNCT
app01-6401	6	1	finally	finally	ADV
app01-6401	6	2	,	,	PUNCT
app01-6401	6	3	we	we	PRON
app01-6401	6	4	solve	solve	VERB
app01-6401	6	5	three	three	NUM
app01-6401	6	6	sample	sample	NOUN
app01-6401	6	7	optimization	optimization	NOUN
app01-6401	6	8	problems	problem	NOUN
app01-6401	6	9	and	and	CCONJ
app01-6401	6	10	conclude	conclude	VERB
app01-6401	6	11	that	that	SCONJ
app01-6401	6	12	the	the	DET
app01-6401	6	13	local	local	ADJ
app01-6401	6	14	optimization	optimization	NOUN
app01-6401	6	15	approaches	approach	NOUN
app01-6401	6	16	may	may	AUX
app01-6401	6	17	indeed	indeed	ADV
app01-6401	6	18	converge	converge	VERB
app01-6401	6	19	to	to	ADP
app01-6401	6	20	local	local	ADJ
app01-6401	6	21	optima	optima	NOUN
app01-6401	6	22	,	,	PUNCT
app01-6401	6	23	without	without	ADP
app01-6401	6	24	any	any	DET
app01-6401	6	25	solution	solution	NOUN
app01-6401	6	26	quality	quality	NOUN
app01-6401	6	27	measure	measure	NOUN
app01-6401	6	28	,	,	PUNCT
app01-6401	6	29	or	or	CCONJ
app01-6401	6	30	even	even	ADV
app01-6401	6	31	to	to	PART
app01-6401	6	32	infeasible	infeasible	VERB
app01-6401	6	33	points	point	NOUN
app01-6401	6	34	.	.	PUNCT
app01-6401	7	1	these	these	DET
app01-6401	7	2	issues	issue	NOUN
app01-6401	7	3	are	be	AUX
app01-6401	7	4	readily	readily	ADV
app01-6401	7	5	overcome	overcome	VERB
app01-6401	7	6	by	by	ADP
app01-6401	7	7	using	use	VERB
app01-6401	7	8	polynomial	polynomial	ADJ
app01-6401	7	9	optimization	optimization	NOUN
app01-6401	7	10	,	,	PUNCT
app01-6401	7	11	which	which	PRON
app01-6401	7	12	exhibits	exhibit	VERB
app01-6401	7	13	a	a	DET
app01-6401	7	14	finite	finite	ADJ
app01-6401	7	15	convergence	convergence	NOUN
app01-6401	7	16	,	,	PUNCT
app01-6401	7	17	at	at	ADP
app01-6401	7	18	the	the	DET
app01-6401	7	19	prize	prize	NOUN
app01-6401	7	20	of	of	ADP
app01-6401	7	21	higher	high	ADJ
app01-6401	7	22	computational	computational	ADJ
app01-6401	7	23	demands	demand	NOUN
app01-6401	7	24	.	.	PUNCT
app01-6401	8	1	keywords	keyword	NOUN
app01-6401	8	2	:	:	PUNCT
app01-6401	8	3	frame	frame	NOUN
app01-6401	8	4	structures	structure	NOUN
app01-6401	8	5	,	,	PUNCT
app01-6401	8	6	global	global	ADJ
app01-6401	8	7	optimum	optimum	NOUN
app01-6401	8	8	,	,	PUNCT
app01-6401	8	9	polynomial	polynomial	ADJ
app01-6401	8	10	optimization	optimization	NOUN
app01-6401	8	11	,	,	PUNCT
app01-6401	8	12	semidefinite	semidefinite	PROPN
app01-6401	8	13	programming	programming	PROPN
app01-6401	8	14	,	,	PUNCT
app01-6401	8	15	topology	topology	NOUN
app01-6401	8	16	optimization	optimization	NOUN
app01-6401	8	17	.	.	PUNCT
app01-6401	9	1	1	1	X
app01-6401	9	2	.	.	X
app01-6401	9	3	introduction	introduction	NOUN
app01-6401	9	4	designing	design	VERB
app01-6401	9	5	economical	economical	ADJ
app01-6401	9	6	,	,	PUNCT
app01-6401	9	7	efficient	efficient	ADJ
app01-6401	9	8	,	,	PUNCT
app01-6401	9	9	and	and	CCONJ
app01-6401	9	10	sustainable	sustainable	ADJ
app01-6401	9	11	structures	structure	NOUN
app01-6401	9	12	represents	represent	VERB
app01-6401	9	13	a	a	DET
app01-6401	9	14	major	major	ADJ
app01-6401	9	15	challenge	challenge	NOUN
app01-6401	9	16	of	of	ADP
app01-6401	9	17	the	the	DET
app01-6401	9	18	contemporary	contemporary	ADJ
app01-6401	9	19	society	society	NOUN
app01-6401	9	20	.	.	PUNCT
app01-6401	10	1	while	while	SCONJ
app01-6401	10	2	structural	structural	ADJ
app01-6401	10	3	engineers	engineer	NOUN
app01-6401	10	4	literally	literally	ADV
app01-6401	10	5	explore	explore	VERB
app01-6401	10	6	designs	design	NOUN
app01-6401	10	7	that	that	PRON
app01-6401	10	8	must	must	AUX
app01-6401	10	9	satisfy	satisfy	VERB
app01-6401	10	10	the	the	DET
app01-6401	10	11	requirements	requirement	NOUN
app01-6401	10	12	of	of	ADP
app01-6401	10	13	limit	limit	NOUN
app01-6401	10	14	states	state	VERB
app01-6401	10	15	analysis	analysis	NOUN
app01-6401	10	16	,	,	PUNCT
app01-6401	10	17	there	there	PRON
app01-6401	10	18	is	be	VERB
app01-6401	10	19	usually	usually	ADV
app01-6401	10	20	an	an	DET
app01-6401	10	21	infinite	infinite	ADJ
app01-6401	10	22	number	number	NOUN
app01-6401	10	23	of	of	ADP
app01-6401	10	24	such	such	ADJ
app01-6401	10	25	designs	design	NOUN
app01-6401	10	26	.	.	PUNCT
app01-6401	11	1	regardless	regardless	ADV
app01-6401	11	2	of	of	ADP
app01-6401	11	3	the	the	DET
app01-6401	11	4	properties	property	NOUN
app01-6401	11	5	of	of	ADP
app01-6401	11	6	this	this	DET
app01-6401	11	7	feasible	feasible	ADJ
app01-6401	11	8	design	design	NOUN
app01-6401	11	9	space	space	NOUN
app01-6401	11	10	,	,	PUNCT
app01-6401	11	11	it	it	PRON
app01-6401	11	12	is	be	AUX
app01-6401	11	13	required	require	VERB
app01-6401	11	14	to	to	PART
app01-6401	11	15	select	select	VERB
app01-6401	11	16	only	only	ADV
app01-6401	11	17	one	one	NUM
app01-6401	11	18	,	,	PUNCT
app01-6401	11	19	the	the	DET
app01-6401	11	20	best	good	ADJ
app01-6401	11	21	design	design	NOUN
app01-6401	11	22	.	.	PUNCT
app01-6401	12	1	this	this	DET
app01-6401	12	2	design	design	NOUN
app01-6401	12	3	quality	quality	NOUN
app01-6401	12	4	is	be	AUX
app01-6401	12	5	measured	measure	VERB
app01-6401	12	6	by	by	ADP
app01-6401	12	7	an	an	DET
app01-6401	12	8	objective	objective	ADJ
app01-6401	12	9	function	function	NOUN
app01-6401	12	10	,	,	PUNCT
app01-6401	12	11	which	which	PRON
app01-6401	12	12	usually	usually	ADV
app01-6401	12	13	approximates	approximate	VERB
app01-6401	12	14	the	the	DET
app01-6401	12	15	expenses	expense	NOUN
app01-6401	12	16	of	of	ADP
app01-6401	12	17	production	production	NOUN
app01-6401	12	18	.	.	PUNCT
app01-6401	13	1	greatly	greatly	ADV
app01-6401	13	2	simplified	simplified	ADJ
app01-6401	13	3	,	,	PUNCT
app01-6401	13	4	one	one	NUM
app01-6401	13	5	such	such	ADJ
app01-6401	13	6	(	(	PUNCT
app01-6401	13	7	most	most	ADV
app01-6401	13	8	common	common	ADJ
app01-6401	13	9	)	)	PUNCT
app01-6401	13	10	criterion	criterion	NOUN
app01-6401	13	11	considers	consider	VERB
app01-6401	13	12	maximization	maximization	NOUN
app01-6401	13	13	of	of	ADP
app01-6401	13	14	structural	structural	ADJ
app01-6401	13	15	stiffness	stiffness	NOUN
app01-6401	13	16	(	(	PUNCT
app01-6401	13	17	while	while	SCONJ
app01-6401	13	18	the	the	DET
app01-6401	13	19	amount	amount	NOUN
app01-6401	13	20	of	of	ADP
app01-6401	13	21	available	available	ADJ
app01-6401	13	22	material	material	NOUN
app01-6401	13	23	is	be	AUX
app01-6401	13	24	limited	limited	ADJ
app01-6401	13	25	)	)	PUNCT
app01-6401	13	26	,	,	PUNCT
app01-6401	13	27	or	or	CCONJ
app01-6401	13	28	,	,	PUNCT
app01-6401	13	29	equivalently	equivalently	ADV
app01-6401	13	30	,	,	PUNCT
app01-6401	13	31	minimization	minimization	NOUN
app01-6401	13	32	of	of	ADP
app01-6401	13	33	structural	structural	ADJ
app01-6401	13	34	volume	volume	NOUN
app01-6401	13	35	(	(	PUNCT
app01-6401	13	36	while	while	SCONJ
app01-6401	13	37	requiring	require	VERB
app01-6401	13	38	a	a	DET
app01-6401	13	39	certain	certain	ADJ
app01-6401	13	40	structural	structural	ADJ
app01-6401	13	41	stiffness	stiffness	NOUN
app01-6401	13	42	)	)	PUNCT
app01-6401	14	1	[	[	X
app01-6401	14	2	1	1	NUM
app01-6401	14	3	]	]	PUNCT
app01-6401	14	4	.	.	PUNCT
app01-6401	15	1	among	among	ADP
app01-6401	15	2	the	the	DET
app01-6401	15	3	structural	structural	ADJ
app01-6401	15	4	optimization	optimization	NOUN
app01-6401	15	5	problems	problem	VERB
app01-6401	15	6	the	the	DET
app01-6401	15	7	greatest	great	ADJ
app01-6401	15	8	progress	progress	NOUN
app01-6401	15	9	has	have	AUX
app01-6401	15	10	been	be	AUX
app01-6401	15	11	achieved	achieve	VERB
app01-6401	15	12	so	so	ADV
app01-6401	15	13	-	-	PUNCT
app01-6401	15	14	far	far	ADV
app01-6401	15	15	in	in	ADP
app01-6401	15	16	optimizing	optimize	VERB
app01-6401	15	17	(	(	PUNCT
app01-6401	15	18	the	the	DET
app01-6401	15	19	cross	cross	ADJ
app01-6401	15	20	-	-	ADJ
app01-6401	15	21	sectional	sectional	ADJ
app01-6401	15	22	areas	area	NOUN
app01-6401	15	23	of	of	ADP
app01-6401	15	24	)	)	PUNCT
app01-6401	15	25	truss	truss	NOUN
app01-6401	15	26	structures	structure	NOUN
app01-6401	15	27	[	[	X
app01-6401	15	28	2	2	NUM
app01-6401	15	29	]	]	PUNCT
app01-6401	15	30	.	.	PUNCT
app01-6401	16	1	this	this	DET
app01-6401	16	2	development	development	NOUN
app01-6401	16	3	can	can	AUX
app01-6401	16	4	be	be	AUX
app01-6401	16	5	attributed	attribute	VERB
app01-6401	16	6	to	to	ADP
app01-6401	16	7	convexity	convexity	NOUN
app01-6401	16	8	of	of	ADP
app01-6401	16	9	the	the	DET
app01-6401	16	10	feasible	feasible	ADJ
app01-6401	16	11	design	design	NOUN
app01-6401	16	12	space	space	NOUN
app01-6401	16	13	[	[	X
app01-6401	16	14	3	3	NUM
app01-6401	16	15	,	,	PUNCT
app01-6401	16	16	sections	section	NOUN
app01-6401	16	17	1.3.5	1.3.5	NUM
app01-6401	16	18	,	,	PUNCT
app01-6401	16	19	3.4.3	3.4.3	NUM
app01-6401	16	20	,	,	PUNCT
app01-6401	16	21	and	and	CCONJ
app01-6401	16	22	4.8	4.8	NUM
app01-6401	16	23	]	]	PUNCT
app01-6401	16	24	,	,	PUNCT
app01-6401	16	25	as	as	SCONJ
app01-6401	16	26	the	the	DET
app01-6401	16	27	(	(	PUNCT
app01-6401	16	28	axial	axial	ADJ
app01-6401	16	29	)	)	PUNCT
app01-6401	16	30	structural	structural	ADJ
app01-6401	16	31	stiffness	stiffness	NOUN
app01-6401	16	32	is	be	AUX
app01-6401	16	33	an	an	DET
app01-6401	16	34	affine	affine	ADJ
app01-6401	16	35	function	function	NOUN
app01-6401	16	36	of	of	ADP
app01-6401	16	37	the	the	DET
app01-6401	16	38	cross	cross	ADJ
app01-6401	16	39	-	-	ADJ
app01-6401	16	40	sectional	sectional	ADJ
app01-6401	16	41	areas	area	NOUN
app01-6401	16	42	.	.	PUNCT
app01-6401	17	1	on	on	ADP
app01-6401	17	2	the	the	DET
app01-6401	17	3	other	other	ADJ
app01-6401	17	4	hand	hand	NOUN
app01-6401	17	5	,	,	PUNCT
app01-6401	17	6	when	when	SCONJ
app01-6401	17	7	the	the	DET
app01-6401	17	8	bending	bend	VERB
app01-6401	17	9	stiffness	stiffness	NOUN
app01-6401	17	10	comes	come	VERB
app01-6401	17	11	into	into	ADP
app01-6401	17	12	a	a	DET
app01-6401	17	13	consideration	consideration	NOUN
app01-6401	17	14	,	,	PUNCT
app01-6401	17	15	convexity	convexity	NOUN
app01-6401	17	16	does	do	AUX
app01-6401	17	17	not	not	PART
app01-6401	17	18	hold	hold	VERB
app01-6401	17	19	in	in	ADP
app01-6401	17	20	general	general	ADJ
app01-6401	17	21	.	.	PUNCT
app01-6401	18	1	quite	quite	ADV
app01-6401	18	2	surprisingly	surprisingly	ADV
app01-6401	18	3	,	,	PUNCT
app01-6401	18	4	these	these	DET
app01-6401	18	5	problems	problem	NOUN
app01-6401	18	6	are	be	AUX
app01-6401	18	7	also	also	ADV
app01-6401	18	8	much	much	ADV
app01-6401	18	9	less	less	ADV
app01-6401	18	10	studied	study	VERB
app01-6401	18	11	,	,	PUNCT
app01-6401	18	12	and	and	CCONJ
app01-6401	18	13	to	to	ADP
app01-6401	18	14	our	our	PRON
app01-6401	18	15	knowledge	knowledge	NOUN
app01-6401	18	16	only	only	ADV
app01-6401	18	17	local	local	ADJ
app01-6401	18	18	optimization	optimization	NOUN
app01-6401	18	19	algorithms	algorithm	NOUN
app01-6401	18	20	have	have	AUX
app01-6401	18	21	yet	yet	ADV
app01-6401	18	22	been	be	AUX
app01-6401	18	23	developed	develop	VERB
app01-6401	18	24	[	[	PUNCT
app01-6401	18	25	4	4	NUM
app01-6401	18	26	,	,	PUNCT
app01-6401	18	27	5	5	NUM
app01-6401	18	28	]	]	PUNCT
app01-6401	18	29	.	.	PUNCT
app01-6401	19	1	in	in	ADP
app01-6401	19	2	this	this	DET
app01-6401	19	3	contribution	contribution	NOUN
app01-6401	19	4	,	,	PUNCT
app01-6401	19	5	we	we	PRON
app01-6401	19	6	investigate	investigate	VERB
app01-6401	19	7	the	the	DET
app01-6401	19	8	problem	problem	NOUN
app01-6401	19	9	of	of	ADP
app01-6401	19	10	optimum	optimum	ADJ
app01-6401	19	11	design	design	NOUN
app01-6401	19	12	of	of	ADP
app01-6401	19	13	frame	frame	NOUN
app01-6401	19	14	structures	structure	NOUN
app01-6401	19	15	.	.	PUNCT
app01-6401	20	1	in	in	ADP
app01-6401	20	2	particular	particular	ADJ
app01-6401	20	3	,	,	PUNCT
app01-6401	20	4	we	we	PRON
app01-6401	20	5	develop	develop	VERB
app01-6401	20	6	four	four	NUM
app01-6401	20	7	different	different	ADJ
app01-6401	20	8	methods	method	NOUN
app01-6401	20	9	in	in	ADP
app01-6401	20	10	section	section	NOUN
app01-6401	20	11	2	2	NUM
app01-6401	20	12	:	:	PUNCT
app01-6401	20	13	(	(	PUNCT
app01-6401	20	14	i	i	NOUN
app01-6401	20	15	)	)	PUNCT
app01-6401	20	16	general	general	ADJ
app01-6401	20	17	non	non	ADJ
app01-6401	20	18	-	-	ADJ
app01-6401	20	19	linear	linear	ADJ
app01-6401	20	20	optimization	optimization	NOUN
app01-6401	20	21	solved	solve	VERB
app01-6401	20	22	by	by	ADP
app01-6401	20	23	the	the	DET
app01-6401	20	24	interior	interior	ADJ
app01-6401	20	25	-	-	PUNCT
app01-6401	20	26	point	point	NOUN
app01-6401	20	27	method	method	NOUN
app01-6401	20	28	of	of	ADP
app01-6401	20	29	fmincon	fmincon	NOUN
app01-6401	20	30	,	,	PUNCT
app01-6401	20	31	(	(	PUNCT
app01-6401	20	32	ii	ii	NOUN
app01-6401	20	33	)	)	PUNCT
app01-6401	20	34	the	the	DET
app01-6401	20	35	first	first	ADJ
app01-6401	20	36	-	-	PUNCT
app01-6401	20	37	order	order	NOUN
app01-6401	20	38	optimality	optimality	NOUN
app01-6401	20	39	criteria	criterion	NOUN
app01-6401	20	40	(	(	PUNCT
app01-6401	20	41	oc	oc	NOUN
app01-6401	20	42	)	)	PUNCT
app01-6401	20	43	method	method	NOUN
app01-6401	20	44	[	[	X
app01-6401	20	45	1	1	NUM
app01-6401	20	46	,	,	PUNCT
app01-6401	20	47	5	5	NUM
app01-6401	20	48	]	]	PUNCT
app01-6401	20	49	,	,	PUNCT
app01-6401	20	50	(	(	PUNCT
app01-6401	20	51	iii	iii	X
app01-6401	20	52	)	)	PUNCT
app01-6401	20	53	reformulation	reformulation	NOUN
app01-6401	20	54	of	of	ADP
app01-6401	20	55	the	the	DET
app01-6401	20	56	problem	problem	NOUN
app01-6401	20	57	into	into	ADP
app01-6401	20	58	a	a	DET
app01-6401	20	59	non	non	ADJ
app01-6401	20	60	-	-	ADJ
app01-6401	20	61	linear	linear	ADJ
app01-6401	20	62	semidefinite	semidefinite	NOUN
app01-6401	20	63	program	program	PROPN
app01-6401	20	64	(	(	PUNCT
app01-6401	20	65	nsdp	nsdp	NOUN
app01-6401	20	66	)	)	PUNCT
app01-6401	20	67	solved	solve	VERB
app01-6401	20	68	by	by	ADP
app01-6401	20	69	penlab	penlab	NOUN
app01-6401	20	70	[	[	X
app01-6401	20	71	6	6	NUM
app01-6401	20	72	]	]	PUNCT
app01-6401	20	73	,	,	PUNCT
app01-6401	20	74	and	and	CCONJ
app01-6401	20	75	(	(	PUNCT
app01-6401	20	76	iv	iv	X
app01-6401	20	77	)	)	PUNCT
app01-6401	20	78	a	a	DET
app01-6401	20	79	suitably	suitably	ADV
app01-6401	20	80	modified	modify	VERB
app01-6401	20	81	polynomial	polynomial	ADJ
app01-6401	20	82	optmization	optmization	NOUN
app01-6401	20	83	(	(	PUNCT
app01-6401	20	84	po	po	NOUN
app01-6401	20	85	)	)	PUNCT
app01-6401	20	86	problem	problem	NOUN
app01-6401	20	87	(	(	PUNCT
app01-6401	20	88	iii	iii	NOUN
app01-6401	20	89	)	)	PUNCT
app01-6401	20	90	solved	solve	VERB
app01-6401	20	91	globally	globally	ADV
app01-6401	20	92	using	use	VERB
app01-6401	20	93	polynomial	polynomial	ADJ
app01-6401	20	94	optimization	optimization	NOUN
app01-6401	20	95	methods	method	NOUN
app01-6401	20	96	[	[	X
app01-6401	20	97	7	7	X
app01-6401	20	98	]	]	PUNCT
app01-6401	20	99	and	and	CCONJ
app01-6401	20	100	the	the	DET
app01-6401	20	101	mosek	mosek	NOUN
app01-6401	21	1	[	[	X
app01-6401	21	2	8	8	NUM
app01-6401	21	3	]	]	PUNCT
app01-6401	21	4	optimizer	optimizer	NOUN
app01-6401	21	5	.	.	PUNCT
app01-6401	22	1	we	we	PRON
app01-6401	22	2	show	show	VERB
app01-6401	22	3	that	that	SCONJ
app01-6401	22	4	the	the	DET
app01-6401	22	5	latter	latter	ADJ
app01-6401	22	6	po	po	NOUN
app01-6401	22	7	approach	approach	NOUN
app01-6401	22	8	generates	generate	VERB
app01-6401	22	9	guaranteed	guarantee	VERB
app01-6401	22	10	lower	low	ADJ
app01-6401	22	11	and	and	CCONJ
app01-6401	22	12	upper	upper	ADJ
app01-6401	22	13	bounds	bound	NOUN
app01-6401	22	14	on	on	ADP
app01-6401	22	15	the	the	DET
app01-6401	22	16	solution	solution	NOUN
app01-6401	22	17	,	,	PUNCT
app01-6401	22	18	providing	provide	VERB
app01-6401	22	19	a	a	DET
app01-6401	22	20	means	means	NOUN
app01-6401	22	21	of	of	ADP
app01-6401	22	22	assessing	assess	VERB
app01-6401	22	23	the	the	DET
app01-6401	22	24	design	design	NOUN
app01-6401	22	25	quality	quality	NOUN
app01-6401	22	26	.	.	PUNCT
app01-6401	23	1	finally	finally	ADV
app01-6401	23	2	,	,	PUNCT
app01-6401	23	3	section	section	NOUN
app01-6401	23	4	3	3	NUM
app01-6401	23	5	introduces	introduce	VERB
app01-6401	23	6	a	a	DET
app01-6401	23	7	set	set	NOUN
app01-6401	23	8	of	of	ADP
app01-6401	23	9	three	three	NUM
app01-6401	23	10	sample	sample	NOUN
app01-6401	23	11	optimization	optimization	NOUN
app01-6401	23	12	problems	problem	NOUN
app01-6401	23	13	to	to	PART
app01-6401	23	14	compare	compare	VERB
app01-6401	23	15	the	the	DET
app01-6401	23	16	optimization	optimization	NOUN
app01-6401	23	17	approaches	approach	NOUN
app01-6401	23	18	.	.	PUNCT
app01-6401	24	1	2	2	X
app01-6401	24	2	.	.	X
app01-6401	24	3	solution	solution	NOUN
app01-6401	24	4	techniques	technique	NOUN
app01-6401	24	5	to	to	PART
app01-6401	24	6	frame	frame	VERB
app01-6401	24	7	optimization	optimization	NOUN
app01-6401	24	8	2.1	2.1	NUM
app01-6401	24	9	.	.	PUNCT
app01-6401	25	1	problem	problem	NOUN
app01-6401	25	2	statement	statement	NOUN
app01-6401	25	3	let	let	VERB
app01-6401	25	4	us	we	PRON
app01-6401	25	5	consider	consider	VERB
app01-6401	25	6	the	the	DET
app01-6401	25	7	problem	problem	NOUN
app01-6401	25	8	of	of	ADP
app01-6401	25	9	optimum	optimum	ADJ
app01-6401	25	10	design	design	NOUN
app01-6401	25	11	of	of	ADP
app01-6401	25	12	frame	frame	NOUN
app01-6401	25	13	structures	structure	NOUN
app01-6401	25	14	composed	compose	VERB
app01-6401	25	15	a	a	DET
app01-6401	25	16	finite	finite	ADJ
app01-6401	25	17	number	number	NOUN
app01-6401	25	18	of	of	ADP
app01-6401	25	19	nodes	node	NOUN
app01-6401	25	20	,	,	PUNCT
app01-6401	25	21	nn	nn	NOUN
app01-6401	25	22	,	,	PUNCT
app01-6401	25	23	and	and	CCONJ
app01-6401	25	24	of	of	ADP
app01-6401	25	25	admissible	admissible	ADJ
app01-6401	25	26	elements	element	NOUN
app01-6401	25	27	,	,	PUNCT
app01-6401	25	28	ne	ne	PROPN
app01-6401	25	29	,	,	PUNCT
app01-6401	25	30	defining	define	VERB
app01-6401	25	31	the	the	DET
app01-6401	25	32	socalled	socalled	ADJ
app01-6401	25	33	ground	ground	NOUN
app01-6401	25	34	structure	structure	NOUN
app01-6401	25	35	[	[	X
app01-6401	25	36	2	2	NUM
app01-6401	25	37	]	]	PUNCT
app01-6401	25	38	.	.	PUNCT
app01-6401	26	1	the	the	DET
app01-6401	26	2	frame	frame	NOUN
app01-6401	26	3	elements	element	NOUN
app01-6401	26	4	are	be	AUX
app01-6401	26	5	attributed	attribute	VERB
app01-6401	26	6	with	with	ADP
app01-6401	26	7	non	non	ADJ
app01-6401	26	8	-	-	ADJ
app01-6401	26	9	negative	negative	ADJ
app01-6401	26	10	,	,	PUNCT
app01-6401	26	11	and	and	CCONJ
app01-6401	26	12	thus	thus	ADV
app01-6401	26	13	possibly	possibly	ADV
app01-6401	26	14	zero	zero	NUM
app01-6401	26	15	,	,	PUNCT
app01-6401	26	16	given	give	VERB
app01-6401	26	17	-	-	PUNCT
app01-6401	26	18	shaped	shape	VERB
app01-6401	26	19	cross	cross	ADJ
app01-6401	26	20	-	-	ADJ
app01-6401	26	21	sectional	sectional	ADJ
app01-6401	26	22	areas	area	NOUN
app01-6401	26	23	a.	a.	VERB
app01-6401	26	24	for	for	ADP
app01-6401	26	25	simplicity	simplicity	NOUN
app01-6401	26	26	,	,	PUNCT
app01-6401	26	27	117	117	NUM
app01-6401	26	28	https://doi.org/10.14311/app.2020.26.0117	https://doi.org/10.14311/app.2020.26.0117	PROPN
app01-6401	26	29	https://ojs.cvut.cz/ojs/index.php/app	https://ojs.cvut.cz/ojs/index.php/app	PROPN
app01-6401	26	30	m.	m.	NOUN
app01-6401	26	31	tyburec	tyburec	NOUN
app01-6401	26	32	,	,	PUNCT
app01-6401	26	33	j.	j.	PROPN
app01-6401	26	34	zeman	zeman	PROPN
app01-6401	26	35	,	,	PUNCT
app01-6401	26	36	m.	m.	NOUN
app01-6401	26	37	kružík	kružík	PROPN
app01-6401	26	38	,	,	PUNCT
app01-6401	26	39	d.	d.	PROPN
app01-6401	26	40	henrion	henrion	PROPN
app01-6401	26	41	acta	acta	PROPN
app01-6401	26	42	polytechnica	polytechnica	PROPN
app01-6401	26	43	ctu	ctu	PROPN
app01-6401	26	44	proceedings	proceeding	NOUN
app01-6401	26	45	ki(ai	ki(ai	PROPN
app01-6401	26	46	)	)	PUNCT
app01-6401	27	1	=	=	SYM
app01-6401	27	2			NOUN
app01-6401	27	3	eiai	eiai	VERB
app01-6401	28	1	`	`	PUNCT
app01-6401	28	2	i	i	NOUN
app01-6401	28	3	0	0	NUM
app01-6401	28	4	0	0	NUM
app01-6401	28	5	−eiai	−eiai	NOUN
app01-6401	29	1	`	`	PUNCT
app01-6401	29	2	i	i	PRON
app01-6401	29	3	0	0	NUM
app01-6401	29	4	0	0	NUM
app01-6401	29	5	12eiii	12eiii	NUM
app01-6401	30	1	`	`	PUNCT
app01-6401	30	2	3	3	NUM
app01-6401	30	3	i	i	PRON
app01-6401	30	4	6eiii	6eiii	NUM
app01-6401	30	5	`	`	PUNCT
app01-6401	30	6	2	2	NUM
app01-6401	30	7	i	i	NOUN
app01-6401	30	8	0	0	NUM
app01-6401	30	9	−	−	NOUN
app01-6401	30	10	12eiii	12eiii	NUM
app01-6401	31	1	`	`	PUNCT
app01-6401	31	2	3	3	NUM
app01-6401	31	3	i	i	PRON
app01-6401	31	4	6eiii	6eiii	NUM
app01-6401	31	5	`	`	PUNCT
app01-6401	31	6	2	2	NUM
app01-6401	31	7	i	i	NOUN
app01-6401	31	8	4eiii	4eiii	NUM
app01-6401	31	9	`	`	PUNCT
app01-6401	31	10	i	i	PRON
app01-6401	31	11	0	0	NUM
app01-6401	31	12	−	−	PROPN
app01-6401	32	1	6eiii	6eiii	NUM
app01-6401	32	2	`	`	PUNCT
app01-6401	32	3	2	2	NUM
app01-6401	32	4	i	i	NOUN
app01-6401	32	5	2eiii	2eiii	NUM
app01-6401	32	6	`	`	PUNCT
app01-6401	32	7	i	i	PRON
app01-6401	32	8	sym	sym	PROPN
app01-6401	32	9	.	.	PUNCT
app01-6401	33	1	eiai	eiai	PROPN
app01-6401	34	1	`	`	PUNCT
app01-6401	34	2	i	i	NOUN
app01-6401	34	3	0	0	NUM
app01-6401	34	4	0	0	NUM
app01-6401	34	5	12eiii	12eiii	NUM
app01-6401	35	1	`	`	PUNCT
app01-6401	35	2	3	3	NUM
app01-6401	35	3	i	i	PRON
app01-6401	35	4	−	−	VERB
app01-6401	35	5	6eiii	6eiii	NUM
app01-6401	35	6	`	`	PUNCT
app01-6401	35	7	2	2	NUM
app01-6401	35	8	i	i	NOUN
app01-6401	35	9	4eiii	4eiii	NUM
app01-6401	35	10	`	`	PUNCT
app01-6401	35	11	i	i	PRON
app01-6401	35	12			ADJ
app01-6401	35	13	(	(	PUNCT
app01-6401	35	14	3	3	X
app01-6401	35	15	)	)	PUNCT
app01-6401	35	16	we	we	PRON
app01-6401	35	17	assume	assume	VERB
app01-6401	35	18	,	,	PUNCT
app01-6401	35	19	in	in	ADP
app01-6401	35	20	the	the	DET
app01-6401	35	21	following	follow	VERB
app01-6401	35	22	text	text	NOUN
app01-6401	35	23	,	,	PUNCT
app01-6401	35	24	that	that	SCONJ
app01-6401	35	25	the	the	DET
app01-6401	35	26	moments	moment	NOUN
app01-6401	35	27	of	of	ADP
app01-6401	35	28	inertia	inertia	NOUN
app01-6401	35	29	of	of	ADP
app01-6401	35	30	individual	individual	ADJ
app01-6401	35	31	cross	cross	ADJ
app01-6401	35	32	-	-	ADJ
app01-6401	35	33	sections	section	NOUN
app01-6401	35	34	ii	ii	NOUN
app01-6401	35	35	are	be	AUX
app01-6401	35	36	polynomials	polynomial	NOUN
app01-6401	35	37	of	of	ADP
app01-6401	35	38	degree	degree	NOUN
app01-6401	35	39	two1	two1	PROPN
app01-6401	35	40	,	,	PUNCT
app01-6401	35	41	i.e.	i.e.	X
app01-6401	35	42	,	,	PUNCT
app01-6401	35	43	ii	ii	PROPN
app01-6401	35	44	=	=	SYM
app01-6401	35	45	ci	ci	PROPN
app01-6401	35	46	,	,	PUNCT
app01-6401	35	47	ia	ia	PROPN
app01-6401	35	48	2	2	NUM
app01-6401	35	49	i	i	PRON
app01-6401	35	50	for	for	ADP
app01-6401	35	51	some	some	DET
app01-6401	35	52	ci	ci	NOUN
app01-6401	35	53	,	,	PUNCT
app01-6401	35	54	i	i	PRON
app01-6401	35	55	>	>	X
app01-6401	35	56	0	0	PROPN
app01-6401	35	57	,	,	PUNCT
app01-6401	35	58	which	which	PRON
app01-6401	35	59	includes	include	VERB
app01-6401	35	60	all	all	DET
app01-6401	35	61	cross	cross	NOUN
app01-6401	35	62	-	-	NOUN
app01-6401	35	63	sections	section	NOUN
app01-6401	35	64	with	with	ADP
app01-6401	35	65	given	give	VERB
app01-6401	35	66	aspect	aspect	NOUN
app01-6401	35	67	ratios	ratio	NOUN
app01-6401	35	68	of	of	ADP
app01-6401	35	69	all	all	PRON
app01-6401	35	70	their	their	PRON
app01-6401	35	71	components	component	NOUN
app01-6401	35	72	.	.	PUNCT
app01-6401	36	1	note	note	VERB
app01-6401	36	2	that	that	SCONJ
app01-6401	36	3	in	in	ADP
app01-6401	36	4	such	such	DET
app01-6401	36	5	a	a	DET
app01-6401	36	6	case	case	NOUN
app01-6401	36	7	,	,	PUNCT
app01-6401	36	8	each	each	DET
app01-6401	36	9	cross	cross	NOUN
app01-6401	36	10	-	-	NOUN
app01-6401	36	11	section	section	NOUN
app01-6401	36	12	is	be	AUX
app01-6401	36	13	fully	fully	ADV
app01-6401	36	14	determined	determine	VERB
app01-6401	36	15	by	by	ADP
app01-6401	36	16	its	its	PRON
app01-6401	36	17	area	area	NOUN
app01-6401	36	18	.	.	PUNCT
app01-6401	37	1	optimizing	optimize	VERB
app01-6401	37	2	the	the	DET
app01-6401	37	3	cross	cross	ADJ
app01-6401	37	4	-	-	ADJ
app01-6401	37	5	sectional	sectional	ADJ
app01-6401	37	6	areas	area	NOUN
app01-6401	37	7	a	a	PRON
app01-6401	37	8	we	we	PRON
app01-6401	37	9	search	search	VERB
app01-6401	37	10	the	the	DET
app01-6401	37	11	maximum	maximum	ADJ
app01-6401	37	12	stiff	stiff	ADJ
app01-6401	37	13	structures	structure	NOUN
app01-6401	37	14	within	within	ADP
app01-6401	37	15	the	the	DET
app01-6401	37	16	available	available	ADJ
app01-6401	37	17	volume	volume	NOUN
app01-6401	37	18	v	v	NOUN
app01-6401	37	19	of	of	ADP
app01-6401	37	20	a	a	DET
app01-6401	37	21	linear	linear	ADJ
app01-6401	37	22	-	-	PUNCT
app01-6401	37	23	elastic	elastic	ADJ
app01-6401	37	24	material	material	NOUN
app01-6401	37	25	.	.	PUNCT
app01-6401	38	1	the	the	DET
app01-6401	38	2	structural	structural	ADJ
app01-6401	38	3	stiffness	stiffness	NOUN
app01-6401	38	4	is	be	AUX
app01-6401	38	5	measured	measure	VERB
app01-6401	38	6	(	(	PUNCT
app01-6401	38	7	inversely	inversely	ADV
app01-6401	38	8	)	)	PUNCT
app01-6401	38	9	by	by	ADP
app01-6401	38	10	the	the	DET
app01-6401	38	11	compliance	compliance	NOUN
app01-6401	38	12	c	c	NOUN
app01-6401	38	13	,	,	PUNCT
app01-6401	38	14	work	work	NOUN
app01-6401	38	15	done	do	VERB
app01-6401	38	16	by	by	ADP
app01-6401	38	17	external	external	ADJ
app01-6401	38	18	forces	force	NOUN
app01-6401	38	19	,	,	PUNCT
app01-6401	38	20	f(a	f(a	PROPN
app01-6401	38	21	)	)	PUNCT
app01-6401	38	22	,	,	PUNCT
app01-6401	38	23	c(a	c(a	ADV
app01-6401	38	24	)	)	PUNCT
app01-6401	38	25	=	=	SYM
app01-6401	39	1	f(a)tu	f(a)tu	PROPN
app01-6401	39	2	=	=	PUNCT
app01-6401	39	3	utk(a)u	utk(a)u	PROPN
app01-6401	39	4	,	,	PUNCT
app01-6401	39	5	(	(	PUNCT
app01-6401	39	6	1	1	X
app01-6401	39	7	)	)	PUNCT
app01-6401	39	8	where	where	SCONJ
app01-6401	39	9	u	u	PRON
app01-6401	39	10	constitutes	constitute	VERB
app01-6401	39	11	the	the	DET
app01-6401	39	12	generalized	generalized	ADJ
app01-6401	39	13	displacement	displacement	NOUN
app01-6401	39	14	vector	vector	NOUN
app01-6401	39	15	,	,	PUNCT
app01-6401	39	16	and	and	CCONJ
app01-6401	39	17	k(a	k(a	NOUN
app01-6401	39	18	)	)	PUNCT
app01-6401	39	19	is	be	AUX
app01-6401	39	20	the	the	DET
app01-6401	39	21	symmetric	symmetric	ADJ
app01-6401	39	22	positive	positive	ADJ
app01-6401	39	23	semi	semi	ADJ
app01-6401	39	24	-	-	ADJ
app01-6401	39	25	definite	definite	ADJ
app01-6401	39	26	stiffness	stiffness	NOUN
app01-6401	39	27	matrix	matrix	NOUN
app01-6401	39	28	—	—	PUNCT
app01-6401	39	29	a	a	DET
app01-6401	39	30	polynomial	polynomial	ADJ
app01-6401	39	31	function	function	NOUN
app01-6401	39	32	of	of	ADP
app01-6401	39	33	a	a	DET
app01-6401	39	34	,	,	PUNCT
app01-6401	39	35	k(a	k(a	PROPN
app01-6401	39	36	)	)	PUNCT
app01-6401	40	1	=	=	SYM
app01-6401	40	2	ne∑	ne∑	PROPN
app01-6401	40	3	i=1	i=1	PROPN
app01-6401	40	4	ki(ai	ki(ai	PROPN
app01-6401	40	5	)	)	PUNCT
app01-6401	40	6	,	,	PUNCT
app01-6401	40	7	(	(	PUNCT
app01-6401	40	8	2	2	X
app01-6401	40	9	)	)	PUNCT
app01-6401	40	10	assembled	assemble	VERB
app01-6401	40	11	from	from	ADP
app01-6401	40	12	contributions	contribution	NOUN
app01-6401	40	13	of	of	ADP
app01-6401	40	14	individual	individual	ADJ
app01-6401	40	15	elements	element	NOUN
app01-6401	40	16	ki(ai	ki(ai	PROPN
app01-6401	40	17	)	)	PUNCT
app01-6401	40	18	.	.	PUNCT
app01-6401	41	1	the	the	PRON
app01-6401	41	2	lower	low	ADJ
app01-6401	41	3	the	the	DET
app01-6401	41	4	compliance	compliance	NOUN
app01-6401	41	5	,	,	PUNCT
app01-6401	41	6	the	the	DET
app01-6401	41	7	stiffer	stiffer	NOUN
app01-6401	41	8	is	be	AUX
app01-6401	41	9	the	the	DET
app01-6401	41	10	structure	structure	NOUN
app01-6401	41	11	with	with	ADP
app01-6401	41	12	respect	respect	NOUN
app01-6401	41	13	to	to	ADP
app01-6401	41	14	the	the	DET
app01-6401	41	15	external	external	ADJ
app01-6401	41	16	forces	force	NOUN
app01-6401	41	17	.	.	PUNCT
app01-6401	42	1	in	in	ADP
app01-6401	42	2	this	this	DET
app01-6401	42	3	contribution	contribution	NOUN
app01-6401	42	4	,	,	PUNCT
app01-6401	42	5	we	we	PRON
app01-6401	42	6	use	use	VERB
app01-6401	42	7	the	the	DET
app01-6401	42	8	element	element	ADJ
app01-6401	42	9	stiffness	stiffness	NOUN
app01-6401	42	10	matrix	matrix	NOUN
app01-6401	42	11	of	of	ADP
app01-6401	42	12	euler	euler	PROPN
app01-6401	42	13	–	–	PUNCT
app01-6401	42	14	bernoulli	bernoulli	PROPN
app01-6401	42	15	frame	frame	NOUN
app01-6401	42	16	elements	element	NOUN
app01-6401	42	17	(	(	PUNCT
app01-6401	42	18	3	3	NUM
app01-6401	42	19	)	)	PUNCT
app01-6401	42	20	,	,	PUNCT
app01-6401	42	21	with	with	ADP
app01-6401	42	22	ei	ei	ADP
app01-6401	42	23	denoting	denote	VERB
app01-6401	42	24	the	the	DET
app01-6401	42	25	young	young	ADJ
app01-6401	42	26	modulus	modulus	NOUN
app01-6401	42	27	.	.	PUNCT
app01-6401	43	1	in	in	ADP
app01-6401	43	2	(	(	PUNCT
app01-6401	43	3	1	1	NUM
app01-6401	43	4	)	)	PUNCT
app01-6401	43	5	,	,	PUNCT
app01-6401	43	6	f(a	f(a	PROPN
app01-6401	43	7	)	)	PUNCT
app01-6401	43	8	is	be	AUX
app01-6401	43	9	the	the	DET
app01-6401	43	10	external	external	ADJ
app01-6401	43	11	force	force	NOUN
app01-6401	43	12	column	column	NOUN
app01-6401	43	13	vector	vector	NOUN
app01-6401	43	14	—	—	PUNCT
app01-6401	43	15	a	a	DET
app01-6401	43	16	linear	linear	ADJ
app01-6401	43	17	function	function	NOUN
app01-6401	43	18	of	of	ADP
app01-6401	43	19	a	a	PRON
app01-6401	43	20	—	—	PUNCT
app01-6401	43	21	to	to	PART
app01-6401	43	22	allow	allow	VERB
app01-6401	43	23	for	for	ADP
app01-6401	43	24	self	self	NOUN
app01-6401	43	25	-	-	PUNCT
app01-6401	43	26	weight	weight	NOUN
app01-6401	43	27	,	,	PUNCT
app01-6401	43	28	assembled	assemble	VERB
app01-6401	43	29	from	from	ADP
app01-6401	43	30	the	the	DET
app01-6401	43	31	contributions	contribution	NOUN
app01-6401	43	32	of	of	ADP
app01-6401	43	33	elements	element	NOUN
app01-6401	43	34	f(ai	f(ai	PROPN
app01-6401	43	35	)	)	PUNCT
app01-6401	43	36	,	,	PUNCT
app01-6401	43	37	f(a	f(a	NOUN
app01-6401	43	38	)	)	PUNCT
app01-6401	44	1	=	=	SYM
app01-6401	44	2	ne∑	ne∑	NOUN
app01-6401	44	3	i=1	i=1	PROPN
app01-6401	44	4	fi(ai	fi(ai	PROPN
app01-6401	44	5	)	)	PUNCT
app01-6401	44	6	.	.	PUNCT
app01-6401	45	1	(	(	PUNCT
app01-6401	45	2	4	4	X
app01-6401	45	3	)	)	PUNCT
app01-6401	45	4	in	in	ADP
app01-6401	45	5	the	the	DET
app01-6401	45	6	following	follow	VERB
app01-6401	45	7	text	text	NOUN
app01-6401	45	8	,	,	PUNCT
app01-6401	45	9	we	we	PRON
app01-6401	45	10	assume	assume	VERB
app01-6401	45	11	that	that	SCONJ
app01-6401	45	12	∀a	∀a	VERB
app01-6401	45	13	>	>	X
app01-6401	45	14	0	0	NUM
app01-6401	45	15	:	:	PUNCT
app01-6401	45	16	k(a	k(a	PROPN
app01-6401	45	17	)	)	PUNCT
app01-6401	45	18	�	�	PROPN
app01-6401	45	19	0	0	NUM
app01-6401	45	20	,	,	PUNCT
app01-6401	45	21	i.e.	i.e.	X
app01-6401	45	22	,	,	PUNCT
app01-6401	45	23	the	the	DET
app01-6401	45	24	structure	structure	NOUN
app01-6401	45	25	is	be	AUX
app01-6401	45	26	not	not	PART
app01-6401	45	27	a	a	DET
app01-6401	45	28	kinematic	kinematic	ADJ
app01-6401	45	29	mechanism	mechanism	NOUN
app01-6401	45	30	and	and	CCONJ
app01-6401	45	31	the	the	DET
app01-6401	45	32	stiffness	stiffness	ADJ
app01-6401	45	33	matrix	matrix	NOUN
app01-6401	45	34	is	be	AUX
app01-6401	45	35	positive	positive	ADJ
app01-6401	45	36	definite	definite	ADJ
app01-6401	45	37	(	(	PUNCT
app01-6401	45	38	which	which	PRON
app01-6401	45	39	is	be	AUX
app01-6401	45	40	denoted	denote	VERB
app01-6401	45	41	by	by	ADP
app01-6401	45	42	“	"	PUNCT
app01-6401	45	43	�	�	PROPN
app01-6401	45	44	0	0	NUM
app01-6401	45	45	”	"	PUNCT
app01-6401	45	46	)	)	PUNCT
app01-6401	45	47	for	for	ADP
app01-6401	45	48	all	all	DET
app01-6401	45	49	positive	positive	ADJ
app01-6401	45	50	cross	cross	ADJ
app01-6401	45	51	-	-	ADJ
app01-6401	45	52	sectional	sectional	ADJ
app01-6401	45	53	areas	area	NOUN
app01-6401	45	54	.	.	PUNCT
app01-6401	46	1	since	since	SCONJ
app01-6401	46	2	k(a	k(a	NOUN
app01-6401	46	3	)	)	PUNCT
app01-6401	46	4	has	have	VERB
app01-6401	46	5	therefore	therefore	ADV
app01-6401	46	6	the	the	DET
app01-6401	46	7	full	full	ADJ
app01-6401	46	8	rank	rank	NOUN
app01-6401	46	9	,	,	PUNCT
app01-6401	46	10	we	we	PRON
app01-6401	46	11	also	also	ADV
app01-6401	46	12	have	have	VERB
app01-6401	46	13	f(a	f(a	NOUN
app01-6401	46	14	)	)	PUNCT
app01-6401	46	15	∈	∈	PROPN
app01-6401	47	1	i	i	PRON
app01-6401	47	2	m	m	VERB
app01-6401	47	3	(	(	PUNCT
app01-6401	47	4	k(a	k(a	PROPN
app01-6401	47	5	)	)	PUNCT
app01-6401	47	6	)	)	PUNCT
app01-6401	47	7	,	,	PUNCT
app01-6401	47	8	where	where	SCONJ
app01-6401	47	9	im(•	im(•	NOUN
app01-6401	47	10	)	)	PUNCT
app01-6401	47	11	is	be	AUX
app01-6401	47	12	the	the	DET
app01-6401	47	13	image	image	NOUN
app01-6401	47	14	of	of	ADP
app01-6401	47	15	•.	•.	NOUN
app01-6401	47	16	1the	1the	DET
app01-6401	47	17	same	same	ADJ
app01-6401	47	18	procedure	procedure	NOUN
app01-6401	47	19	can	can	AUX
app01-6401	47	20	be	be	AUX
app01-6401	47	21	employed	employ	VERB
app01-6401	47	22	for	for	ADP
app01-6401	47	23	higher	high	ADJ
app01-6401	47	24	-	-	PUNCT
app01-6401	47	25	degree	degree	NOUN
app01-6401	47	26	polynomials	polynomial	NOUN
app01-6401	47	27	,	,	PUNCT
app01-6401	47	28	so	so	SCONJ
app01-6401	47	29	that	that	SCONJ
app01-6401	47	30	all	all	DET
app01-6401	47	31	cross	cross	ADJ
app01-6401	47	32	-	-	ADJ
app01-6401	47	33	sectional	sectional	ADJ
app01-6401	47	34	parameters	parameter	NOUN
app01-6401	47	35	can	can	AUX
app01-6401	47	36	be	be	AUX
app01-6401	47	37	optimized	optimize	VERB
app01-6401	47	38	concurrently	concurrently	ADV
app01-6401	47	39	.	.	PUNCT
app01-6401	48	1	we	we	PRON
app01-6401	48	2	restrict	restrict	VERB
app01-6401	48	3	ourselves	ourselves	PRON
app01-6401	48	4	,	,	PUNCT
app01-6401	48	5	however	however	ADV
app01-6401	48	6	,	,	PUNCT
app01-6401	48	7	to	to	ADP
app01-6401	48	8	the	the	DET
app01-6401	48	9	polynomials	polynomial	NOUN
app01-6401	48	10	of	of	ADP
app01-6401	48	11	degree	degree	NOUN
app01-6401	48	12	two	two	NUM
app01-6401	48	13	to	to	PART
app01-6401	48	14	maintain	maintain	VERB
app01-6401	48	15	a	a	DET
app01-6401	48	16	simpler	simple	ADJ
app01-6401	48	17	notation	notation	NOUN
app01-6401	48	18	.	.	PUNCT
app01-6401	49	1	this	this	DET
app01-6401	49	2	optimization	optimization	NOUN
app01-6401	49	3	problem	problem	NOUN
app01-6401	49	4	is	be	AUX
app01-6401	49	5	formalized	formalize	VERB
app01-6401	49	6	as	as	ADP
app01-6401	49	7	min	min	PROPN
app01-6401	49	8	a	a	PROPN
app01-6401	49	9	,	,	PUNCT
app01-6401	49	10	u	u	PROPN
app01-6401	49	11	f(a)tu	f(a)tu	PROPN
app01-6401	49	12	(	(	PUNCT
app01-6401	49	13	5a	5a	NUM
app01-6401	49	14	)	)	PUNCT
app01-6401	49	15	s.t	s.t	PROPN
app01-6401	49	16	.	.	PROPN
app01-6401	49	17	k(a)u	k(a)u	PROPN
app01-6401	49	18	=	=	SYM
app01-6401	49	19	f(a	f(a	PROPN
app01-6401	49	20	)	)	PUNCT
app01-6401	49	21	,	,	PUNCT
app01-6401	49	22	(	(	PUNCT
app01-6401	49	23	5b	5b	NUM
app01-6401	49	24	)	)	PUNCT
app01-6401	49	25	`	`	PUNCT
app01-6401	49	26	ta	ta	X
app01-6401	49	27	≤	≤	NUM
app01-6401	49	28	v	v	NOUN
app01-6401	49	29	,	,	PUNCT
app01-6401	49	30	(	(	PUNCT
app01-6401	49	31	5c	5c	NUM
app01-6401	49	32	)	)	PUNCT
app01-6401	49	33	a	a	DET
app01-6401	49	34	≥	≥	NOUN
app01-6401	49	35	0	0	NUM
app01-6401	49	36	,	,	PUNCT
app01-6401	49	37	(	(	PUNCT
app01-6401	49	38	5d	5d	NUM
app01-6401	49	39	)	)	PUNCT
app01-6401	49	40	with	with	ADP
app01-6401	49	41	`	`	PUNCT
app01-6401	49	42	being	be	AUX
app01-6401	49	43	the	the	DET
app01-6401	49	44	column	column	NOUN
app01-6401	49	45	vector	vector	NOUN
app01-6401	49	46	of	of	ADP
app01-6401	49	47	the	the	DET
app01-6401	49	48	frame	frame	NOUN
app01-6401	49	49	elements	element	NOUN
app01-6401	49	50	lengths	length	NOUN
app01-6401	49	51	.	.	PUNCT
app01-6401	50	1	notice	notice	VERB
app01-6401	50	2	that	that	SCONJ
app01-6401	50	3	in	in	ADP
app01-6401	50	4	general	general	ADJ
app01-6401	50	5	,	,	PUNCT
app01-6401	50	6	(	(	PUNCT
app01-6401	50	7	5	5	X
app01-6401	50	8	)	)	PUNCT
app01-6401	50	9	constitutes	constitute	VERB
app01-6401	50	10	a	a	DET
app01-6401	50	11	nonconvex	nonconvex	NOUN
app01-6401	50	12	non	non	ADJ
app01-6401	50	13	-	-	ADJ
app01-6401	50	14	linear	linear	ADJ
app01-6401	50	15	optimization	optimization	NOUN
app01-6401	50	16	problem	problem	NOUN
app01-6401	50	17	because	because	SCONJ
app01-6401	50	18	of	of	ADP
app01-6401	50	19	the	the	DET
app01-6401	50	20	bilinear	bilinear	ADJ
app01-6401	50	21	objective	objective	ADJ
app01-6401	50	22	function	function	NOUN
app01-6401	50	23	(	(	PUNCT
app01-6401	50	24	5a	5a	NUM
app01-6401	50	25	)	)	PUNCT
app01-6401	50	26	and	and	CCONJ
app01-6401	50	27	the	the	DET
app01-6401	50	28	polynomial	polynomial	ADJ
app01-6401	50	29	equilibrium	equilibrium	NOUN
app01-6401	50	30	equality	equality	NOUN
app01-6401	50	31	(	(	PUNCT
app01-6401	50	32	5b	5b	NUM
app01-6401	50	33	)	)	PUNCT
app01-6401	50	34	with	with	ADP
app01-6401	50	35	possibly	possibly	ADV
app01-6401	50	36	singular	singular	ADJ
app01-6401	50	37	k(a	k(a	NOUN
app01-6401	50	38	)	)	PUNCT
app01-6401	50	39	.	.	PUNCT
app01-6401	51	1	on	on	ADP
app01-6401	51	2	the	the	DET
app01-6401	51	3	other	other	ADJ
app01-6401	51	4	hand	hand	NOUN
app01-6401	51	5	,	,	PUNCT
app01-6401	51	6	the	the	DET
app01-6401	51	7	volume	volume	NOUN
app01-6401	51	8	constraint	constraint	NOUN
app01-6401	51	9	(	(	PUNCT
app01-6401	51	10	5c	5c	NUM
app01-6401	51	11	)	)	PUNCT
app01-6401	51	12	and	and	CCONJ
app01-6401	51	13	the	the	DET
app01-6401	51	14	cross	cross	ADJ
app01-6401	51	15	-	-	ADJ
app01-6401	51	16	sectional	sectional	ADJ
app01-6401	51	17	areas	area	NOUN
app01-6401	51	18	non	non	ADJ
app01-6401	51	19	-	-	ADJ
app01-6401	51	20	negativity	negativity	ADJ
app01-6401	51	21	constraint	constraint	NOUN
app01-6401	51	22	(	(	PUNCT
app01-6401	51	23	5d	5d	NUM
app01-6401	51	24	)	)	PUNCT
app01-6401	51	25	are	be	AUX
app01-6401	51	26	affine	affine	NOUN
app01-6401	51	27	functions	function	NOUN
app01-6401	51	28	of	of	ADP
app01-6401	51	29	the	the	DET
app01-6401	51	30	design	design	NOUN
app01-6401	51	31	variables	variable	NOUN
app01-6401	51	32	,	,	PUNCT
app01-6401	51	33	u	u	NOUN
app01-6401	51	34	and	and	CCONJ
app01-6401	51	35	a	a	PRON
app01-6401	51	36	,	,	PUNCT
app01-6401	51	37	and	and	CCONJ
app01-6401	51	38	are	be	AUX
app01-6401	51	39	in	in	ADP
app01-6401	51	40	turn	turn	NOUN
app01-6401	51	41	convex	convex	PROPN
app01-6401	51	42	.	.	PUNCT
app01-6401	52	1	the	the	DET
app01-6401	52	2	optimization	optimization	NOUN
app01-6401	52	3	problem	problem	NOUN
app01-6401	52	4	(	(	PUNCT
app01-6401	52	5	5	5	X
app01-6401	52	6	)	)	PUNCT
app01-6401	52	7	can	can	AUX
app01-6401	52	8	be	be	AUX
app01-6401	52	9	solved	solve	VERB
app01-6401	52	10	to	to	ADP
app01-6401	52	11	local	local	ADJ
app01-6401	52	12	optimality	optimality	NOUN
app01-6401	52	13	using	use	VERB
app01-6401	52	14	standard	standard	ADJ
app01-6401	52	15	numerical	numerical	ADJ
app01-6401	52	16	optimization	optimization	NOUN
app01-6401	52	17	techniques	technique	NOUN
app01-6401	52	18	.	.	PUNCT
app01-6401	53	1	in	in	ADP
app01-6401	53	2	particular	particular	ADJ
app01-6401	53	3	,	,	PUNCT
app01-6401	53	4	we	we	PRON
app01-6401	53	5	will	will	AUX
app01-6401	53	6	solve	solve	VERB
app01-6401	53	7	this	this	DET
app01-6401	53	8	problem	problem	NOUN
app01-6401	53	9	using	use	VERB
app01-6401	53	10	the	the	DET
app01-6401	53	11	interior	interior	ADJ
app01-6401	53	12	-	-	PUNCT
app01-6401	53	13	point	point	NOUN
app01-6401	53	14	method	method	NOUN
app01-6401	53	15	implemented	implement	VERB
app01-6401	53	16	in	in	ADP
app01-6401	53	17	the	the	DET
app01-6401	53	18	fmincon	fmincon	NOUN
app01-6401	53	19	function	function	NOUN
app01-6401	53	20	of	of	ADP
app01-6401	53	21	matlab	matlab	PROPN
app01-6401	53	22	.	.	PUNCT
app01-6401	54	1	2.2	2.2	NUM
app01-6401	54	2	.	.	PUNCT
app01-6401	54	3	optimality	optimality	NOUN
app01-6401	54	4	criteria	criterion	NOUN
app01-6401	54	5	the	the	DET
app01-6401	54	6	inherent	inherent	ADJ
app01-6401	54	7	difficulty	difficulty	NOUN
app01-6401	54	8	of	of	ADP
app01-6401	54	9	singularity	singularity	NOUN
app01-6401	54	10	of	of	ADP
app01-6401	54	11	k(a	k(a	NOUN
app01-6401	54	12	)	)	PUNCT
app01-6401	54	13	in	in	ADP
app01-6401	54	14	(	(	PUNCT
app01-6401	54	15	5b	5b	NOUN
app01-6401	54	16	)	)	PUNCT
app01-6401	54	17	can	can	AUX
app01-6401	54	18	be	be	AUX
app01-6401	54	19	circumvented	circumvent	VERB
app01-6401	54	20	by	by	ADP
app01-6401	54	21	assuming	assume	VERB
app01-6401	54	22	a	a	DET
app01-6401	54	23	small	small	ADJ
app01-6401	54	24	positive	positive	ADJ
app01-6401	54	25	lower	lower	ADV
app01-6401	54	26	-	-	PUNCT
app01-6401	54	27	bound	bind	VERB
app01-6401	54	28	on	on	ADP
app01-6401	54	29	the	the	DET
app01-6401	54	30	cross	cross	ADJ
app01-6401	54	31	-	-	ADJ
app01-6401	54	32	sectional	sectional	ADJ
app01-6401	54	33	areas	area	NOUN
app01-6401	54	34	[	[	X
app01-6401	54	35	1	1	NUM
app01-6401	54	36	]	]	PUNCT
app01-6401	54	37	,	,	PUNCT
app01-6401	54	38	which	which	PRON
app01-6401	54	39	is	be	AUX
app01-6401	54	40	denoted	denote	VERB
app01-6401	54	41	by	by	ADP
app01-6401	54	42	ε	ε	PROPN
app01-6401	54	43	in	in	ADP
app01-6401	54	44	this	this	DET
app01-6401	54	45	study	study	NOUN
app01-6401	54	46	.	.	PUNCT
app01-6401	55	1	consequently	consequently	ADV
app01-6401	55	2	,	,	PUNCT
app01-6401	55	3	the	the	DET
app01-6401	55	4	former	former	ADJ
app01-6401	55	5	topology	topology	NOUN
app01-6401	55	6	optimization	optimization	NOUN
app01-6401	55	7	problem	problem	NOUN
app01-6401	55	8	(	(	PUNCT
app01-6401	55	9	5	5	NUM
app01-6401	55	10	)	)	PUNCT
app01-6401	55	11	is	be	AUX
app01-6401	55	12	effectively	effectively	ADV
app01-6401	55	13	transformed	transform	VERB
app01-6401	55	14	into	into	ADP
app01-6401	55	15	the	the	DET
app01-6401	55	16	sizing	sizing	NOUN
app01-6401	55	17	one	one	NUM
app01-6401	55	18	and	and	CCONJ
app01-6401	55	19	the	the	DET
app01-6401	55	20	displacement	displacement	ADJ
app01-6401	55	21	field	field	NOUN
app01-6401	55	22	u	u	NOUN
app01-6401	55	23	can	can	AUX
app01-6401	55	24	be	be	AUX
app01-6401	55	25	excluded	exclude	VERB
app01-6401	55	26	from	from	ADP
app01-6401	55	27	the	the	DET
app01-6401	55	28	design	design	NOUN
app01-6401	55	29	variables2	variables2	PROPN
app01-6401	55	30	.	.	PUNCT
app01-6401	56	1	notice	notice	VERB
app01-6401	56	2	that	that	SCONJ
app01-6401	56	3	in	in	ADP
app01-6401	56	4	the	the	DET
app01-6401	56	5	limit	limit	NOUN
app01-6401	56	6	when	when	SCONJ
app01-6401	56	7	ε	ε	PROPN
app01-6401	56	8	→	→	SYM
app01-6401	56	9	0	0	PROPN
app01-6401	56	10	,	,	PUNCT
app01-6401	56	11	these	these	DET
app01-6401	56	12	problems	problem	NOUN
app01-6401	56	13	are	be	AUX
app01-6401	56	14	equivalent	equivalent	ADJ
app01-6401	56	15	,	,	PUNCT
app01-6401	56	16	but	but	CCONJ
app01-6401	56	17	the	the	DET
app01-6401	56	18	smaller	small	ADJ
app01-6401	56	19	ε	ε	PROPN
app01-6401	56	20	the	the	PRON
app01-6401	56	21	higher	high	ADJ
app01-6401	56	22	the	the	DET
app01-6401	56	23	condition	condition	NOUN
app01-6401	56	24	number	number	NOUN
app01-6401	56	25	of	of	ADP
app01-6401	56	26	k(a	k(a	NOUN
app01-6401	56	27	)	)	PUNCT
app01-6401	56	28	,	,	PUNCT
app01-6401	56	29	and	and	CCONJ
app01-6401	56	30	thus	thus	ADV
app01-6401	56	31	it	it	PRON
app01-6401	56	32	is	be	AUX
app01-6401	56	33	more	more	ADV
app01-6401	56	34	difficult	difficult	ADJ
app01-6401	56	35	to	to	PART
app01-6401	56	36	solve	solve	VERB
app01-6401	56	37	(	(	PUNCT
app01-6401	56	38	5b	5b	NUM
app01-6401	56	39	)	)	PUNCT
app01-6401	56	40	.	.	PUNCT
app01-6401	57	1	hence	hence	ADV
app01-6401	57	2	,	,	PUNCT
app01-6401	57	3	we	we	PRON
app01-6401	57	4	assume	assume	VERB
app01-6401	57	5	ε	ε	PROPN
app01-6401	57	6	=	=	SYM
app01-6401	57	7	10−6	10−6	NUM
app01-6401	57	8	in	in	ADP
app01-6401	57	9	this	this	DET
app01-6401	57	10	study	study	NOUN
app01-6401	57	11	.	.	PUNCT
app01-6401	58	1	considering	consider	VERB
app01-6401	58	2	(	(	PUNCT
app01-6401	58	3	5	5	NUM
app01-6401	58	4	)	)	PUNCT
app01-6401	58	5	with	with	ADP
app01-6401	58	6	ε1	ε1	PROPN
app01-6401	58	7	≤	≤	ADV
app01-6401	58	8	a	a	PRON
app01-6401	58	9	,	,	PUNCT
app01-6401	58	10	its	its	PRON
app01-6401	58	11	lagrangian	lagrangian	ADJ
app01-6401	58	12	function	function	NOUN
app01-6401	58	13	reads	read	VERB
app01-6401	58	14	as	as	ADP
app01-6401	58	15	l(a	l(a	PROPN
app01-6401	58	16	,	,	PUNCT
app01-6401	58	17	u	u	NOUN
app01-6401	58	18	,	,	PUNCT
app01-6401	58	19	λ	λ	PROPN
app01-6401	58	20	,	,	PUNCT
app01-6401	58	21	µ,ν	µ,ν	ADV
app01-6401	58	22	)	)	PUNCT
app01-6401	58	23	=	=	SYM
app01-6401	58	24	f(a)tu	f(a)tu	PROPN
app01-6401	59	1	+	+	CCONJ
app01-6401	59	2	λt	λt	ADP
app01-6401	59	3	[	[	X
app01-6401	59	4	f(a)−k(a)u	f(a)−k(a)u	NOUN
app01-6401	59	5	]	]	X
app01-6401	59	6	+	+	NOUN
app01-6401	59	7	µ	µ	X
app01-6401	59	8	(	(	PUNCT
app01-6401	59	9	`	`	PUNCT
app01-6401	59	10	ta	ta	X
app01-6401	59	11	−	−	NOUN
app01-6401	59	12	v	v	NOUN
app01-6401	59	13	)	)	PUNCT
app01-6401	60	1	+	+	CCONJ
app01-6401	60	2	νt	νt	X
app01-6401	60	3	(	(	PUNCT
app01-6401	60	4	ε1−	ε1−	NOUN
app01-6401	60	5	a	a	NOUN
app01-6401	60	6	)	)	PUNCT
app01-6401	60	7	,	,	PUNCT
app01-6401	60	8	(	(	PUNCT
app01-6401	60	9	6	6	NUM
app01-6401	60	10	)	)	PUNCT
app01-6401	60	11	with	with	ADP
app01-6401	60	12	the	the	DET
app01-6401	60	13	lagrange	lagrange	PROPN
app01-6401	60	14	multipliers	multipliers	PROPN
app01-6401	60	15	λ	λ	PROPN
app01-6401	60	16	,	,	PUNCT
app01-6401	60	17	µ	µ	NOUN
app01-6401	60	18	,	,	PUNCT
app01-6401	60	19	and	and	CCONJ
app01-6401	60	20	ν	ν	NOUN
app01-6401	60	21	;	;	PUNCT
app01-6401	60	22	and	and	CCONJ
app01-6401	60	23	1	1	NUM
app01-6401	60	24	denoting	denote	VERB
app01-6401	60	25	the	the	DET
app01-6401	60	26	vector	vector	NOUN
app01-6401	60	27	of	of	ADP
app01-6401	60	28	all	all	DET
app01-6401	60	29	ones	one	NOUN
app01-6401	60	30	.	.	PUNCT
app01-6401	61	1	in	in	ADP
app01-6401	61	2	addition	addition	NOUN
app01-6401	61	3	to	to	ADP
app01-6401	61	4	the	the	DET
app01-6401	61	5	primal	primal	ADJ
app01-6401	61	6	feasibility	feasibility	NOUN
app01-6401	61	7	(	(	PUNCT
app01-6401	61	8	5b)–(5d	5b)–(5d	NOUN
app01-6401	61	9	)	)	PUNCT
app01-6401	61	10	,	,	PUNCT
app01-6401	61	11	the	the	DET
app01-6401	61	12	karush	karush	NOUN
app01-6401	61	13	–	–	PUNCT
app01-6401	61	14	kuhn	kuhn	PROPN
app01-6401	61	15	–	–	PUNCT
app01-6401	61	16	tucker	tucker	PROPN
app01-6401	61	17	conditions	condition	NOUN
app01-6401	61	18	require	require	VERB
app01-6401	61	19	feasibility	feasibility	NOUN
app01-6401	61	20	of	of	ADP
app01-6401	61	21	the	the	DET
app01-6401	61	22	dual	dual	ADJ
app01-6401	61	23	and	and	CCONJ
app01-6401	61	24	complementary	complementary	ADJ
app01-6401	61	25	2at	2at	NOUN
app01-6401	61	26	the	the	DET
app01-6401	61	27	price	price	NOUN
app01-6401	61	28	of	of	ADP
app01-6401	61	29	solving	solve	VERB
app01-6401	61	30	the	the	DET
app01-6401	61	31	equilibrium	equilibrium	NOUN
app01-6401	61	32	equation	equation	NOUN
app01-6401	61	33	in	in	ADP
app01-6401	61	34	each	each	DET
app01-6401	61	35	iteration	iteration	NOUN
app01-6401	61	36	.	.	PUNCT
app01-6401	62	1	118	118	NUM
app01-6401	62	2	vol	vol	NOUN
app01-6401	62	3	.	.	PUNCT
app01-6401	63	1	26/2020	26/2020	NUM
app01-6401	63	2	on	on	ADP
app01-6401	63	3	optimum	optimum	ADJ
app01-6401	63	4	design	design	NOUN
app01-6401	63	5	of	of	ADP
app01-6401	63	6	frame	frame	NOUN
app01-6401	63	7	structures	structure	NOUN
app01-6401	63	8	slackness	slackness	NOUN
app01-6401	63	9	,	,	PUNCT
app01-6401	63	10	µ	µ	X
app01-6401	63	11	≥	≥	NOUN
app01-6401	63	12	0	0	NUM
app01-6401	63	13	,	,	PUNCT
app01-6401	63	14	(	(	PUNCT
app01-6401	63	15	7a	7a	X
app01-6401	63	16	)	)	PUNCT
app01-6401	63	17	µ	µ	X
app01-6401	63	18	(	(	PUNCT
app01-6401	63	19	`	`	PUNCT
app01-6401	63	20	ta	ta	X
app01-6401	63	21	−	−	NOUN
app01-6401	63	22	v	v	NOUN
app01-6401	63	23	)	)	PUNCT
app01-6401	63	24	=	=	SYM
app01-6401	63	25	0	0	NUM
app01-6401	63	26	,	,	PUNCT
app01-6401	63	27	(	(	PUNCT
app01-6401	63	28	7b	7b	NOUN
app01-6401	63	29	)	)	PUNCT
app01-6401	63	30	ν	ν	X
app01-6401	63	31	≥	≥	NOUN
app01-6401	63	32	0	0	NUM
app01-6401	63	33	,	,	PUNCT
app01-6401	63	34	(	(	PUNCT
app01-6401	63	35	7c	7c	NOUN
app01-6401	63	36	)	)	PUNCT
app01-6401	63	37	νt	νt	NOUN
app01-6401	63	38	(	(	PUNCT
app01-6401	63	39	ε1−	ε1−	NOUN
app01-6401	63	40	a	a	NOUN
app01-6401	63	41	)	)	PUNCT
app01-6401	63	42	=	=	SYM
app01-6401	63	43	0	0	NUM
app01-6401	63	44	,	,	PUNCT
app01-6401	63	45	(	(	PUNCT
app01-6401	63	46	7d	7d	NUM
app01-6401	63	47	)	)	PUNCT
app01-6401	63	48	together	together	ADV
app01-6401	63	49	with	with	ADP
app01-6401	63	50	the	the	DET
app01-6401	63	51	stationarity	stationarity	NOUN
app01-6401	63	52	of	of	ADP
app01-6401	63	53	the	the	DET
app01-6401	63	54	lagrangian	lagrangian	NOUN
app01-6401	63	55	with	with	ADP
app01-6401	63	56	respect	respect	NOUN
app01-6401	63	57	to	to	ADP
app01-6401	63	58	u	u	NOUN
app01-6401	63	59	,	,	PUNCT
app01-6401	63	60	0	0	NUM
app01-6401	63	61	=	=	SYM
app01-6401	63	62	dl(a	dl(a	X
app01-6401	63	63	,	,	PUNCT
app01-6401	63	64	u	u	NOUN
app01-6401	63	65	,	,	PUNCT
app01-6401	63	66	λ	λ	PROPN
app01-6401	63	67	,	,	PUNCT
app01-6401	63	68	µ,ν	µ,ν	ADV
app01-6401	63	69	)	)	PUNCT
app01-6401	63	70	du	du	NOUN
app01-6401	64	1	=	=	SYM
app01-6401	65	1	[	[	X
app01-6401	65	2	f(a)−k(a)λ]t	f(a)−k(a)λ]t	PROPN
app01-6401	65	3	,	,	PUNCT
app01-6401	65	4	(	(	PUNCT
app01-6401	65	5	8)	8)	NUM
app01-6401	65	6	and	and	CCONJ
app01-6401	65	7	a.	a.	NOUN
app01-6401	65	8	however	however	ADV
app01-6401	65	9	,	,	PUNCT
app01-6401	65	10	because	because	SCONJ
app01-6401	65	11	the	the	DET
app01-6401	65	12	equation	equation	NOUN
app01-6401	65	13	k(a)λ	k(a)λ	PROPN
app01-6401	65	14	=	=	SYM
app01-6401	65	15	f(a	f(a	PROPN
app01-6401	65	16	)	)	PUNCT
app01-6401	65	17	in	in	ADP
app01-6401	65	18	(	(	PUNCT
app01-6401	65	19	8)	8)	NUM
app01-6401	65	20	possesses	possess	VERB
app01-6401	65	21	a	a	DET
app01-6401	65	22	unique	unique	ADJ
app01-6401	65	23	solution	solution	NOUN
app01-6401	65	24	due	due	ADJ
app01-6401	65	25	to	to	ADP
app01-6401	65	26	k(a	k(a	PROPN
app01-6401	65	27	)	)	PUNCT
app01-6401	65	28	�	�	PROPN
app01-6401	65	29	0	0	NUM
app01-6401	65	30	,	,	PUNCT
app01-6401	65	31	we	we	PRON
app01-6401	65	32	have	have	VERB
app01-6401	65	33	λ	λ	NOUN
app01-6401	65	34	=	=	PUNCT
app01-6401	65	35	u.	u.	PROPN
app01-6401	65	36	using	use	VERB
app01-6401	65	37	this	this	DET
app01-6401	65	38	observation	observation	NOUN
app01-6401	65	39	,	,	PUNCT
app01-6401	65	40	the	the	DET
app01-6401	65	41	necessary	necessary	ADJ
app01-6401	65	42	first	first	ADJ
app01-6401	65	43	-	-	PUNCT
app01-6401	65	44	order	order	NOUN
app01-6401	65	45	optimality	optimality	NOUN
app01-6401	65	46	conditions	condition	NOUN
app01-6401	65	47	read	read	VERB
app01-6401	65	48	as	as	ADP
app01-6401	65	49	0	0	NUM
app01-6401	65	50	=	=	SYM
app01-6401	65	51	∂l	∂l	PROPN
app01-6401	65	52	∂ai	∂ai	PROPN
app01-6401	65	53	=	=	SYM
app01-6401	65	54	2ut	2ut	NOUN
app01-6401	65	55	∂f(a	∂f(a	PROPN
app01-6401	65	56	)	)	PUNCT
app01-6401	66	1	∂ai	∂ai	PROPN
app01-6401	66	2	−	−	PROPN
app01-6401	66	3	ut	ut	PROPN
app01-6401	66	4	∂k(a	∂k(a	PROPN
app01-6401	66	5	)	)	PUNCT
app01-6401	67	1	∂ai	∂ai	PROPN
app01-6401	67	2	u	u	NOUN
app01-6401	67	3	+	+	CCONJ
app01-6401	67	4	µ`i	µ`i	NOUN
app01-6401	67	5	−	−	PROPN
app01-6401	67	6	νi	νi	NOUN
app01-6401	67	7	.	.	PUNCT
app01-6401	68	1	(	(	PUNCT
app01-6401	68	2	9	9	NUM
app01-6401	68	3	)	)	PUNCT
app01-6401	68	4	conditions	condition	NOUN
app01-6401	68	5	(	(	PUNCT
app01-6401	68	6	9	9	NUM
app01-6401	68	7	)	)	PUNCT
app01-6401	68	8	and	and	CCONJ
app01-6401	68	9	(	(	PUNCT
app01-6401	68	10	7d	7d	NUM
app01-6401	68	11	)	)	PUNCT
app01-6401	68	12	then	then	ADV
app01-6401	68	13	imply	imply	VERB
app01-6401	68	14	that	that	SCONJ
app01-6401	68	15	at	at	ADP
app01-6401	68	16	the	the	DET
app01-6401	68	17	optimum	optimum	NOUN
app01-6401	68	18	,	,	PUNCT
app01-6401	68	19	the	the	DET
app01-6401	68	20	frame	frame	NOUN
app01-6401	68	21	elements	element	NOUN
app01-6401	68	22	with	with	ADP
app01-6401	68	23	ai	ai	INTJ
app01-6401	68	24	>	>	X
app01-6401	68	25	ε	ε	PROPN
app01-6401	68	26	have	have	VERB
app01-6401	68	27	equal	equal	ADJ
app01-6401	68	28	constant	constant	ADJ
app01-6401	68	29	energy	energy	NOUN
app01-6401	68	30	µ	µ	X
app01-6401	68	31	=	=	SYM
app01-6401	68	32	1	1	NUM
app01-6401	68	33	`	`	PUNCT
app01-6401	68	34	i	i	PRON
app01-6401	68	35	ut	ut	PROPN
app01-6401	68	36	∂k(a	∂k(a	PROPN
app01-6401	68	37	)	)	PUNCT
app01-6401	69	1	∂ai	∂ai	PROPN
app01-6401	69	2	u−	u−	NOUN
app01-6401	69	3	2	2	NUM
app01-6401	69	4	`	`	PUNCT
app01-6401	69	5	i	i	PRON
app01-6401	69	6	ut	ut	PROPN
app01-6401	69	7	∂f(a	∂f(a	PROPN
app01-6401	69	8	)	)	PUNCT
app01-6401	70	1	∂ai	∂ai	PROPN
app01-6401	70	2	.	.	PUNCT
app01-6401	71	1	(	(	PUNCT
app01-6401	71	2	10	10	NUM
app01-6401	71	3	)	)	PUNCT
app01-6401	71	4	aiming	aim	VERB
app01-6401	71	5	to	to	PART
app01-6401	71	6	satisfy	satisfy	VERB
app01-6401	71	7	(	(	PUNCT
app01-6401	71	8	10	10	NUM
app01-6401	71	9	)	)	PUNCT
app01-6401	71	10	,	,	PUNCT
app01-6401	71	11	optimality	optimality	NOUN
app01-6401	71	12	criteria	criterion	NOUN
app01-6401	71	13	methods	method	NOUN
app01-6401	71	14	[	[	X
app01-6401	71	15	1	1	X
app01-6401	71	16	]	]	PUNCT
app01-6401	71	17	build	build	VERB
app01-6401	71	18	update	update	NOUN
app01-6401	71	19	schemes	scheme	NOUN
app01-6401	71	20	which	which	PRON
app01-6401	71	21	increase	increase	VERB
app01-6401	71	22	stiffnesses	stiffness	NOUN
app01-6401	71	23	of	of	ADP
app01-6401	71	24	elements	element	NOUN
app01-6401	71	25	with	with	ADP
app01-6401	71	26	energies	energy	NOUN
app01-6401	71	27	higher	high	ADJ
app01-6401	71	28	than	than	ADP
app01-6401	71	29	µ	µ	NUM
app01-6401	71	30	,	,	PUNCT
app01-6401	71	31	and	and	CCONJ
app01-6401	71	32	,	,	PUNCT
app01-6401	71	33	conversely	conversely	ADV
app01-6401	71	34	,	,	PUNCT
app01-6401	71	35	decrease	decrease	VERB
app01-6401	71	36	stiffnesses	stiffness	NOUN
app01-6401	71	37	of	of	ADP
app01-6401	71	38	elements	element	NOUN
app01-6401	71	39	with	with	ADP
app01-6401	71	40	the	the	DET
app01-6401	71	41	energy	energy	NOUN
app01-6401	71	42	lower	low	ADJ
app01-6401	71	43	than	than	ADP
app01-6401	71	44	µ.	µ.	VERB
app01-6401	71	45	the	the	DET
app01-6401	71	46	levels	level	NOUN
app01-6401	71	47	are	be	AUX
app01-6401	71	48	balanced	balance	VERB
app01-6401	71	49	in	in	ADP
app01-6401	71	50	an	an	DET
app01-6401	71	51	iterative	iterative	NOUN
app01-6401	71	52	process	process	NOUN
app01-6401	71	53	,	,	PUNCT
app01-6401	71	54	based	base	VERB
app01-6401	71	55	on	on	ADP
app01-6401	71	56	the	the	DET
app01-6401	71	57	value	value	NOUN
app01-6401	71	58	of	of	ADP
app01-6401	71	59	µ.	µ.	NOUN
app01-6401	71	60	in	in	ADP
app01-6401	71	61	each	each	DET
app01-6401	71	62	iteration	iteration	NOUN
app01-6401	71	63	,	,	PUNCT
app01-6401	71	64	the	the	DET
app01-6401	71	65	relative	relative	ADJ
app01-6401	71	66	change	change	NOUN
app01-6401	71	67	of	of	ADP
app01-6401	71	68	the	the	DET
app01-6401	71	69	design	design	NOUN
app01-6401	71	70	variables	variable	NOUN
app01-6401	71	71	is	be	AUX
app01-6401	71	72	bounded	bound	VERB
app01-6401	71	73	by	by	ADP
app01-6401	71	74	the	the	DET
app01-6401	71	75	move	move	NOUN
app01-6401	71	76	limit	limit	NOUN
app01-6401	71	77	ζ	ζ	NOUN
app01-6401	71	78	,	,	PUNCT
app01-6401	71	79	assumed	assume	VERB
app01-6401	71	80	as	as	ADP
app01-6401	71	81	ζ	ζ	NOUN
app01-6401	71	82	=	=	NOUN
app01-6401	71	83	0.2	0.2	NUM
app01-6401	71	84	in	in	ADP
app01-6401	71	85	this	this	DET
app01-6401	71	86	paper	paper	NOUN
app01-6401	71	87	.	.	PUNCT
app01-6401	72	1	consequently	consequently	ADV
app01-6401	72	2	,	,	PUNCT
app01-6401	72	3	the	the	DET
app01-6401	72	4	fix	fix	NOUN
app01-6401	72	5	-	-	PUNCT
app01-6401	72	6	point	point	NOUN
app01-6401	72	7	update	update	NOUN
app01-6401	72	8	scheme	scheme	NOUN
app01-6401	72	9	reads	read	NOUN
app01-6401	72	10	as	as	ADP
app01-6401	72	11	a	a	DET
app01-6401	72	12	(	(	PUNCT
app01-6401	72	13	k+1	k+1	NOUN
app01-6401	72	14	)	)	PUNCT
app01-6401	72	15	i	i	NOUN
app01-6401	72	16	=	=	SYM
app01-6401	72	17	max	max	PROPN
app01-6401	72	18	{	{	PUNCT
app01-6401	72	19	max	max	PROPN
app01-6401	72	20	{	{	PUNCT
app01-6401	72	21	(	(	PUNCT
app01-6401	72	22	1−	1−	NUM
app01-6401	72	23	ζ)a(k	ζ)a(k	NOUN
app01-6401	72	24	)	)	PUNCT
app01-6401	72	25	i	i	PRON
app01-6401	72	26	,	,	PUNCT
app01-6401	72	27	ε	ε	PROPN
app01-6401	72	28	}	}	PUNCT
app01-6401	72	29	,	,	PUNCT
app01-6401	72	30	a	a	DET
app01-6401	72	31	(	(	PUNCT
app01-6401	72	32	k	k	NOUN
app01-6401	72	33	)	)	PUNCT
app01-6401	72	34	i	i	PRON
app01-6401	73	1	[	[	PUNCT
app01-6401	73	2	b	b	X
app01-6401	73	3	(	(	PUNCT
app01-6401	73	4	k	k	NOUN
app01-6401	73	5	)	)	PUNCT
app01-6401	73	6	i	i	PRON
app01-6401	73	7	]	]	X
app01-6401	73	8	η	η	X
app01-6401	73	9	}	}	PUNCT
app01-6401	73	10	(	(	PUNCT
app01-6401	73	11	11	11	NUM
app01-6401	73	12	)	)	PUNCT
app01-6401	73	13	with	with	ADP
app01-6401	73	14	the	the	DET
app01-6401	73	15	tuning	tuning	NOUN
app01-6401	73	16	parameter	parameter	NOUN
app01-6401	73	17	η	η	PROPN
app01-6401	73	18	=	=	PROPN
app01-6401	73	19	0.3	0.3	NUM
app01-6401	73	20	and	and	CCONJ
app01-6401	73	21	with	with	ADP
app01-6401	73	22	b	b	PROPN
app01-6401	73	23	(	(	PUNCT
app01-6401	73	24	k	k	NOUN
app01-6401	73	25	)	)	PUNCT
app01-6401	74	1	i	i	PRON
app01-6401	74	2	=	=	SYM
app01-6401	74	3	ut	ut	PROPN
app01-6401	74	4	∂k(a	∂k(a	PROPN
app01-6401	74	5	)	)	PUNCT
app01-6401	75	1	∂ai	∂ai	PROPN
app01-6401	75	2	u−	u−	NUM
app01-6401	75	3	2ut	2ut	NOUN
app01-6401	75	4	∂f(a	∂f(a	PROPN
app01-6401	75	5	)	)	PUNCT
app01-6401	76	1	∂ai	∂ai	PROPN
app01-6401	76	2	µ`i	µ`i	NOUN
app01-6401	76	3	.	.	PUNCT
app01-6401	77	1	(	(	PUNCT
app01-6401	77	2	12	12	NUM
app01-6401	77	3	)	)	PUNCT
app01-6401	77	4	clearly	clearly	ADV
app01-6401	77	5	,	,	PUNCT
app01-6401	77	6	if	if	SCONJ
app01-6401	77	7	∀i	∀i	NOUN
app01-6401	77	8	∈	∈	NOUN
app01-6401	77	9	{	{	PUNCT
app01-6401	77	10	1	1	NUM
app01-6401	77	11	,	,	PUNCT
app01-6401	77	12	.	.	PUNCT
app01-6401	77	13	.	.	PUNCT
app01-6401	77	14	.	.	PUNCT
app01-6401	78	1	,	,	PUNCT
app01-6401	78	2	ne	ne	PROPN
app01-6401	78	3	}	}	PUNCT
app01-6401	78	4	:	:	PUNCT
app01-6401	78	5	b(k	b(k	NOUN
app01-6401	78	6	)	)	PUNCT
app01-6401	79	1	i	i	PRON
app01-6401	79	2	=	=	NOUN
app01-6401	79	3	1	1	NUM
app01-6401	79	4	,	,	PUNCT
app01-6401	79	5	we	we	PRON
app01-6401	79	6	reach	reach	VERB
app01-6401	79	7	a	a	DET
app01-6401	79	8	local	local	ADJ
app01-6401	79	9	minimum	minimum	NOUN
app01-6401	79	10	as	as	ADP
app01-6401	79	11	(	(	PUNCT
app01-6401	79	12	10	10	NUM
app01-6401	79	13	)	)	PUNCT
app01-6401	79	14	is	be	AUX
app01-6401	79	15	satisfied	satisfied	ADJ
app01-6401	79	16	.	.	PUNCT
app01-6401	80	1	combination	combination	NOUN
app01-6401	80	2	of	of	ADP
app01-6401	80	3	(	(	PUNCT
app01-6401	80	4	11	11	NUM
app01-6401	80	5	)	)	PUNCT
app01-6401	80	6	,	,	PUNCT
app01-6401	80	7	(	(	PUNCT
app01-6401	80	8	12	12	NUM
app01-6401	80	9	)	)	PUNCT
app01-6401	80	10	with	with	ADP
app01-6401	80	11	(	(	PUNCT
app01-6401	80	12	5c	5c	NUM
app01-6401	80	13	)	)	PUNCT
app01-6401	80	14	allows	allow	VERB
app01-6401	80	15	us	we	PRON
app01-6401	80	16	to	to	PART
app01-6401	80	17	write	write	VERB
app01-6401	80	18	the	the	DET
app01-6401	80	19	(	(	PUNCT
app01-6401	80	20	current	current	ADJ
app01-6401	80	21	)	)	PUNCT
app01-6401	80	22	volume	volume	NOUN
app01-6401	80	23	v	v	X
app01-6401	80	24	=	=	SYM
app01-6401	80	25	`	`	PUNCT
app01-6401	80	26	ta(k+1	ta(k+1	NOUN
app01-6401	80	27	)	)	PUNCT
app01-6401	80	28	as	as	ADP
app01-6401	80	29	a	a	DET
app01-6401	80	30	continuous	continuous	ADJ
app01-6401	80	31	function	function	NOUN
app01-6401	80	32	of	of	ADP
app01-6401	80	33	the	the	DET
app01-6401	80	34	multiplier	multipli	ADJ
app01-6401	80	35	µ.	µ.	NOUN
app01-6401	80	36	it	it	PRON
app01-6401	80	37	can	can	AUX
app01-6401	80	38	be	be	AUX
app01-6401	80	39	seen	see	VERB
app01-6401	80	40	from	from	ADP
app01-6401	80	41	(	(	PUNCT
app01-6401	80	42	12	12	NUM
app01-6401	80	43	)	)	PUNCT
app01-6401	80	44	that	that	SCONJ
app01-6401	80	45	v	v	NOUN
app01-6401	80	46	is	be	AUX
app01-6401	80	47	a	a	DET
app01-6401	80	48	non	non	ADJ
app01-6401	80	49	-	-	ADJ
app01-6401	80	50	increasing	increasing	ADJ
app01-6401	80	51	function	function	NOUN
app01-6401	80	52	of	of	ADP
app01-6401	80	53	µ.	µ.	NOUN
app01-6401	80	54	in	in	ADP
app01-6401	80	55	fact	fact	NOUN
app01-6401	80	56	,	,	PUNCT
app01-6401	80	57	strict	strict	ADJ
app01-6401	80	58	decreasing	decreasing	NOUN
app01-6401	80	59	occurs	occur	NOUN
app01-6401	80	60	when	when	SCONJ
app01-6401	80	61	εi	εi	VERB
app01-6401	80	62	<	<	X
app01-6401	80	63	a.	a.	NOUN
app01-6401	80	64	consequently	consequently	ADV
app01-6401	80	65	,	,	PUNCT
app01-6401	80	66	the	the	DET
app01-6401	80	67	bisection	bisection	NOUN
app01-6401	80	68	algorithm	algorithm	NOUN
app01-6401	80	69	is	be	AUX
app01-6401	80	70	used	use	VERB
app01-6401	80	71	to	to	PART
app01-6401	80	72	find	find	VERB
app01-6401	80	73	µ	µ	PRON
app01-6401	80	74	such	such	ADJ
app01-6401	80	75	that	that	SCONJ
app01-6401	80	76	the	the	DET
app01-6401	80	77	volume	volume	NOUN
app01-6401	80	78	constraint	constraint	NOUN
app01-6401	80	79	is	be	AUX
app01-6401	80	80	satisfied	satisfied	ADJ
app01-6401	80	81	.	.	PUNCT
app01-6401	81	1	2.3	2.3	NUM
app01-6401	81	2	.	.	PUNCT
app01-6401	82	1	nonlinear	nonlinear	ADJ
app01-6401	82	2	semidefinite	semidefinite	PROPN
app01-6401	82	3	programming	programming	NOUN
app01-6401	82	4	in	in	ADP
app01-6401	82	5	this	this	DET
app01-6401	82	6	section	section	NOUN
app01-6401	82	7	,	,	PUNCT
app01-6401	82	8	we	we	PRON
app01-6401	82	9	describe	describe	VERB
app01-6401	82	10	another	another	DET
app01-6401	82	11	approach	approach	NOUN
app01-6401	82	12	to	to	PART
app01-6401	82	13	eliminate	eliminate	VERB
app01-6401	82	14	the	the	DET
app01-6401	82	15	displacement	displacement	ADJ
app01-6401	82	16	field	field	NOUN
app01-6401	82	17	variables	variable	VERB
app01-6401	82	18	u	u	NOUN
app01-6401	82	19	from	from	ADP
app01-6401	82	20	the	the	DET
app01-6401	82	21	optimization	optimization	NOUN
app01-6401	82	22	problem	problem	NOUN
app01-6401	82	23	formulation	formulation	NOUN
app01-6401	82	24	.	.	PUNCT
app01-6401	83	1	first	first	ADV
app01-6401	83	2	,	,	PUNCT
app01-6401	83	3	let	let	VERB
app01-6401	83	4	us	we	PRON
app01-6401	83	5	rewrite	rewrite	VERB
app01-6401	83	6	(	(	PUNCT
app01-6401	83	7	5	5	NUM
app01-6401	83	8	)	)	PUNCT
app01-6401	83	9	as	as	ADP
app01-6401	83	10	min	min	PROPN
app01-6401	83	11	a	a	PROPN
app01-6401	83	12	,	,	PUNCT
app01-6401	83	13	c	c	PROPN
app01-6401	83	14	c	c	X
app01-6401	83	15	(	(	PUNCT
app01-6401	83	16	13a	13a	PROPN
app01-6401	83	17	)	)	PUNCT
app01-6401	83	18	s.t	s.t	PROPN
app01-6401	83	19	.	.	PUNCT
app01-6401	83	20	c−	c−	PROPN
app01-6401	83	21	f(a)tk(a)†f(a	f(a)tk(a)†f(a	PROPN
app01-6401	83	22	)	)	PUNCT
app01-6401	83	23	=	=	SYM
app01-6401	83	24	0	0	NUM
app01-6401	83	25	,	,	PUNCT
app01-6401	83	26	(	(	PUNCT
app01-6401	83	27	13b	13b	NOUN
app01-6401	83	28	)	)	PUNCT
app01-6401	83	29	`	`	PUNCT
app01-6401	83	30	ta	ta	X
app01-6401	83	31	≤	≤	NUM
app01-6401	83	32	v	v	NOUN
app01-6401	83	33	,	,	PUNCT
app01-6401	83	34	(	(	PUNCT
app01-6401	83	35	13c	13c	NOUN
app01-6401	83	36	)	)	PUNCT
app01-6401	83	37	a	a	DET
app01-6401	83	38	≥	≥	NOUN
app01-6401	83	39	0	0	NUM
app01-6401	83	40	,	,	PUNCT
app01-6401	83	41	(	(	PUNCT
app01-6401	83	42	13d	13d	NOUN
app01-6401	83	43	)	)	PUNCT
app01-6401	83	44	where	where	SCONJ
app01-6401	83	45	k(a)†	k(a)†	PROPN
app01-6401	83	46	denotes	denote	VERB
app01-6401	83	47	the	the	DET
app01-6401	83	48	moore	moore	PROPN
app01-6401	83	49	-	-	PUNCT
app01-6401	83	50	penrose	penrose	PROPN
app01-6401	83	51	pseudoinverse	pseudoinverse	NOUN
app01-6401	83	52	of	of	ADP
app01-6401	83	53	k(a	k(a	NOUN
app01-6401	83	54	)	)	PUNCT
app01-6401	83	55	.	.	PUNCT
app01-6401	84	1	because	because	SCONJ
app01-6401	84	2	we	we	PRON
app01-6401	84	3	require	require	VERB
app01-6401	84	4	that	that	SCONJ
app01-6401	84	5	∀a	∀a	NOUN
app01-6401	84	6	>	>	X
app01-6401	84	7	0	0	NUM
app01-6401	84	8	:	:	PUNCT
app01-6401	84	9	k(a	k(a	PROPN
app01-6401	84	10	)	)	PUNCT
app01-6401	84	11	�	�	PROPN
app01-6401	84	12	0	0	NUM
app01-6401	84	13	,	,	PUNCT
app01-6401	84	14	the	the	DET
app01-6401	84	15	(	(	PUNCT
app01-6401	84	16	possible	possible	ADJ
app01-6401	84	17	)	)	PUNCT
app01-6401	84	18	singularity	singularity	NOUN
app01-6401	84	19	of	of	ADP
app01-6401	84	20	k(a	k(a	NOUN
app01-6401	84	21	)	)	PUNCT
app01-6401	84	22	is	be	AUX
app01-6401	84	23	caused	cause	VERB
app01-6401	84	24	exclusively	exclusively	ADV
app01-6401	84	25	by	by	ADP
app01-6401	84	26	zero	zero	NUM
app01-6401	84	27	rows	row	NOUN
app01-6401	84	28	and	and	CCONJ
app01-6401	84	29	columns	column	NOUN
app01-6401	84	30	belonging	belong	VERB
app01-6401	84	31	to	to	ADP
app01-6401	84	32	the	the	DET
app01-6401	84	33	degrees	degree	NOUN
app01-6401	84	34	of	of	ADP
app01-6401	84	35	freedom	freedom	NOUN
app01-6401	84	36	without	without	ADP
app01-6401	84	37	any	any	DET
app01-6401	84	38	attached	attach	VERB
app01-6401	84	39	finite	finite	NOUN
app01-6401	84	40	element	element	NOUN
app01-6401	84	41	(	(	PUNCT
app01-6401	84	42	or	or	CCONJ
app01-6401	84	43	,	,	PUNCT
app01-6401	84	44	equivalently	equivalently	ADV
app01-6401	84	45	,	,	PUNCT
app01-6401	84	46	ai	ai	VERB
app01-6401	84	47	=	=	NOUN
app01-6401	84	48	0	0	NUM
app01-6401	84	49	for	for	ADP
app01-6401	84	50	all	all	DET
app01-6401	84	51	attached	attach	VERB
app01-6401	84	52	elements	element	NOUN
app01-6401	84	53	in	in	ADP
app01-6401	84	54	that	that	DET
app01-6401	84	55	node	node	NOUN
app01-6401	84	56	)	)	PUNCT
app01-6401	84	57	.	.	PUNCT
app01-6401	85	1	this	this	DET
app01-6401	85	2	assumption	assumption	NOUN
app01-6401	85	3	allows	allow	VERB
app01-6401	85	4	us	we	PRON
app01-6401	85	5	to	to	PART
app01-6401	85	6	partition	partition	VERB
app01-6401	85	7	the	the	DET
app01-6401	85	8	stiffness	stiffness	ADJ
app01-6401	85	9	matrix	matrix	NOUN
app01-6401	85	10	into	into	ADP
app01-6401	85	11	a	a	DET
app01-6401	85	12	positive	positive	ADJ
app01-6401	85	13	definite	definite	ADJ
app01-6401	85	14	principal	principal	ADJ
app01-6401	85	15	submatrix	submatrix	NOUN
app01-6401	85	16	k̂(a	k̂(a	NOUN
app01-6401	85	17	)	)	PUNCT
app01-6401	85	18	and	and	CCONJ
app01-6401	85	19	zero	zero	NUM
app01-6401	85	20	blocks	block	NOUN
app01-6401	85	21	,	,	PUNCT
app01-6401	85	22	so	so	SCONJ
app01-6401	85	23	that	that	SCONJ
app01-6401	85	24	the	the	DET
app01-6401	85	25	pseudo	pseudo	NOUN
app01-6401	85	26	-	-	ADJ
app01-6401	85	27	inverse	inverse	NOUN
app01-6401	85	28	equals	equal	VERB
app01-6401	85	29	k(a)†	k(a)†	PROPN
app01-6401	85	30	=	=	PUNCT
app01-6401	85	31	(	(	PUNCT
app01-6401	86	1	k̂(a)−1	k̂(a)−1	NUM
app01-6401	86	2	0	0	NUM
app01-6401	86	3	0	0	NUM
app01-6401	86	4	t	t	NOUN
app01-6401	86	5	0	0	NUM
app01-6401	86	6	)	)	PUNCT
app01-6401	86	7	.	.	PUNCT
app01-6401	87	1	(	(	PUNCT
app01-6401	87	2	14	14	NUM
app01-6401	87	3	)	)	PUNCT
app01-6401	87	4	using	use	VERB
app01-6401	87	5	the	the	DET
app01-6401	87	6	same	same	ADJ
app01-6401	87	7	partitioning	partitioning	NOUN
app01-6401	87	8	,	,	PUNCT
app01-6401	87	9	the	the	DET
app01-6401	87	10	force	force	NOUN
app01-6401	87	11	vector	vector	PROPN
app01-6401	87	12	f(a	f(a	PROPN
app01-6401	87	13	)	)	PUNCT
app01-6401	87	14	is	be	AUX
app01-6401	87	15	split	split	VERB
app01-6401	87	16	into	into	ADP
app01-6401	87	17	(	(	PUNCT
app01-6401	87	18	f̂(a)t	f̂(a)t	PROPN
app01-6401	87	19	0	0	NUM
app01-6401	87	20	t	t	NOUN
app01-6401	87	21	)	)	PUNCT
app01-6401	87	22	t	t	NOUN
app01-6401	87	23	,	,	PUNCT
app01-6401	87	24	in	in	ADP
app01-6401	87	25	which	which	PRON
app01-6401	87	26	the	the	DET
app01-6401	87	27	term	term	NOUN
app01-6401	87	28	0	0	NUM
app01-6401	87	29	t	t	PROPN
app01-6401	87	30	appears	appear	VERB
app01-6401	87	31	due	due	ADP
app01-6401	87	32	to	to	ADP
app01-6401	87	33	the	the	DET
app01-6401	87	34	original	original	ADJ
app01-6401	87	35	assumption	assumption	NOUN
app01-6401	87	36	that	that	SCONJ
app01-6401	87	37	f(a	f(a	NOUN
app01-6401	87	38	)	)	PUNCT
app01-6401	87	39	∈	∈	PROPN
app01-6401	87	40	im(k(a	im(k(a	NOUN
app01-6401	87	41	)	)	PUNCT
app01-6401	87	42	)	)	PUNCT
app01-6401	87	43	.	.	PUNCT
app01-6401	88	1	consequently	consequently	ADV
app01-6401	88	2	,	,	PUNCT
app01-6401	88	3	we	we	PRON
app01-6401	88	4	see	see	VERB
app01-6401	88	5	that	that	PRON
app01-6401	88	6	(	(	PUNCT
app01-6401	88	7	13b	13b	NOUN
app01-6401	88	8	)	)	PUNCT
app01-6401	88	9	can	can	AUX
app01-6401	88	10	be	be	AUX
app01-6401	88	11	rewritten	rewrite	VERB
app01-6401	88	12	to	to	ADP
app01-6401	88	13	c−	c−	ADJ
app01-6401	88	14	f̂(a)tk̂(a)−1f̂(a	f̂(a)tk̂(a)−1f̂(a	NOUN
app01-6401	88	15	)	)	PUNCT
app01-6401	88	16	=	=	SYM
app01-6401	88	17	0	0	NUM
app01-6401	88	18	,	,	PUNCT
app01-6401	88	19	(	(	PUNCT
app01-6401	88	20	15	15	NUM
app01-6401	88	21	)	)	PUNCT
app01-6401	88	22	and	and	CCONJ
app01-6401	88	23	(	(	PUNCT
app01-6401	88	24	13	13	NUM
app01-6401	88	25	)	)	PUNCT
app01-6401	88	26	is	be	AUX
app01-6401	88	27	therefore	therefore	ADV
app01-6401	88	28	equivalent	equivalent	ADJ
app01-6401	88	29	to	to	ADP
app01-6401	88	30	(	(	PUNCT
app01-6401	88	31	5	5	NUM
app01-6401	88	32	)	)	PUNCT
app01-6401	88	33	.	.	PUNCT
app01-6401	89	1	from	from	ADP
app01-6401	89	2	(	(	PUNCT
app01-6401	89	3	14	14	NUM
app01-6401	89	4	)	)	PUNCT
app01-6401	89	5	we	we	PRON
app01-6401	89	6	have	have	VERB
app01-6401	89	7	k†(a	k†(a	VERB
app01-6401	89	8	)	)	PUNCT
app01-6401	89	9	�	�	PROPN
app01-6401	89	10	0	0	NUM
app01-6401	89	11	,	,	PUNCT
app01-6401	89	12	so	so	SCONJ
app01-6401	89	13	that	that	SCONJ
app01-6401	89	14	c	c	PROPN
app01-6401	89	15	≥	≥	X
app01-6401	89	16	0	0	NUM
app01-6401	89	17	based	base	VERB
app01-6401	89	18	on	on	ADP
app01-6401	89	19	(	(	PUNCT
app01-6401	89	20	13b	13b	NOUN
app01-6401	89	21	)	)	PUNCT
app01-6401	89	22	.	.	PUNCT
app01-6401	90	1	moreover	moreover	ADV
app01-6401	90	2	,	,	PUNCT
app01-6401	90	3	iff	iff	NOUN
app01-6401	90	4	f̂(a	f̂(a	NOUN
app01-6401	90	5	)	)	PUNCT
app01-6401	90	6	6=	6=	ADP
app01-6401	90	7	0	0	NUM
app01-6401	90	8	,	,	PUNCT
app01-6401	90	9	we	we	PRON
app01-6401	90	10	have	have	VERB
app01-6401	90	11	both	both	DET
app01-6401	90	12	f(a)tk(a)†f(a	f(a)tk(a)†f(a	PROPN
app01-6401	90	13	)	)	PUNCT
app01-6401	90	14	>	>	X
app01-6401	90	15	0	0	PUNCT
app01-6401	91	1	and	and	CCONJ
app01-6401	91	2	c	c	X
app01-6401	91	3	>	>	X
app01-6401	91	4	0	0	NUM
app01-6401	91	5	.	.	PUNCT
app01-6401	92	1	because	because	SCONJ
app01-6401	92	2	we	we	PRON
app01-6401	92	3	minimize	minimize	VERB
app01-6401	92	4	c	c	PROPN
app01-6401	92	5	(	(	PUNCT
app01-6401	92	6	13a	13a	NUM
app01-6401	92	7	)	)	PUNCT
app01-6401	92	8	and	and	CCONJ
app01-6401	92	9	f(a)tk(a)†f(a	f(a)tk(a)†f(a	PROPN
app01-6401	92	10	)	)	PUNCT
app01-6401	92	11	is	be	AUX
app01-6401	92	12	bounded	bound	VERB
app01-6401	92	13	from	from	ADP
app01-6401	92	14	below	below	ADV
app01-6401	92	15	,	,	PUNCT
app01-6401	92	16	(	(	PUNCT
app01-6401	92	17	13b	13b	NOUN
app01-6401	92	18	)	)	PUNCT
app01-6401	92	19	can	can	AUX
app01-6401	92	20	be	be	AUX
app01-6401	92	21	simplified	simplify	VERB
app01-6401	92	22	to	to	ADP
app01-6401	92	23	the	the	DET
app01-6401	92	24	one	one	NUM
app01-6401	92	25	-	-	PUNCT
app01-6401	92	26	sided	sided	ADJ
app01-6401	92	27	inequality	inequality	NOUN
app01-6401	92	28	c−	c−	PROPN
app01-6401	92	29	f(a)tk(a)†f(a	f(a)tk(a)†f(a	PROPN
app01-6401	92	30	)	)	PUNCT
app01-6401	92	31	≥	≥	NOUN
app01-6401	92	32	0	0	NUM
app01-6401	92	33	.	.	PUNCT
app01-6401	93	1	(	(	PUNCT
app01-6401	93	2	16	16	NUM
app01-6401	93	3	)	)	PUNCT
app01-6401	93	4	to	to	PART
app01-6401	93	5	use	use	VERB
app01-6401	93	6	the	the	DET
app01-6401	93	7	generalized	generalize	VERB
app01-6401	93	8	schur	schur	PROPN
app01-6401	93	9	complement	complement	PROPN
app01-6401	93	10	lemma	lemma	PROPN
app01-6401	93	11	,	,	PUNCT
app01-6401	93	12	e.g.	e.g.	ADV
app01-6401	93	13	,	,	PUNCT
app01-6401	93	14	[	[	X
app01-6401	93	15	9	9	NUM
app01-6401	93	16	,	,	PUNCT
app01-6401	93	17	theorem	theorem	VERB
app01-6401	93	18	16.1	16.1	NUM
app01-6401	93	19	]	]	PUNCT
app01-6401	93	20	,	,	PUNCT
app01-6401	93	21	we	we	PRON
app01-6401	93	22	further	far	ADV
app01-6401	93	23	need	need	VERB
app01-6401	93	24	to	to	PART
app01-6401	93	25	show	show	VERB
app01-6401	93	26	that	that	SCONJ
app01-6401	93	27	[	[	PUNCT
app01-6401	93	28	i−k(a)k(a)†	i−k(a)k(a)†	X
app01-6401	93	29	]	]	PUNCT
app01-6401	93	30	f(a	f(a	NOUN
app01-6401	93	31	)	)	PUNCT
app01-6401	94	1	=	=	SYM
app01-6401	94	2	0	0	NUM
app01-6401	95	1	(	(	PUNCT
app01-6401	95	2	17	17	NUM
app01-6401	95	3	)	)	PUNCT
app01-6401	95	4	holds	hold	VERB
app01-6401	95	5	,	,	PUNCT
app01-6401	95	6	with	with	ADP
app01-6401	95	7	i	i	PRON
app01-6401	95	8	denoting	denote	VERB
app01-6401	95	9	the	the	DET
app01-6401	95	10	identity	identity	NOUN
app01-6401	95	11	matrix	matrix	NOUN
app01-6401	95	12	.	.	PUNCT
app01-6401	96	1	indeed	indeed	ADV
app01-6401	96	2	,	,	PUNCT
app01-6401	96	3	(	(	PUNCT
app01-6401	96	4	17	17	NUM
app01-6401	96	5	)	)	PUNCT
app01-6401	96	6	is	be	AUX
app01-6401	96	7	always	always	ADV
app01-6401	96	8	satisfied	satisfied	ADJ
app01-6401	96	9	because	because	SCONJ
app01-6401	96	10	f(a	f(a	NOUN
app01-6401	96	11	)	)	PUNCT
app01-6401	96	12	∈	∈	PROPN
app01-6401	96	13	im(k(a	im(k(a	NOUN
app01-6401	96	14	)	)	PUNCT
app01-6401	96	15	)	)	PUNCT
app01-6401	96	16	,	,	PUNCT
app01-6401	96	17	so	so	SCONJ
app01-6401	96	18	that	that	SCONJ
app01-6401	96	19	we	we	PRON
app01-6401	96	20	can	can	AUX
app01-6401	96	21	substitute	substitute	VERB
app01-6401	96	22	f(a	f(a	PROPN
app01-6401	96	23	)	)	PUNCT
app01-6401	96	24	by	by	ADP
app01-6401	96	25	k(a)v	k(a)v	PROPN
app01-6401	96	26	,	,	PUNCT
app01-6401	96	27	where	where	SCONJ
app01-6401	96	28	v	v	NOUN
app01-6401	96	29	is	be	AUX
app01-6401	96	30	a	a	DET
app01-6401	96	31	vector	vector	NOUN
app01-6401	96	32	of	of	ADP
app01-6401	96	33	coefficients	coefficient	NOUN
app01-6401	96	34	of	of	ADP
app01-6401	96	35	the	the	DET
app01-6401	96	36	linear	linear	ADJ
app01-6401	96	37	combination	combination	NOUN
app01-6401	96	38	.	.	PUNCT
app01-6401	97	1	then	then	ADV
app01-6401	97	2	,	,	PUNCT
app01-6401	97	3	(	(	PUNCT
app01-6401	97	4	17	17	NUM
app01-6401	97	5	)	)	PUNCT
app01-6401	97	6	is	be	AUX
app01-6401	97	7	equivalent	equivalent	ADJ
app01-6401	97	8	to	to	ADP
app01-6401	97	9	[	[	PUNCT
app01-6401	97	10	k(a)−k(a)k(a)†k(a	k(a)−k(a)k(a)†k(a	PROPN
app01-6401	97	11	)	)	PUNCT
app01-6401	97	12	]	]	PUNCT
app01-6401	98	1	v	v	X
app01-6401	98	2	=	=	SYM
app01-6401	98	3	0	0	NUM
app01-6401	98	4	,	,	PUNCT
app01-6401	98	5	(	(	PUNCT
app01-6401	98	6	18	18	NUM
app01-6401	98	7	)	)	PUNCT
app01-6401	98	8	with	with	ADP
app01-6401	98	9	the	the	DET
app01-6401	98	10	term	term	NOUN
app01-6401	98	11	in	in	ADP
app01-6401	98	12	the	the	DET
app01-6401	98	13	square	square	ADJ
app01-6401	98	14	brackets	bracket	NOUN
app01-6401	98	15	always	always	ADV
app01-6401	98	16	zero	zero	NUM
app01-6401	99	1	[	[	X
app01-6401	99	2	9	9	NUM
app01-6401	99	3	,	,	PUNCT
app01-6401	99	4	lemma	lemma	PROPN
app01-6401	99	5	14.1	14.1	NUM
app01-6401	99	6	]	]	PUNCT
app01-6401	99	7	,	,	PUNCT
app01-6401	99	8	as	as	ADP
app01-6401	99	9	k(a	k(a	NOUN
app01-6401	99	10	)	)	PUNCT
app01-6401	99	11	is	be	AUX
app01-6401	99	12	symmetric	symmetric	ADJ
app01-6401	99	13	.	.	PUNCT
app01-6401	100	1	finally	finally	ADV
app01-6401	100	2	,	,	PUNCT
app01-6401	100	3	application	application	NOUN
app01-6401	100	4	of	of	ADP
app01-6401	100	5	the	the	DET
app01-6401	100	6	generalized	generalize	VERB
app01-6401	100	7	schur	schur	PROPN
app01-6401	100	8	complement	complement	PROPN
app01-6401	100	9	lemma	lemma	PROPN
app01-6401	100	10	to	to	ADP
app01-6401	100	11	(	(	PUNCT
app01-6401	100	12	16	16	NUM
app01-6401	100	13	)	)	PUNCT
app01-6401	100	14	and	and	CCONJ
app01-6401	100	15	(	(	PUNCT
app01-6401	100	16	18	18	NUM
app01-6401	100	17	)	)	PUNCT
app01-6401	100	18	provides	provide	VERB
app01-6401	100	19	us	we	PRON
app01-6401	100	20	with	with	ADP
app01-6401	100	21	min	min	PROPN
app01-6401	100	22	a	a	PROPN
app01-6401	100	23	,	,	PUNCT
app01-6401	100	24	c	c	PROPN
app01-6401	100	25	c	c	X
app01-6401	100	26	(	(	PUNCT
app01-6401	100	27	19a	19a	NUM
app01-6401	100	28	)	)	PUNCT
app01-6401	100	29	s.t	s.t	PROPN
app01-6401	100	30	.	.	PUNCT
app01-6401	101	1	(	(	PUNCT
app01-6401	101	2	c	c	PROPN
app01-6401	101	3	−f(a)t	−f(a)t	PROPN
app01-6401	101	4	−f(a)t	−f(a)t	PROPN
app01-6401	101	5	k(a	k(a	PROPN
app01-6401	101	6	)	)	PUNCT
app01-6401	101	7	)	)	PUNCT
app01-6401	101	8	�	�	PROPN
app01-6401	101	9	0	0	NUM
app01-6401	101	10	,	,	PUNCT
app01-6401	101	11	(	(	PUNCT
app01-6401	101	12	19b	19b	NOUN
app01-6401	101	13	)	)	PUNCT
app01-6401	101	14	`	`	PUNCT
app01-6401	101	15	ta	ta	ADP
app01-6401	101	16	≤	≤	NUM
app01-6401	101	17	v	v	NOUN
app01-6401	101	18	,	,	PUNCT
app01-6401	101	19	(	(	PUNCT
app01-6401	101	20	19c	19c	X
app01-6401	101	21	)	)	PUNCT
app01-6401	101	22	a	a	DET
app01-6401	101	23	≥	≥	NOUN
app01-6401	101	24	0	0	NUM
app01-6401	101	25	,	,	PUNCT
app01-6401	101	26	(	(	PUNCT
app01-6401	101	27	19d	19d	NOUN
app01-6401	101	28	)	)	PUNCT
app01-6401	101	29	119	119	NUM
app01-6401	101	30	m.	m.	NOUN
app01-6401	101	31	tyburec	tyburec	NOUN
app01-6401	101	32	,	,	PUNCT
app01-6401	101	33	j.	j.	PROPN
app01-6401	101	34	zeman	zeman	PROPN
app01-6401	101	35	,	,	PUNCT
app01-6401	101	36	m.	m.	NOUN
app01-6401	101	37	kružík	kružík	PROPN
app01-6401	101	38	,	,	PUNCT
app01-6401	101	39	d.	d.	PROPN
app01-6401	101	40	henrion	henrion	PROPN
app01-6401	101	41	acta	acta	PROPN
app01-6401	101	42	polytechnica	polytechnica	PROPN
app01-6401	101	43	ctu	ctu	NOUN
app01-6401	101	44	proceedings	proceeding	NOUN
app01-6401	101	45	which	which	PRON
app01-6401	101	46	is	be	AUX
app01-6401	101	47	a	a	DET
app01-6401	101	48	non	non	ADJ
app01-6401	101	49	-	-	ADJ
app01-6401	101	50	linear	linear	ADJ
app01-6401	101	51	semidefinite	semidefinite	NOUN
app01-6401	101	52	program	program	NOUN
app01-6401	101	53	equivalent	equivalent	ADJ
app01-6401	101	54	to	to	ADP
app01-6401	101	55	both	both	PRON
app01-6401	101	56	(	(	PUNCT
app01-6401	101	57	13	13	NUM
app01-6401	101	58	)	)	PUNCT
app01-6401	101	59	and	and	CCONJ
app01-6401	101	60	(	(	PUNCT
app01-6401	101	61	5	5	NUM
app01-6401	101	62	)	)	PUNCT
app01-6401	101	63	.	.	PUNCT
app01-6401	102	1	moreover	moreover	ADV
app01-6401	102	2	,	,	PUNCT
app01-6401	102	3	if	if	SCONJ
app01-6401	102	4	we	we	PRON
app01-6401	102	5	substitute	substitute	VERB
app01-6401	102	6	c	c	PROPN
app01-6401	102	7	with	with	ADP
app01-6401	102	8	1	1	NUM
app01-6401	102	9	/	/	SYM
app01-6401	102	10	s	s	NOUN
app01-6401	102	11	,	,	PUNCT
app01-6401	102	12	where	where	SCONJ
app01-6401	102	13	0	0	PUNCT
app01-6401	102	14	<	<	X
app01-6401	102	15	s	s	X
app01-6401	102	16	<	<	X
app01-6401	102	17	∞	∞	PROPN
app01-6401	102	18	is	be	AUX
app01-6401	102	19	a	a	DET
app01-6401	102	20	measure	measure	NOUN
app01-6401	102	21	of	of	ADP
app01-6401	102	22	stiffness	stiffness	NOUN
app01-6401	102	23	,	,	PUNCT
app01-6401	102	24	(	(	PUNCT
app01-6401	102	25	19	19	NUM
app01-6401	102	26	)	)	PUNCT
app01-6401	102	27	is	be	AUX
app01-6401	102	28	,	,	PUNCT
app01-6401	102	29	after	after	ADP
app01-6401	102	30	the	the	DET
app01-6401	102	31	application	application	NOUN
app01-6401	102	32	of	of	ADP
app01-6401	102	33	the	the	DET
app01-6401	102	34	(	(	PUNCT
app01-6401	102	35	standard	standard	NOUN
app01-6401	102	36	)	)	PUNCT
app01-6401	102	37	schur	schur	PROPN
app01-6401	102	38	complement	complement	PROPN
app01-6401	102	39	lemma	lemma	PROPN
app01-6401	102	40	,	,	PUNCT
app01-6401	102	41	e.g.	e.g.	ADV
app01-6401	102	42	,	,	PUNCT
app01-6401	102	43	[	[	X
app01-6401	102	44	9	9	NUM
app01-6401	102	45	,	,	PUNCT
app01-6401	102	46	proposition	proposition	NOUN
app01-6401	102	47	16.1	16.1	NUM
app01-6401	102	48	]	]	PUNCT
app01-6401	102	49	,	,	PUNCT
app01-6401	102	50	reducible	reducible	ADJ
app01-6401	102	51	to	to	ADP
app01-6401	102	52	max	max	PROPN
app01-6401	102	53	a	a	PRON
app01-6401	102	54	,	,	PUNCT
app01-6401	102	55	s	s	NOUN
app01-6401	102	56	s	s	X
app01-6401	102	57	(	(	PUNCT
app01-6401	102	58	20a	20a	NOUN
app01-6401	102	59	)	)	PUNCT
app01-6401	102	60	s.t	s.t	PROPN
app01-6401	102	61	.	.	PROPN
app01-6401	102	62	k(a)−	k(a)−	PROPN
app01-6401	102	63	sf(a)f(a)t	sf(a)f(a)t	ADV
app01-6401	102	64	�	�	PROPN
app01-6401	102	65	0	0	NUM
app01-6401	102	66	,	,	PUNCT
app01-6401	102	67	(	(	PUNCT
app01-6401	102	68	20b	20b	NOUN
app01-6401	102	69	)	)	PUNCT
app01-6401	102	70	`	`	PUNCT
app01-6401	102	71	ta	ta	X
app01-6401	102	72	≤	≤	NUM
app01-6401	102	73	v	v	NOUN
app01-6401	102	74	,	,	PUNCT
app01-6401	102	75	(	(	PUNCT
app01-6401	102	76	20c	20c	NOUN
app01-6401	102	77	)	)	PUNCT
app01-6401	102	78	a	a	DET
app01-6401	102	79	≥	≥	NOUN
app01-6401	102	80	0	0	NUM
app01-6401	102	81	,	,	PUNCT
app01-6401	102	82	(	(	PUNCT
app01-6401	102	83	20d	20d	NOUN
app01-6401	102	84	)	)	PUNCT
app01-6401	102	85	which	which	PRON
app01-6401	102	86	is	be	AUX
app01-6401	102	87	a	a	DET
app01-6401	102	88	useful	useful	ADJ
app01-6401	102	89	reformulation	reformulation	NOUN
app01-6401	102	90	when	when	SCONJ
app01-6401	102	91	f	f	PROPN
app01-6401	102	92	is	be	AUX
app01-6401	102	93	constant	constant	ADJ
app01-6401	102	94	,	,	PUNCT
app01-6401	102	95	i.e.	i.e.	X
app01-6401	102	96	,	,	PUNCT
app01-6401	102	97	self	self	NOUN
app01-6401	102	98	-	-	PUNCT
app01-6401	102	99	weight	weight	NOUN
app01-6401	102	100	is	be	AUX
app01-6401	102	101	not	not	PART
app01-6401	102	102	considered	consider	VERB
app01-6401	102	103	.	.	PUNCT
app01-6401	103	1	it	it	PRON
app01-6401	103	2	shall	shall	AUX
app01-6401	103	3	be	be	AUX
app01-6401	103	4	noted	note	VERB
app01-6401	103	5	that	that	SCONJ
app01-6401	103	6	due	due	ADP
app01-6401	103	7	to	to	ADP
app01-6401	103	8	the	the	DET
app01-6401	103	9	polynomial	polynomial	ADJ
app01-6401	103	10	matrix	matrix	NOUN
app01-6401	103	11	inequalities	inequality	NOUN
app01-6401	103	12	(	(	PUNCT
app01-6401	103	13	19b	19b	NOUN
app01-6401	103	14	)	)	PUNCT
app01-6401	103	15	and	and	CCONJ
app01-6401	103	16	(	(	PUNCT
app01-6401	103	17	20b	20b	NOUN
app01-6401	103	18	)	)	PUNCT
app01-6401	103	19	both	both	CCONJ
app01-6401	103	20	the	the	DET
app01-6401	103	21	optimization	optimization	NOUN
app01-6401	103	22	problems	problem	NOUN
app01-6401	103	23	are	be	AUX
app01-6401	103	24	non	non	ADJ
app01-6401	103	25	-	-	ADJ
app01-6401	103	26	convex	convex	ADJ
app01-6401	103	27	in	in	ADP
app01-6401	103	28	general	general	ADJ
app01-6401	103	29	.	.	PUNCT
app01-6401	104	1	they	they	PRON
app01-6401	104	2	can	can	AUX
app01-6401	104	3	still	still	ADV
app01-6401	104	4	be	be	AUX
app01-6401	104	5	solved	solve	VERB
app01-6401	104	6	efficiently	efficiently	ADV
app01-6401	104	7	(	(	PUNCT
app01-6401	104	8	to	to	ADP
app01-6401	104	9	local	local	ADJ
app01-6401	104	10	optimality	optimality	NOUN
app01-6401	104	11	)	)	PUNCT
app01-6401	104	12	using	using	NOUN
app01-6401	104	13	,	,	PUNCT
app01-6401	104	14	e.g.	e.g.	ADV
app01-6401	104	15	,	,	PUNCT
app01-6401	104	16	augmented	augment	VERB
app01-6401	104	17	lagrangian	lagrangian	ADJ
app01-6401	104	18	methods	method	NOUN
app01-6401	104	19	[	[	X
app01-6401	104	20	6	6	NUM
app01-6401	104	21	,	,	PUNCT
app01-6401	104	22	10	10	NUM
app01-6401	104	23	]	]	PUNCT
app01-6401	104	24	.	.	PUNCT
app01-6401	105	1	in	in	ADP
app01-6401	105	2	this	this	DET
app01-6401	105	3	contribution	contribution	NOUN
app01-6401	105	4	,	,	PUNCT
app01-6401	105	5	we	we	PRON
app01-6401	105	6	solve	solve	VERB
app01-6401	105	7	these	these	DET
app01-6401	105	8	problems	problem	NOUN
app01-6401	105	9	using	use	VERB
app01-6401	105	10	the	the	DET
app01-6401	105	11	open	open	ADJ
app01-6401	105	12	-	-	PUNCT
app01-6401	105	13	source	source	NOUN
app01-6401	105	14	penlab	penlab	NOUN
app01-6401	105	15	optimizer	optimizer	NOUN
app01-6401	105	16	[	[	X
app01-6401	105	17	6	6	NUM
app01-6401	105	18	]	]	PUNCT
app01-6401	105	19	.	.	PUNCT
app01-6401	106	1	2.4	2.4	NUM
app01-6401	106	2	.	.	PUNCT
app01-6401	107	1	polynomial	polynomial	ADJ
app01-6401	107	2	optimization	optimization	NOUN
app01-6401	107	3	having	having	AUX
app01-6401	107	4	introduced	introduce	VERB
app01-6401	107	5	three	three	NUM
app01-6401	107	6	different	different	ADJ
app01-6401	107	7	local	local	ADJ
app01-6401	107	8	approaches	approach	NOUN
app01-6401	107	9	to	to	PART
app01-6401	107	10	frame	frame	VERB
app01-6401	107	11	structure	structure	NOUN
app01-6401	107	12	optimization	optimization	NOUN
app01-6401	107	13	,	,	PUNCT
app01-6401	107	14	it	it	PRON
app01-6401	107	15	is	be	AUX
app01-6401	107	16	natural	natural	ADJ
app01-6401	107	17	and	and	CCONJ
app01-6401	107	18	expected	expect	VERB
app01-6401	107	19	that	that	SCONJ
app01-6401	107	20	one	one	PRON
app01-6401	107	21	asks	ask	VERB
app01-6401	107	22	for	for	ADP
app01-6401	107	23	a	a	DET
app01-6401	107	24	global	global	ADJ
app01-6401	107	25	optimization	optimization	NOUN
app01-6401	107	26	technique	technique	NOUN
app01-6401	107	27	.	.	PUNCT
app01-6401	108	1	in	in	ADP
app01-6401	108	2	this	this	DET
app01-6401	108	3	section	section	NOUN
app01-6401	108	4	,	,	PUNCT
app01-6401	108	5	we	we	PRON
app01-6401	108	6	exploit	exploit	VERB
app01-6401	108	7	the	the	DET
app01-6401	108	8	fact	fact	NOUN
app01-6401	108	9	that	that	SCONJ
app01-6401	108	10	although	although	SCONJ
app01-6401	108	11	(	(	PUNCT
app01-6401	108	12	19	19	NUM
app01-6401	108	13	)	)	PUNCT
app01-6401	108	14	is	be	AUX
app01-6401	108	15	non	non	ADJ
app01-6401	108	16	-	-	ADJ
app01-6401	108	17	convex	convex	ADJ
app01-6401	108	18	it	it	PRON
app01-6401	108	19	is	be	AUX
app01-6401	108	20	indeed	indeed	ADV
app01-6401	108	21	a	a	DET
app01-6401	108	22	polynomial	polynomial	ADJ
app01-6401	108	23	optimization	optimization	NOUN
app01-6401	108	24	(	(	PUNCT
app01-6401	108	25	po	po	NOUN
app01-6401	108	26	)	)	PUNCT
app01-6401	108	27	problem	problem	NOUN
app01-6401	108	28	at	at	ADP
app01-6401	108	29	the	the	DET
app01-6401	108	30	same	same	ADJ
app01-6401	108	31	time	time	NOUN
app01-6401	108	32	,	,	PUNCT
app01-6401	108	33	which	which	PRON
app01-6401	108	34	allows	allow	VERB
app01-6401	108	35	us	we	PRON
app01-6401	108	36	to	to	PART
app01-6401	108	37	employ	employ	VERB
app01-6401	108	38	modern	modern	ADJ
app01-6401	108	39	po	po	NOUN
app01-6401	108	40	techniques	technique	NOUN
app01-6401	108	41	,	,	PUNCT
app01-6401	108	42	namely	namely	ADV
app01-6401	108	43	the	the	DET
app01-6401	108	44	lasserre	lasserre	ADJ
app01-6401	108	45	hierarchy	hierarchy	NOUN
app01-6401	109	1	[	[	X
app01-6401	109	2	7	7	NUM
app01-6401	109	3	,	,	PUNCT
app01-6401	109	4	11	11	NUM
app01-6401	109	5	]	]	PUNCT
app01-6401	109	6	,	,	PUNCT
app01-6401	109	7	successively	successively	ADV
app01-6401	109	8	building	build	VERB
app01-6401	109	9	tighter	tight	ADJ
app01-6401	109	10	and	and	CCONJ
app01-6401	109	11	tighter	tight	ADJ
app01-6401	109	12	convex	convex	VERB
app01-6401	109	13	outer	outer	ADJ
app01-6401	109	14	semidefinite	semidefinite	NOUN
app01-6401	109	15	programming	programming	NOUN
app01-6401	109	16	(	(	PUNCT
app01-6401	109	17	sdp	sdp	NOUN
app01-6401	109	18	)	)	PUNCT
app01-6401	109	19	approximations	approximation	NOUN
app01-6401	109	20	called	call	VERB
app01-6401	109	21	relaxations	relaxation	NOUN
app01-6401	109	22	[	[	X
app01-6401	109	23	7	7	NUM
app01-6401	109	24	,	,	PUNCT
app01-6401	109	25	corollary	corollary	NOUN
app01-6401	109	26	4.3	4.3	NUM
app01-6401	109	27	]	]	PUNCT
app01-6401	109	28	.	.	PUNCT
app01-6401	110	1	to	to	PART
app01-6401	110	2	develop	develop	VERB
app01-6401	110	3	a	a	DET
app01-6401	110	4	more	more	ADV
app01-6401	110	5	efficient	efficient	ADJ
app01-6401	110	6	formulation	formulation	NOUN
app01-6401	110	7	suitable	suitable	ADJ
app01-6401	110	8	for	for	ADP
app01-6401	110	9	po	po	NOUN
app01-6401	110	10	,	,	PUNCT
app01-6401	110	11	we	we	PRON
app01-6401	110	12	first	first	ADV
app01-6401	110	13	recognize	recognize	VERB
app01-6401	110	14	that	that	SCONJ
app01-6401	110	15	the	the	DET
app01-6401	110	16	design	design	NOUN
app01-6401	110	17	variables	variable	VERB
app01-6401	110	18	in	in	ADP
app01-6401	110	19	(	(	PUNCT
app01-6401	110	20	19	19	NUM
app01-6401	110	21	)	)	PUNCT
app01-6401	110	22	are	be	AUX
app01-6401	110	23	all	all	PRON
app01-6401	110	24	bounded	bound	VERB
app01-6401	110	25	both	both	CCONJ
app01-6401	110	26	from	from	ADP
app01-6401	110	27	below	below	ADP
app01-6401	110	28	and	and	CCONJ
app01-6401	110	29	above	above	ADV
app01-6401	110	30	:	:	PUNCT
app01-6401	110	31	0≤ai≤	0≤ai≤	NUM
app01-6401	110	32	v	v	X
app01-6401	110	33	`	`	PUNCT
app01-6401	110	34	i	i	PRON
app01-6401	110	35	,	,	PUNCT
app01-6401	110	36	∀i	∀i	NOUN
app01-6401	110	37	∈	∈	NOUN
app01-6401	110	38	{	{	PUNCT
app01-6401	110	39	1	1	NUM
app01-6401	110	40	,	,	PUNCT
app01-6401	110	41	.	.	PUNCT
app01-6401	110	42	.	.	PUNCT
app01-6401	111	1	.	.	PUNCT
app01-6401	111	2	,	,	PUNCT
app01-6401	111	3	ne	ne	PROPN
app01-6401	111	4	}	}	PUNCT
app01-6401	111	5	,	,	PUNCT
app01-6401	111	6	(	(	PUNCT
app01-6401	111	7	21a	21a	X
app01-6401	111	8	)	)	PUNCT
app01-6401	111	9	0≤	0≤	NUM
app01-6401	111	10	c	c	NOUN
app01-6401	111	11	≤	≤	NUM
app01-6401	111	12	ĉ.	ĉ.	NOUN
app01-6401	111	13	(	(	PUNCT
app01-6401	111	14	21b	21b	NOUN
app01-6401	111	15	)	)	PUNCT
app01-6401	111	16	while	while	SCONJ
app01-6401	111	17	the	the	PRON
app01-6401	111	18	lower	low	ADJ
app01-6401	111	19	bound	bind	VERB
app01-6401	111	20	in	in	ADP
app01-6401	111	21	(	(	PUNCT
app01-6401	111	22	21a	21a	NUM
app01-6401	111	23	)	)	PUNCT
app01-6401	111	24	is	be	AUX
app01-6401	111	25	caused	cause	VERB
app01-6401	111	26	by	by	ADP
app01-6401	111	27	the	the	DET
app01-6401	111	28	nonnegativity	nonnegativity	NOUN
app01-6401	111	29	of	of	ADP
app01-6401	111	30	the	the	DET
app01-6401	111	31	cross	cross	ADJ
app01-6401	111	32	-	-	ADJ
app01-6401	111	33	sectional	sectional	ADJ
app01-6401	111	34	areas	area	NOUN
app01-6401	111	35	(	(	PUNCT
app01-6401	111	36	19d	19d	NUM
app01-6401	111	37	)	)	PUNCT
app01-6401	111	38	,	,	PUNCT
app01-6401	111	39	the	the	DET
app01-6401	111	40	upper	upper	ADJ
app01-6401	111	41	bounds	bound	NOUN
app01-6401	111	42	arise	arise	VERB
app01-6401	111	43	from	from	ADP
app01-6401	111	44	the	the	DET
app01-6401	111	45	volume	volume	NOUN
app01-6401	111	46	constraint	constraint	NOUN
app01-6401	111	47	(	(	PUNCT
app01-6401	111	48	19c	19c	NUM
app01-6401	111	49	):	):	PUNCT
app01-6401	111	50	none	none	NOUN
app01-6401	111	51	of	of	ADP
app01-6401	111	52	the	the	DET
app01-6401	111	53	structural	structural	ADJ
app01-6401	111	54	elements	element	NOUN
app01-6401	111	55	can	can	AUX
app01-6401	111	56	occupy	occupy	VERB
app01-6401	111	57	larger	large	ADJ
app01-6401	111	58	volume	volume	NOUN
app01-6401	111	59	than	than	ADP
app01-6401	111	60	v	v	NOUN
app01-6401	111	61	.	.	PUNCT
app01-6401	112	1	in	in	ADP
app01-6401	112	2	the	the	DET
app01-6401	112	3	compliance	compliance	NOUN
app01-6401	112	4	case	case	NOUN
app01-6401	112	5	(	(	PUNCT
app01-6401	112	6	21b	21b	NUM
app01-6401	112	7	)	)	PUNCT
app01-6401	112	8	,	,	PUNCT
app01-6401	112	9	the	the	DET
app01-6401	112	10	lower	low	ADJ
app01-6401	112	11	bound3	bound3	NOUN
app01-6401	112	12	is	be	AUX
app01-6401	112	13	due	due	ADJ
app01-6401	112	14	to	to	ADP
app01-6401	112	15	k(a	k(a	NOUN
app01-6401	112	16	)	)	PUNCT
app01-6401	112	17	�	�	PROPN
app01-6401	112	18	0	0	NUM
app01-6401	112	19	,	,	PUNCT
app01-6401	112	20	recall	recall	VERB
app01-6401	112	21	the	the	DET
app01-6401	112	22	discussion	discussion	NOUN
app01-6401	112	23	in	in	ADP
app01-6401	112	24	section	section	NOUN
app01-6401	112	25	2.3	2.3	NUM
app01-6401	112	26	,	,	PUNCT
app01-6401	112	27	and	and	CCONJ
app01-6401	112	28	the	the	DET
app01-6401	112	29	upper	upper	ADJ
app01-6401	112	30	bound	bound	NOUN
app01-6401	112	31	is	be	AUX
app01-6401	112	32	provided	provide	VERB
app01-6401	112	33	by	by	ADP
app01-6401	112	34	an	an	DET
app01-6401	112	35	arbitrary	arbitrary	ADJ
app01-6401	112	36	feasible	feasible	ADJ
app01-6401	112	37	design	design	NOUN
app01-6401	112	38	,	,	PUNCT
app01-6401	112	39	e.g.	e.g.	ADV
app01-6401	112	40	,	,	PUNCT
app01-6401	112	41	the	the	DET
app01-6401	112	42	uniform	uniform	ADJ
app01-6401	112	43	cross	cross	ADJ
app01-6401	112	44	-	-	ADJ
app01-6401	112	45	sectional	sectional	ADJ
app01-6401	112	46	areas	area	NOUN
app01-6401	112	47	a	a	DET
app01-6401	112	48	=	=	NOUN
app01-6401	112	49	v	v	ADP
app01-6401	112	50	1	1	NUM
app01-6401	112	51	t	t	PROPN
app01-6401	112	52	`	`	PROPN
app01-6401	112	53	1	1	NUM
app01-6401	112	54	,	,	PUNCT
app01-6401	112	55	(	(	PUNCT
app01-6401	112	56	22	22	NUM
app01-6401	112	57	)	)	PUNCT
app01-6401	112	58	which	which	PRON
app01-6401	112	59	are	be	AUX
app01-6401	112	60	used	use	VERB
app01-6401	112	61	for	for	ADP
app01-6401	112	62	the	the	DET
app01-6401	112	63	upper	upper	ADV
app01-6401	112	64	-	-	PUNCT
app01-6401	112	65	bound	bind	VERB
app01-6401	112	66	computation	computation	NOUN
app01-6401	112	67	in	in	ADP
app01-6401	112	68	this	this	DET
app01-6401	112	69	paper	paper	NOUN
app01-6401	112	70	.	.	PUNCT
app01-6401	113	1	then	then	ADV
app01-6401	113	2	,	,	PUNCT
app01-6401	113	3	the	the	DET
app01-6401	113	4	compliance	compliance	NOUN
app01-6401	113	5	bound	bind	VERB
app01-6401	113	6	is	be	AUX
app01-6401	113	7	computed	compute	VERB
app01-6401	113	8	from	from	ADP
app01-6401	113	9	ĉ	ĉ	X
app01-6401	113	10	=	=	SYM
app01-6401	113	11	f(a)tk(a)†f(a	f(a)tk(a)†f(a	PROPN
app01-6401	113	12	)	)	PUNCT
app01-6401	113	13	,	,	PUNCT
app01-6401	113	14	(	(	PUNCT
app01-6401	113	15	23	23	NUM
app01-6401	113	16	)	)	PUNCT
app01-6401	113	17	3	3	NUM
app01-6401	113	18	in	in	ADP
app01-6401	113	19	fact	fact	NOUN
app01-6401	113	20	the	the	DET
app01-6401	113	21	strict	strict	ADJ
app01-6401	113	22	inequality	inequality	NOUN
app01-6401	113	23	0	0	PUNCT
app01-6401	113	24	<	<	X
app01-6401	113	25	c	c	PROPN
app01-6401	113	26	is	be	AUX
app01-6401	113	27	satisfied	satisfied	ADJ
app01-6401	113	28	in	in	ADP
app01-6401	113	29	all	all	DET
app01-6401	113	30	nontrivial	nontrivial	ADJ
app01-6401	113	31	optimization	optimization	NOUN
app01-6401	113	32	problems	problem	NOUN
app01-6401	113	33	.	.	PUNCT
app01-6401	114	1	where	where	SCONJ
app01-6401	114	2	k(a)†	k(a)†	PROPN
app01-6401	114	3	reduces	reduce	VERB
app01-6401	114	4	to	to	PART
app01-6401	114	5	k(a)−1	k(a)−1	VERB
app01-6401	114	6	in	in	ADP
app01-6401	114	7	the	the	DET
app01-6401	114	8	case	case	NOUN
app01-6401	114	9	of	of	ADP
app01-6401	114	10	(	(	PUNCT
app01-6401	114	11	22	22	NUM
app01-6401	114	12	)	)	PUNCT
app01-6401	114	13	.	.	PUNCT
app01-6401	115	1	to	to	PART
app01-6401	115	2	improve	improve	VERB
app01-6401	115	3	numerical	numerical	ADJ
app01-6401	115	4	stability	stability	NOUN
app01-6401	115	5	of	of	ADP
app01-6401	115	6	the	the	DET
app01-6401	115	7	solution	solution	NOUN
app01-6401	115	8	process	process	NOUN
app01-6401	115	9	,	,	PUNCT
app01-6401	115	10	we	we	PRON
app01-6401	115	11	state	state	VERB
app01-6401	115	12	the	the	DET
app01-6401	115	13	optimization	optimization	NOUN
app01-6401	115	14	problem	problem	NOUN
app01-6401	115	15	in	in	ADP
app01-6401	115	16	terms	term	NOUN
app01-6401	115	17	of	of	ADP
app01-6401	115	18	the	the	DET
app01-6401	115	19	scaled	scale	VERB
app01-6401	115	20	cross	cross	ADJ
app01-6401	115	21	-	-	ADJ
app01-6401	115	22	sectional	sectional	ADJ
app01-6401	115	23	areas	area	NOUN
app01-6401	115	24	asc	asc	PROPN
app01-6401	115	25	and	and	CCONJ
app01-6401	115	26	scaled	scale	VERB
app01-6401	115	27	compliance	compliance	NOUN
app01-6401	115	28	csc	csc	PROPN
app01-6401	115	29	instead	instead	ADV
app01-6401	115	30	of	of	ADP
app01-6401	115	31	the	the	DET
app01-6401	115	32	original	original	ADJ
app01-6401	115	33	a	a	PRON
app01-6401	115	34	and	and	CCONJ
app01-6401	115	35	c	c	NOUN
app01-6401	115	36	,	,	PUNCT
app01-6401	115	37	where	where	SCONJ
app01-6401	115	38	the	the	DET
app01-6401	115	39	scaled	scale	VERB
app01-6401	115	40	variables	variable	NOUN
app01-6401	115	41	are	be	AUX
app01-6401	115	42	defined	define	VERB
app01-6401	115	43	in	in	ADP
app01-6401	115	44	the	the	DET
app01-6401	115	45	[	[	X
app01-6401	115	46	−1	−1	NOUN
app01-6401	115	47	,	,	PUNCT
app01-6401	115	48	1	1	NUM
app01-6401	115	49	]	]	ADJ
app01-6401	115	50	domain	domain	NOUN
app01-6401	115	51	.	.	PUNCT
app01-6401	116	1	therefore	therefore	ADV
app01-6401	116	2	,	,	PUNCT
app01-6401	116	3	we	we	PRON
app01-6401	116	4	have	have	AUX
app01-6401	116	5	ai	ai	NOUN
app01-6401	116	6	=	=	SYM
app01-6401	116	7	v	v	PROPN
app01-6401	116	8	(	(	PUNCT
app01-6401	116	9	asc	asc	PROPN
app01-6401	116	10	,	,	PUNCT
app01-6401	116	11	i	i	PROPN
app01-6401	116	12	+	+	NOUN
app01-6401	116	13	1	1	X
app01-6401	116	14	)	)	PUNCT
app01-6401	116	15	2`i	2`i	NUM
app01-6401	116	16	(	(	PUNCT
app01-6401	116	17	24	24	NUM
app01-6401	116	18	)	)	PUNCT
app01-6401	116	19	and	and	CCONJ
app01-6401	116	20	c	c	X
app01-6401	117	1	=	=	SYM
app01-6401	117	2	ĉ(csc	ĉ(csc	PROPN
app01-6401	117	3	+	+	NOUN
app01-6401	117	4	1	1	NUM
app01-6401	117	5	)	)	PUNCT
app01-6401	117	6	2	2	NUM
app01-6401	117	7	.	.	PUNCT
app01-6401	118	1	(	(	PUNCT
app01-6401	118	2	25	25	NUM
app01-6401	118	3	)	)	PUNCT
app01-6401	118	4	rewriting	rewrite	VERB
app01-6401	118	5	(	(	PUNCT
app01-6401	118	6	21	21	NUM
app01-6401	118	7	)	)	PUNCT
app01-6401	118	8	in	in	ADP
app01-6401	118	9	terms	term	NOUN
app01-6401	118	10	of	of	ADP
app01-6401	118	11	asc	asc	PROPN
app01-6401	118	12	,	,	PUNCT
app01-6401	118	13	i	i	PRON
app01-6401	118	14	and	and	CCONJ
app01-6401	118	15	csc	csc	PROPN
app01-6401	118	16	as	as	ADP
app01-6401	118	17	unit	unit	NOUN
app01-6401	118	18	ball	ball	NOUN
app01-6401	118	19	constraints	constraints	PROPN
app01-6401	118	20	a2	a2	PROPN
app01-6401	118	21	sc	sc	PROPN
app01-6401	118	22	,	,	PUNCT
app01-6401	118	23	i	i	PROPN
app01-6401	118	24	≤	≤	ADV
app01-6401	118	25	1	1	NUM
app01-6401	118	26	,	,	PUNCT
app01-6401	118	27	∀i	∀i	NOUN
app01-6401	118	28	∈	∈	NOUN
app01-6401	118	29	{	{	PUNCT
app01-6401	118	30	1	1	NUM
app01-6401	118	31	,	,	PUNCT
app01-6401	118	32	.	.	PUNCT
app01-6401	118	33	.	.	PUNCT
app01-6401	118	34	.	.	PUNCT
app01-6401	119	1	,	,	PUNCT
app01-6401	119	2	ne	ne	PROPN
app01-6401	119	3	}	}	PUNCT
app01-6401	119	4	,	,	PUNCT
app01-6401	119	5	(	(	PUNCT
app01-6401	119	6	26a	26a	NOUN
app01-6401	119	7	)	)	PUNCT
app01-6401	119	8	c2	c2	PROPN
app01-6401	119	9	sc	sc	PROPN
app01-6401	119	10	≤	≤	ADV
app01-6401	119	11	1	1	NUM
app01-6401	119	12	,	,	PUNCT
app01-6401	119	13	(	(	PUNCT
app01-6401	119	14	26b	26b	NOUN
app01-6401	119	15	)	)	PUNCT
app01-6401	119	16	we	we	PRON
app01-6401	119	17	finally	finally	ADV
app01-6401	119	18	arrive	arrive	VERB
app01-6401	119	19	at	at	ADP
app01-6401	119	20	an	an	DET
app01-6401	119	21	equivalent	equivalent	ADJ
app01-6401	119	22	formulation	formulation	NOUN
app01-6401	119	23	to	to	ADP
app01-6401	119	24	(	(	PUNCT
app01-6401	119	25	19	19	NUM
app01-6401	119	26	)	)	PUNCT
app01-6401	119	27	,	,	PUNCT
app01-6401	119	28	min	min	PROPN
app01-6401	119	29	asc	asc	PROPN
app01-6401	119	30	,	,	PUNCT
app01-6401	119	31	csc	csc	PROPN
app01-6401	119	32	0.5ĉ(csc	0.5ĉ(csc	NUM
app01-6401	119	33	+	+	CCONJ
app01-6401	119	34	1	1	NUM
app01-6401	119	35	)	)	PUNCT
app01-6401	119	36	(	(	PUNCT
app01-6401	119	37	27a	27a	NUM
app01-6401	119	38	)	)	PUNCT
app01-6401	119	39	s.t	s.t	PROPN
app01-6401	119	40	.	.	PUNCT
app01-6401	119	41	(	(	PUNCT
app01-6401	119	42	0.5ĉ(csc	0.5ĉ(csc	NUM
app01-6401	119	43	+	+	CCONJ
app01-6401	119	44	1	1	NUM
app01-6401	119	45	)	)	PUNCT
app01-6401	119	46	−f(asc)t	−f(asc)t	PRON
app01-6401	120	1	−f(asc)t	−f(asc)t	NUM
app01-6401	120	2	k(asc	k(asc	NOUN
app01-6401	120	3	)	)	PUNCT
app01-6401	120	4	)	)	PUNCT
app01-6401	120	5	�	�	PROPN
app01-6401	120	6	0	0	NUM
app01-6401	120	7	,	,	PUNCT
app01-6401	120	8	(	(	PUNCT
app01-6401	120	9	27b	27b	NUM
app01-6401	120	10	)	)	PUNCT
app01-6401	120	11	2−	2−	NUM
app01-6401	120	12	ne	ne	NOUN
app01-6401	120	13	−	−	PROPN
app01-6401	120	14	1tasc	1tasc	NUM
app01-6401	120	15	≥	≥	NOUN
app01-6401	120	16	0	0	NUM
app01-6401	120	17	,	,	PUNCT
app01-6401	120	18	(	(	PUNCT
app01-6401	120	19	27c	27c	NUM
app01-6401	120	20	)	)	PUNCT
app01-6401	120	21	1−	1−	NUM
app01-6401	120	22	a2	a2	PROPN
app01-6401	120	23	sc	sc	PROPN
app01-6401	120	24	,	,	PUNCT
app01-6401	120	25	i	i	PRON
app01-6401	120	26	≥	≥	VERB
app01-6401	120	27	0	0	NUM
app01-6401	120	28	,	,	PUNCT
app01-6401	120	29	(	(	PUNCT
app01-6401	120	30	27d	27d	NUM
app01-6401	120	31	)	)	PUNCT
app01-6401	120	32	1−	1−	NUM
app01-6401	121	1	c2	c2	PROPN
app01-6401	121	2	sc	sc	PROPN
app01-6401	121	3	≥	≥	PROPN
app01-6401	121	4	0	0	NUM
app01-6401	121	5	.	.	PUNCT
app01-6401	121	6	(	(	PUNCT
app01-6401	121	7	27e	27e	NOUN
app01-6401	121	8	)	)	PUNCT
app01-6401	121	9	in	in	ADP
app01-6401	121	10	(	(	PUNCT
app01-6401	121	11	27	27	NUM
app01-6401	121	12	)	)	PUNCT
app01-6401	121	13	,	,	PUNCT
app01-6401	121	14	the	the	DET
app01-6401	121	15	objective	objective	ADJ
app01-6401	121	16	function	function	NOUN
app01-6401	121	17	(	(	PUNCT
app01-6401	121	18	27a	27a	NUM
app01-6401	121	19	)	)	PUNCT
app01-6401	121	20	and	and	CCONJ
app01-6401	121	21	also	also	ADV
app01-6401	121	22	the	the	DET
app01-6401	121	23	constraints	constraint	NOUN
app01-6401	121	24	(	(	PUNCT
app01-6401	121	25	27b)–(27e	27b)–(27e	NUM
app01-6401	121	26	)	)	PUNCT
app01-6401	121	27	are	be	AUX
app01-6401	121	28	all	all	ADV
app01-6401	121	29	polynomial	polynomial	ADJ
app01-6401	121	30	inequalities4	inequalities4	NOUN
app01-6401	121	31	non	non	ADJ
app01-6401	121	32	-	-	ADJ
app01-6401	121	33	negative	negative	ADJ
app01-6401	121	34	in	in	ADP
app01-6401	121	35	the	the	DET
app01-6401	121	36	feasible	feasible	ADJ
app01-6401	121	37	region	region	NOUN
app01-6401	121	38	of	of	ADP
app01-6401	121	39	(	(	PUNCT
app01-6401	121	40	27	27	NUM
app01-6401	121	41	)	)	PUNCT
app01-6401	121	42	,	,	PUNCT
app01-6401	121	43	which	which	PRON
app01-6401	121	44	is	be	AUX
app01-6401	121	45	therefore	therefore	ADV
app01-6401	121	46	a	a	DET
app01-6401	121	47	semi	semi	ADJ
app01-6401	121	48	-	-	ADJ
app01-6401	121	49	algebraic	algebraic	ADJ
app01-6401	121	50	set	set	NOUN
app01-6401	121	51	.	.	PUNCT
app01-6401	122	1	4the	4the	NUM
app01-6401	122	2	entries	entry	NOUN
app01-6401	122	3	in	in	ADP
app01-6401	122	4	the	the	DET
app01-6401	122	5	pmi	pmi	PROPN
app01-6401	122	6	(	(	PUNCT
app01-6401	122	7	27b	27b	NUM
app01-6401	122	8	)	)	PUNCT
app01-6401	122	9	are	be	AUX
app01-6401	122	10	polynomials	polynomial	NOUN
app01-6401	122	11	,	,	PUNCT
app01-6401	122	12	so	so	SCONJ
app01-6401	122	13	that	that	SCONJ
app01-6401	122	14	the	the	DET
app01-6401	122	15	feasible	feasible	ADJ
app01-6401	122	16	region	region	NOUN
app01-6401	122	17	of	of	ADP
app01-6401	122	18	the	the	DET
app01-6401	122	19	pmi	pmi	PROPN
app01-6401	122	20	is	be	AUX
app01-6401	122	21	a	a	DET
app01-6401	122	22	semi	semi	ADJ
app01-6401	122	23	-	-	ADJ
app01-6401	122	24	algebraic	algebraic	ADJ
app01-6401	122	25	set	set	NOUN
app01-6401	122	26	.	.	PUNCT
app01-6401	123	1	alternatively	alternatively	ADV
app01-6401	123	2	,	,	PUNCT
app01-6401	123	3	we	we	PRON
app01-6401	123	4	may	may	AUX
app01-6401	123	5	require	require	VERB
app01-6401	123	6	the	the	DET
app01-6401	123	7	roots	root	NOUN
app01-6401	123	8	of	of	ADP
app01-6401	123	9	the	the	DET
app01-6401	123	10	characteristic	characteristic	ADJ
app01-6401	123	11	polynomial	polynomial	NOUN
app01-6401	123	12	of	of	ADP
app01-6401	123	13	(	(	PUNCT
app01-6401	123	14	27b	27b	NUM
app01-6401	123	15	)	)	PUNCT
app01-6401	123	16	to	to	PART
app01-6401	123	17	be	be	AUX
app01-6401	123	18	non	non	ADJ
app01-6401	123	19	-	-	ADJ
app01-6401	123	20	negative	negative	ADJ
app01-6401	123	21	.	.	PUNCT
app01-6401	124	1	we	we	PRON
app01-6401	124	2	refer	refer	VERB
app01-6401	124	3	to	to	ADP
app01-6401	124	4	[	[	X
app01-6401	124	5	12	12	NUM
app01-6401	124	6	]	]	PUNCT
app01-6401	124	7	for	for	ADP
app01-6401	124	8	more	more	ADJ
app01-6401	124	9	details	detail	NOUN
app01-6401	124	10	.	.	PUNCT
app01-6401	125	1	120	120	NUM
app01-6401	125	2	vol	vol	NOUN
app01-6401	125	3	.	.	PUNCT
app01-6401	126	1	26/2020	26/2020	NUM
app01-6401	126	2	on	on	ADP
app01-6401	126	3	optimum	optimum	ADJ
app01-6401	126	4	design	design	NOUN
app01-6401	126	5	of	of	ADP
app01-6401	126	6	frame	frame	NOUN
app01-6401	126	7	structures	structure	NOUN
app01-6401	126	8	the	the	DET
app01-6401	126	9	optimization	optimization	NOUN
app01-6401	126	10	problem	problem	NOUN
app01-6401	126	11	(	(	PUNCT
app01-6401	126	12	27	27	NUM
app01-6401	126	13	)	)	PUNCT
app01-6401	126	14	can	can	AUX
app01-6401	126	15	readily	readily	ADV
app01-6401	126	16	be	be	AUX
app01-6401	126	17	solved	solve	VERB
app01-6401	126	18	by	by	ADP
app01-6401	126	19	building	build	VERB
app01-6401	126	20	the	the	DET
app01-6401	126	21	(	(	PUNCT
app01-6401	126	22	lasserre	lasserre	PROPN
app01-6401	126	23	)	)	PUNCT
app01-6401	126	24	hierarchy	hierarchy	NOUN
app01-6401	126	25	of	of	ADP
app01-6401	126	26	convex	convex	ADJ
app01-6401	126	27	linear	linear	ADJ
app01-6401	126	28	sdp	sdp	NOUN
app01-6401	126	29	relaxations	relaxation	NOUN
app01-6401	126	30	,	,	PUNCT
app01-6401	126	31	with	with	ADP
app01-6401	126	32	a	a	DET
app01-6401	126	33	monotonously	monotonously	ADV
app01-6401	126	34	converging	converge	VERB
app01-6401	126	35	objective	objective	ADJ
app01-6401	126	36	functions	function	NOUN
app01-6401	126	37	to	to	ADP
app01-6401	126	38	the	the	DET
app01-6401	126	39	global	global	ADJ
app01-6401	126	40	optimum	optimum	NOUN
app01-6401	126	41	.	.	PUNCT
app01-6401	127	1	the	the	DET
app01-6401	127	2	hierarchy	hierarchy	NOUN
app01-6401	127	3	is	be	AUX
app01-6401	127	4	generated	generate	VERB
app01-6401	127	5	by	by	ADP
app01-6401	127	6	the	the	DET
app01-6401	127	7	gloptipoly	gloptipoly	ADJ
app01-6401	127	8	[	[	X
app01-6401	127	9	13	13	NUM
app01-6401	127	10	]	]	PUNCT
app01-6401	127	11	software	software	NOUN
app01-6401	127	12	package	package	NOUN
app01-6401	127	13	interfaced	interface	VERB
app01-6401	127	14	with	with	ADP
app01-6401	127	15	the	the	DET
app01-6401	127	16	yalmip	yalmip	NOUN
app01-6401	127	17	[	[	X
app01-6401	127	18	14	14	NUM
app01-6401	127	19	]	]	X
app01-6401	127	20	toolbox	toolbox	NOUN
app01-6401	127	21	,	,	PUNCT
app01-6401	127	22	and	and	CCONJ
app01-6401	127	23	the	the	DET
app01-6401	127	24	underlying	underlie	VERB
app01-6401	127	25	sdp	sdp	NOUN
app01-6401	127	26	relaxations	relaxation	NOUN
app01-6401	127	27	are	be	AUX
app01-6401	127	28	solved	solve	VERB
app01-6401	127	29	by	by	ADP
app01-6401	127	30	the	the	DET
app01-6401	127	31	state	state	NOUN
app01-6401	127	32	-	-	PUNCT
app01-6401	127	33	of	of	ADP
app01-6401	127	34	-	-	PUNCT
app01-6401	127	35	the	the	DET
app01-6401	127	36	-	-	PUNCT
app01-6401	127	37	art	art	NOUN
app01-6401	127	38	mosek	mosek	NOUN
app01-6401	127	39	optimizer	optimizer	NOUN
app01-6401	128	1	[	[	X
app01-6401	128	2	8	8	NUM
app01-6401	128	3	]	]	PUNCT
app01-6401	128	4	.	.	PUNCT
app01-6401	129	1	2.4.1	2.4.1	NUM
app01-6401	129	2	.	.	PUNCT
app01-6401	129	3	solution	solution	NOUN
app01-6401	129	4	process	process	NOUN
app01-6401	129	5	to	to	PART
app01-6401	129	6	simplify	simplify	VERB
app01-6401	129	7	the	the	DET
app01-6401	129	8	notation	notation	NOUN
app01-6401	129	9	,	,	PUNCT
app01-6401	129	10	let	let	VERB
app01-6401	129	11	us	we	PRON
app01-6401	129	12	now	now	ADV
app01-6401	129	13	denote	denote	VERB
app01-6401	129	14	the	the	DET
app01-6401	129	15	objective	objective	ADJ
app01-6401	129	16	function	function	NOUN
app01-6401	129	17	polynomial	polynomial	ADJ
app01-6401	129	18	(	(	PUNCT
app01-6401	129	19	27a	27a	NUM
app01-6401	129	20	)	)	PUNCT
app01-6401	129	21	by	by	ADP
app01-6401	129	22	p0	p0	NOUN
app01-6401	129	23	,	,	PUNCT
app01-6401	129	24	and	and	CCONJ
app01-6401	129	25	the	the	DET
app01-6401	129	26	constraining	constrain	VERB
app01-6401	129	27	polynomials	polynomial	NOUN
app01-6401	129	28	(	(	PUNCT
app01-6401	129	29	27c	27c	NOUN
app01-6401	129	30	)	)	PUNCT
app01-6401	129	31	to	to	ADP
app01-6401	129	32	(	(	PUNCT
app01-6401	129	33	27e	27e	NOUN
app01-6401	129	34	)	)	PUNCT
app01-6401	129	35	by	by	ADP
app01-6401	129	36	p1	p1	PROPN
app01-6401	129	37	to	to	ADP
app01-6401	129	38	p3	p3	PROPN
app01-6401	129	39	,	,	PUNCT
app01-6401	129	40	respectively	respectively	ADV
app01-6401	129	41	.	.	PUNCT
app01-6401	130	1	further	far	ADV
app01-6401	130	2	,	,	PUNCT
app01-6401	130	3	let	let	VERB
app01-6401	130	4	p4	p4	ADJ
app01-6401	130	5	denote	denote	VERB
app01-6401	130	6	the	the	DET
app01-6401	130	7	pmi	pmi	PROPN
app01-6401	130	8	(	(	PUNCT
app01-6401	130	9	27b	27b	NUM
app01-6401	130	10	)	)	PUNCT
app01-6401	130	11	and	and	CCONJ
app01-6401	130	12	let	let	VERB
app01-6401	130	13	x	x	PUNCT
app01-6401	130	14	=	=	PRON
app01-6401	130	15	(	(	PUNCT
app01-6401	130	16	csc	csc	PROPN
app01-6401	130	17	asc,1	asc,1	PROPN
app01-6401	130	18	.	.	PUNCT
app01-6401	130	19	.	.	PUNCT
app01-6401	130	20	.	.	PUNCT
app01-6401	131	1	asc	asc	PROPN
app01-6401	131	2	,	,	PUNCT
app01-6401	131	3	ne	ne	PROPN
app01-6401	131	4	)	)	PUNCT
app01-6401	131	5	t	t	PROPN
app01-6401	131	6	(	(	PUNCT
app01-6401	131	7	28	28	NUM
app01-6401	131	8	)	)	PUNCT
app01-6401	131	9	be	be	AUX
app01-6401	131	10	the	the	DET
app01-6401	131	11	vector	vector	NOUN
app01-6401	131	12	of	of	ADP
app01-6401	131	13	the	the	DET
app01-6401	131	14	design	design	NOUN
app01-6401	131	15	variables	variable	NOUN
app01-6401	131	16	.	.	PUNCT
app01-6401	132	1	moreover	moreover	ADV
app01-6401	132	2	,	,	PUNCT
app01-6401	132	3	let	let	VERB
app01-6401	132	4	br(x	br(x	X
app01-6401	132	5	)	)	PUNCT
app01-6401	132	6	=	=	PUNCT
app01-6401	133	1	(	(	PUNCT
app01-6401	133	2	1	1	NUM
app01-6401	133	3	x1	x1	NUM
app01-6401	133	4	x2	x2	INTJ
app01-6401	133	5	.	.	PUNCT
app01-6401	133	6	.	.	PUNCT
app01-6401	133	7	.	.	PUNCT
app01-6401	134	1	xne+1	xne+1	PROPN
app01-6401	134	2	x2	x2	PROPN
app01-6401	134	3	1	1	NUM
app01-6401	134	4	x1x2	x1x2	PUNCT
app01-6401	134	5	.	.	PUNCT
app01-6401	134	6	.	.	PUNCT
app01-6401	134	7	.	.	PUNCT
app01-6401	135	1	x1xne+1	x1xne+1	PROPN
app01-6401	136	1	x2	x2	PROPN
app01-6401	137	1	2	2	NUM
app01-6401	137	2	x2x3	x2x3	INTJ
app01-6401	137	3	.	.	PUNCT
app01-6401	137	4	.	.	PUNCT
app01-6401	137	5	.	.	PUNCT
app01-6401	138	1	x2	x2	PROPN
app01-6401	138	2	ne+1	ne+1	PROPN
app01-6401	138	3	.	.	PUNCT
app01-6401	138	4	.	.	PUNCT
app01-6401	138	5	.	.	PUNCT
app01-6401	139	1	xr1	xr1	PROPN
app01-6401	139	2	.	.	PUNCT
app01-6401	139	3	.	.	PUNCT
app01-6401	139	4	.	.	PUNCT
app01-6401	140	1	xrne+1	xrne+1	PROPN
app01-6401	140	2	)	)	PUNCT
app01-6401	141	1	t	t	PROPN
app01-6401	141	2	(	(	PUNCT
app01-6401	141	3	29	29	NUM
app01-6401	141	4	)	)	PUNCT
app01-6401	141	5	denote	denote	VERB
app01-6401	141	6	the	the	DET
app01-6401	141	7	polynomial	polynomial	ADJ
app01-6401	141	8	space	space	NOUN
app01-6401	141	9	basis	basis	NOUN
app01-6401	141	10	of	of	ADP
app01-6401	141	11	the	the	DET
app01-6401	141	12	maximum	maximum	PROPN
app01-6401	141	13	degree	degree	NOUN
app01-6401	141	14	r.	r.	PROPN
app01-6401	141	15	then	then	ADV
app01-6401	141	16	,	,	PUNCT
app01-6401	141	17	we	we	PRON
app01-6401	141	18	can	can	AUX
app01-6401	141	19	express	express	VERB
app01-6401	141	20	each	each	PRON
app01-6401	141	21	of	of	ADP
app01-6401	141	22	the	the	DET
app01-6401	141	23	polynomials	polynomial	NOUN
app01-6401	141	24	pj	pj	PROPN
app01-6401	141	25	,	,	PUNCT
app01-6401	141	26	j	j	PROPN
app01-6401	141	27	∈	∈	PROPN
app01-6401	141	28	{	{	PUNCT
app01-6401	141	29	0	0	NUM
app01-6401	141	30	,	,	PUNCT
app01-6401	141	31	.	.	PUNCT
app01-6401	141	32	.	.	PUNCT
app01-6401	142	1	.	.	PUNCT
app01-6401	143	1	,	,	PUNCT
app01-6401	143	2	3	3	X
app01-6401	143	3	}	}	PUNCT
app01-6401	143	4	as	as	ADP
app01-6401	143	5	a	a	DET
app01-6401	143	6	linear	linear	ADJ
app01-6401	143	7	combination	combination	NOUN
app01-6401	143	8	pj(x	pj(x	NOUN
app01-6401	143	9	)	)	PUNCT
app01-6401	144	1	=	=	SYM
app01-6401	144	2	|br(x)|∑	|br(x)|∑	X
app01-6401	144	3	β=1	β=1	SYM
app01-6401	144	4	pα	pα	PROPN
app01-6401	144	5	,	,	PUNCT
app01-6401	144	6	j	j	NOUN
app01-6401	144	7	,	,	PUNCT
app01-6401	144	8	β(xα)β	β(xα)β	NOUN
app01-6401	144	9	(	(	PUNCT
app01-6401	144	10	30	30	NUM
app01-6401	144	11	)	)	PUNCT
app01-6401	144	12	of	of	ADP
app01-6401	144	13	monomials	monomial	NOUN
app01-6401	144	14	xα	xα	PUNCT
app01-6401	144	15	=	=	PUNCT
app01-6401	144	16	ne+1∏	ne+1∏	PROPN
app01-6401	144	17	m=1	m=1	X
app01-6401	144	18	xαm	xαm	PROPN
app01-6401	144	19	m	m	PROPN
app01-6401	144	20	,	,	PUNCT
app01-6401	144	21	ne+1∑	ne+1∑	PROPN
app01-6401	144	22	m=1	m=1	PROPN
app01-6401	144	23	αm	αm	NOUN
app01-6401	144	24	≤	≤	PROPN
app01-6401	144	25	r	r	NOUN
app01-6401	144	26	,	,	PUNCT
app01-6401	144	27	(	(	PUNCT
app01-6401	144	28	31	31	NUM
app01-6401	144	29	)	)	PUNCT
app01-6401	144	30	indexed	index	VERB
app01-6401	144	31	in	in	ADP
app01-6401	144	32	the	the	DET
app01-6401	144	33	basis	basis	NOUN
app01-6401	144	34	br(x	br(x	NOUN
app01-6401	144	35	)	)	PUNCT
app01-6401	144	36	.	.	PUNCT
app01-6401	145	1	the	the	DET
app01-6401	145	2	vectors	vector	NOUN
app01-6401	145	3	α	α	PROPN
app01-6401	145	4	associate	associate	VERB
app01-6401	145	5	a	a	DET
app01-6401	145	6	non	non	ADJ
app01-6401	145	7	-	-	ADJ
app01-6401	145	8	negative	negative	ADJ
app01-6401	145	9	integer	integer	NOUN
app01-6401	145	10	number	number	NOUN
app01-6401	145	11	with	with	ADP
app01-6401	145	12	each	each	DET
app01-6401	145	13	element	element	NOUN
app01-6401	145	14	in	in	ADP
app01-6401	145	15	x	x	NOUN
app01-6401	145	16	,	,	PUNCT
app01-6401	145	17	and	and	CCONJ
app01-6401	145	18	the	the	DET
app01-6401	145	19	vector	vector	NOUN
app01-6401	145	20	pα	pα	PROPN
app01-6401	145	21	,	,	PUNCT
app01-6401	145	22	j	j	PROPN
app01-6401	145	23	contains	contain	VERB
app01-6401	145	24	coefficients	coefficient	NOUN
app01-6401	145	25	of	of	ADP
app01-6401	145	26	the	the	DET
app01-6401	145	27	linear	linear	ADJ
app01-6401	145	28	combinations	combination	NOUN
app01-6401	145	29	of	of	ADP
app01-6401	145	30	the	the	DET
app01-6401	145	31	monomials	monomial	NOUN
app01-6401	145	32	.	.	PUNCT
app01-6401	146	1	notice	notice	VERB
app01-6401	146	2	that∑ne+1	that∑ne+1	PROPN
app01-6401	146	3	m=1	m=1	PROPN
app01-6401	146	4	αm	αm	NOUN
app01-6401	146	5	≤	≤	NOUN
app01-6401	146	6	dj	dj	NOUN
app01-6401	146	7	,	,	PUNCT
app01-6401	146	8	where	where	SCONJ
app01-6401	146	9	dj	dj	NOUN
app01-6401	146	10	stands	stand	VERB
app01-6401	146	11	for	for	ADP
app01-6401	146	12	the	the	DET
app01-6401	146	13	degree	degree	NOUN
app01-6401	146	14	of	of	ADP
app01-6401	146	15	the	the	DET
app01-6401	146	16	polynomial	polynomial	ADJ
app01-6401	146	17	pj	pj	PROPN
app01-6401	146	18	.	.	PUNCT
app01-6401	147	1	a	a	DET
app01-6401	147	2	similar	similar	ADJ
app01-6401	147	3	approach	approach	NOUN
app01-6401	147	4	is	be	AUX
app01-6401	147	5	also	also	ADV
app01-6401	147	6	applied	apply	VERB
app01-6401	147	7	to	to	ADP
app01-6401	147	8	the	the	DET
app01-6401	147	9	elements	element	NOUN
app01-6401	147	10	of	of	ADP
app01-6401	147	11	p4	p4	ADJ
app01-6401	147	12	[	[	X
app01-6401	147	13	12	12	NUM
app01-6401	147	14	]	]	PUNCT
app01-6401	147	15	.	.	PUNCT
app01-6401	148	1	further	far	ADV
app01-6401	148	2	,	,	PUNCT
app01-6401	148	3	introducing	introduce	VERB
app01-6401	148	4	y	y	PROPN
app01-6401	148	5	,	,	PUNCT
app01-6401	148	6	with	with	ADP
app01-6401	148	7	its	its	PRON
app01-6401	148	8	components	component	NOUN
app01-6401	148	9	yβ	yβ	NOUN
app01-6401	148	10	corresponding	correspond	VERB
app01-6401	148	11	to	to	ADP
app01-6401	148	12	a	a	DET
app01-6401	148	13	monomial	monomial	NOUN
app01-6401	148	14	in	in	ADP
app01-6401	148	15	the	the	DET
app01-6401	148	16	basis	basis	NOUN
app01-6401	148	17	br(x	br(x	NOUN
app01-6401	148	18	)	)	PUNCT
app01-6401	148	19	,	,	PUNCT
app01-6401	148	20	we	we	PRON
app01-6401	148	21	build	build	VERB
app01-6401	148	22	the	the	DET
app01-6401	148	23	lasserre	lasserre	ADJ
app01-6401	148	24	hierarchy	hierarchy	NOUN
app01-6401	148	25	of	of	ADP
app01-6401	148	26	convex	convex	ADJ
app01-6401	148	27	linear	linear	ADJ
app01-6401	148	28	semidefinite	semidefinite	NOUN
app01-6401	148	29	programming	programming	NOUN
app01-6401	148	30	relaxations	relaxation	NOUN
app01-6401	148	31	min	min	PROPN
app01-6401	148	32	y	y	PROPN
app01-6401	148	33	|br(x)|∑	|br(x)|∑	PROPN
app01-6401	148	34	β=1	β=1	X
app01-6401	148	35	pα,0,βyβ	pα,0,βyβ	ADJ
app01-6401	148	36	(	(	PUNCT
app01-6401	148	37	32a	32a	NOUN
app01-6401	148	38	)	)	PUNCT
app01-6401	149	1	s.t	s.t	PROPN
app01-6401	149	2	.	.	PROPN
app01-6401	149	3	mr(y	mr(y	PROPN
app01-6401	149	4	)	)	PUNCT
app01-6401	149	5	�	�	PROPN
app01-6401	149	6	0	0	NUM
app01-6401	149	7	,	,	PUNCT
app01-6401	149	8	(	(	PUNCT
app01-6401	149	9	32b	32b	NOUN
app01-6401	149	10	)	)	PUNCT
app01-6401	149	11	mr−dj	mr−dj	NOUN
app01-6401	149	12	(	(	PUNCT
app01-6401	149	13	y	y	NOUN
app01-6401	149	14	)	)	PUNCT
app01-6401	149	15	�	�	PROPN
app01-6401	149	16	0	0	NUM
app01-6401	149	17	,	,	PUNCT
app01-6401	149	18	∀j	∀j	PROPN
app01-6401	149	19	∈	∈	PROPN
app01-6401	149	20	{	{	PUNCT
app01-6401	149	21	1	1	NUM
app01-6401	149	22	,	,	PUNCT
app01-6401	149	23	.	.	PUNCT
app01-6401	149	24	.	.	PUNCT
app01-6401	149	25	.	.	PUNCT
app01-6401	150	1	,	,	PUNCT
app01-6401	150	2	4	4	NUM
app01-6401	150	3	}	}	PUNCT
app01-6401	150	4	,	,	PUNCT
app01-6401	150	5	(	(	PUNCT
app01-6401	150	6	32c	32c	NOUN
app01-6401	150	7	)	)	PUNCT
app01-6401	150	8	and	and	CCONJ
app01-6401	150	9	solve	solve	VERB
app01-6401	150	10	it	it	PRON
app01-6401	150	11	successively	successively	ADV
app01-6401	150	12	with	with	ADP
app01-6401	150	13	an	an	DET
app01-6401	150	14	increasing	increase	VERB
app01-6401	150	15	relaxation	relaxation	NOUN
app01-6401	150	16	order	order	NOUN
app01-6401	150	17	r	r	NOUN
app01-6401	150	18	until	until	SCONJ
app01-6401	150	19	the	the	DET
app01-6401	150	20	globally	globally	ADV
app01-6401	150	21	optimal	optimal	ADJ
app01-6401	150	22	solution(s	solution(s	NOUN
app01-6401	150	23	)	)	PUNCT
app01-6401	150	24	are	be	AUX
app01-6401	150	25	found	find	VERB
app01-6401	150	26	.	.	PUNCT
app01-6401	151	1	for	for	ADP
app01-6401	151	2	all	all	DET
app01-6401	151	3	our	our	PRON
app01-6401	151	4	test	test	NOUN
app01-6401	151	5	cases	case	NOUN
app01-6401	151	6	,	,	PUNCT
app01-6401	151	7	this	this	DET
app01-6401	151	8	convergence	convergence	NOUN
app01-6401	151	9	was	be	AUX
app01-6401	151	10	always	always	ADV
app01-6401	151	11	finite	finite	ADJ
app01-6401	151	12	.	.	PUNCT
app01-6401	152	1	in	in	ADP
app01-6401	152	2	(	(	PUNCT
app01-6401	152	3	32	32	NUM
app01-6401	152	4	)	)	PUNCT
app01-6401	152	5	,	,	PUNCT
app01-6401	152	6	the	the	DET
app01-6401	152	7	matrix	matrix	NOUN
app01-6401	152	8	mr(y	mr(y	VERB
app01-6401	152	9	)	)	PUNCT
app01-6401	152	10	is	be	AUX
app01-6401	152	11	the	the	DET
app01-6401	152	12	moment	moment	NOUN
app01-6401	152	13	matrix	matrix	NOUN
app01-6401	152	14	of	of	ADP
app01-6401	152	15	the	the	DET
app01-6401	152	16	r	r	NOUN
app01-6401	152	17	-	-	PUNCT
app01-6401	152	18	th	th	VERB
app01-6401	152	19	order	order	NOUN
app01-6401	152	20	,	,	PUNCT
app01-6401	152	21	and	and	CCONJ
app01-6401	152	22	mr−dj	mr−dj	NOUN
app01-6401	152	23	is	be	AUX
app01-6401	152	24	the	the	DET
app01-6401	152	25	(	(	PUNCT
app01-6401	152	26	r	r	NOUN
app01-6401	152	27	−	−	NOUN
app01-6401	152	28	dj)-order	dj)-order	NOUN
app01-6401	152	29	localization	localization	NOUN
app01-6401	152	30	matrix	matrix	NOUN
app01-6401	152	31	associated	associate	VERB
app01-6401	152	32	with	with	ADP
app01-6401	152	33	pj	pj	PROPN
app01-6401	152	34	or	or	CCONJ
app01-6401	152	35	pj	pj	PROPN
app01-6401	152	36	.	.	PUNCT
app01-6401	153	1	for	for	ADP
app01-6401	153	2	more	more	ADJ
app01-6401	153	3	details	detail	NOUN
app01-6401	153	4	about	about	ADP
app01-6401	153	5	these	these	DET
app01-6401	153	6	matrices	matrix	NOUN
app01-6401	153	7	,	,	PUNCT
app01-6401	153	8	we	we	PRON
app01-6401	153	9	refer	refer	VERB
app01-6401	153	10	the	the	DET
app01-6401	153	11	reader	reader	NOUN
app01-6401	153	12	to	to	ADP
app01-6401	153	13	[	[	X
app01-6401	153	14	7	7	NUM
app01-6401	153	15	,	,	PUNCT
app01-6401	153	16	12	12	NUM
app01-6401	153	17	]	]	PUNCT
app01-6401	153	18	.	.	PUNCT
app01-6401	154	1	2.4.2	2.4.2	NUM
app01-6401	154	2	.	.	PUNCT
app01-6401	155	1	recognizing	recognize	VERB
app01-6401	155	2	global	global	ADJ
app01-6401	155	3	optimality	optimality	NOUN
app01-6401	155	4	there	there	PRON
app01-6401	155	5	are	be	VERB
app01-6401	155	6	(	(	PUNCT
app01-6401	155	7	at	at	ADP
app01-6401	155	8	least	least	ADJ
app01-6401	155	9	)	)	PUNCT
app01-6401	155	10	two	two	NUM
app01-6401	155	11	ways	way	NOUN
app01-6401	155	12	to	to	PART
app01-6401	155	13	recognize	recognize	VERB
app01-6401	155	14	whether	whether	SCONJ
app01-6401	155	15	y∗r	y∗r	NUM
app01-6401	155	16	,	,	PUNCT
app01-6401	155	17	a	a	DET
app01-6401	155	18	r	r	NOUN
app01-6401	155	19	-	-	PUNCT
app01-6401	155	20	th	th	VERB
app01-6401	155	21	order	order	NOUN
app01-6401	155	22	relaxation	relaxation	NOUN
app01-6401	155	23	solution	solution	NOUN
app01-6401	155	24	to	to	ADP
app01-6401	155	25	(	(	PUNCT
app01-6401	155	26	32	32	NUM
app01-6401	155	27	)	)	PUNCT
app01-6401	155	28	,	,	PUNCT
app01-6401	155	29	is	be	AUX
app01-6401	155	30	globally	globally	ADV
app01-6401	155	31	optimal	optimal	ADJ
app01-6401	155	32	.	.	PUNCT
app01-6401	156	1	the	the	DET
app01-6401	156	2	first	first	ADJ
app01-6401	156	3	(	(	PUNCT
app01-6401	156	4	common	common	ADJ
app01-6401	156	5	)	)	PUNCT
app01-6401	156	6	way	way	NOUN
app01-6401	156	7	is	be	AUX
app01-6401	156	8	based	base	VERB
app01-6401	156	9	a	a	DET
app01-6401	156	10	sufficient	sufficient	ADJ
app01-6401	156	11	condition	condition	NOUN
app01-6401	156	12	for	for	ADP
app01-6401	156	13	global	global	ADJ
app01-6401	156	14	optimality	optimality	NOUN
app01-6401	156	15	of	of	ADP
app01-6401	156	16	(	(	PUNCT
app01-6401	156	17	32	32	NUM
app01-6401	156	18	)	)	PUNCT
app01-6401	157	1	[	[	X
app01-6401	157	2	15	15	NUM
app01-6401	157	3	,	,	PUNCT
app01-6401	157	4	16	16	NUM
app01-6401	157	5	]	]	PUNCT
app01-6401	157	6	,	,	PUNCT
app01-6401	157	7	rank	rank	NOUN
app01-6401	157	8	mr(y∗r	mr(y∗r	NOUN
app01-6401	157	9	)	)	PUNCT
app01-6401	157	10	=	=	VERB
app01-6401	157	11	rank	rank	NOUN
app01-6401	157	12	mr−d(y∗r	mr−d(y∗r	NOUN
app01-6401	157	13	)	)	PUNCT
app01-6401	157	14	,	,	PUNCT
app01-6401	157	15	(	(	PUNCT
app01-6401	157	16	33	33	NUM
app01-6401	157	17	)	)	PUNCT
app01-6401	157	18	in	in	ADP
app01-6401	157	19	which	which	PRON
app01-6401	157	20	y∗	y∗	ADV
app01-6401	157	21	constitutes	constitute	VERB
app01-6401	157	22	the	the	DET
app01-6401	157	23	optimal	optimal	ADJ
app01-6401	157	24	solution	solution	NOUN
app01-6401	157	25	in	in	ADP
app01-6401	157	26	the	the	DET
app01-6401	157	27	basis	basis	NOUN
app01-6401	157	28	br(csc	br(csc	PROPN
app01-6401	157	29	,	,	PUNCT
app01-6401	157	30	asc	asc	PROPN
app01-6401	157	31	)	)	PUNCT
app01-6401	157	32	,	,	PUNCT
app01-6401	157	33	and	and	CCONJ
app01-6401	157	34	rank	rank	PROPN
app01-6401	157	35	mr(y∗	mr(y∗	PROPN
app01-6401	157	36	)	)	PUNCT
app01-6401	157	37	is	be	AUX
app01-6401	157	38	less	less	ADV
app01-6401	157	39	or	or	CCONJ
app01-6401	157	40	equal	equal	ADJ
app01-6401	157	41	to	to	ADP
app01-6401	157	42	the	the	DET
app01-6401	157	43	number	number	NOUN
app01-6401	157	44	of	of	ADP
app01-6401	157	45	these	these	DET
app01-6401	157	46	solutions	solution	NOUN
app01-6401	157	47	[	[	X
app01-6401	157	48	7	7	NUM
app01-6401	157	49	]	]	PUNCT
app01-6401	157	50	.	.	PUNCT
app01-6401	158	1	the	the	DET
app01-6401	158	2	values	value	NOUN
app01-6401	158	3	of	of	ADP
app01-6401	158	4	the	the	DET
app01-6401	158	5	original	original	ADJ
app01-6401	158	6	design	design	NOUN
app01-6401	158	7	variables	variable	NOUN
app01-6401	158	8	can	can	AUX
app01-6401	158	9	be	be	AUX
app01-6401	158	10	extracted	extract	VERB
app01-6401	158	11	using	use	VERB
app01-6401	158	12	cholesky	cholesky	NOUN
app01-6401	158	13	or	or	CCONJ
app01-6401	158	14	singular	singular	ADJ
app01-6401	158	15	value	value	NOUN
app01-6401	158	16	decompositions	decomposition	NOUN
app01-6401	158	17	[	[	X
app01-6401	158	18	16	16	NUM
app01-6401	158	19	]	]	PUNCT
app01-6401	158	20	.	.	PUNCT
app01-6401	159	1	for	for	ADP
app01-6401	159	2	the	the	DET
app01-6401	159	3	optimization	optimization	NOUN
app01-6401	159	4	problem	problem	NOUN
app01-6401	159	5	(	(	PUNCT
app01-6401	159	6	27	27	NUM
app01-6401	159	7	)	)	PUNCT
app01-6401	159	8	,	,	PUNCT
app01-6401	159	9	we	we	PRON
app01-6401	159	10	introduce	introduce	VERB
app01-6401	159	11	another	another	DET
app01-6401	159	12	sufficient	sufficient	ADJ
app01-6401	159	13	condition	condition	NOUN
app01-6401	159	14	for	for	ADP
app01-6401	159	15	global	global	ADJ
app01-6401	159	16	optimality	optimality	NOUN
app01-6401	159	17	.	.	PUNCT
app01-6401	160	1	let	let	VERB
app01-6401	160	2	ãr	ãr	PRON
app01-6401	160	3	be	be	AUX
app01-6401	160	4	the	the	DET
app01-6401	160	5	(	(	PUNCT
app01-6401	160	6	optimized	optimize	VERB
app01-6401	160	7	)	)	PUNCT
app01-6401	160	8	values	value	NOUN
app01-6401	160	9	of	of	ADP
app01-6401	160	10	the	the	DET
app01-6401	160	11	cross	cross	ADJ
app01-6401	160	12	-	-	ADJ
app01-6401	160	13	sectional	sectional	ADJ
app01-6401	160	14	areas	area	NOUN
app01-6401	160	15	and	and	CCONJ
app01-6401	160	16	let	let	VERB
app01-6401	160	17	c̃r	c̃r	PRON
app01-6401	160	18	denote	denote	VERB
app01-6401	160	19	the	the	DET
app01-6401	160	20	compliance	compliance	NOUN
app01-6401	160	21	found	find	VERB
app01-6401	160	22	in	in	ADP
app01-6401	160	23	the	the	DET
app01-6401	160	24	r	r	NOUN
app01-6401	160	25	-	-	PUNCT
app01-6401	160	26	th	th	VERB
app01-6401	160	27	order	order	NOUN
app01-6401	160	28	relaxation	relaxation	NOUN
app01-6401	160	29	.	.	PUNCT
app01-6401	161	1	indeed	indeed	ADV
app01-6401	161	2	,	,	PUNCT
app01-6401	161	3	c̃r	c̃r	DET
app01-6401	161	4	≤	≤	X
app01-6401	161	5	c∗	c∗	NOUN
app01-6401	162	1	[	[	X
app01-6401	162	2	7	7	NUM
app01-6401	162	3	]	]	PUNCT
app01-6401	162	4	.	.	PUNCT
app01-6401	163	1	moreover	moreover	ADV
app01-6401	163	2	,	,	PUNCT
app01-6401	163	3	because	because	SCONJ
app01-6401	163	4	any	any	DET
app01-6401	163	5	feasible	feasible	ADJ
app01-6401	163	6	design	design	NOUN
app01-6401	163	7	a	a	DET
app01-6401	163	8	generates	generate	VERB
app01-6401	163	9	an	an	DET
app01-6401	163	10	upper	upper	ADJ
app01-6401	163	11	bound	bind	VERB
app01-6401	163	12	ĉr	ĉr	NOUN
app01-6401	163	13	,	,	PUNCT
app01-6401	163	14	recall	recall	VERB
app01-6401	163	15	eq	eq	ADP
app01-6401	163	16	.	.	PUNCT
app01-6401	164	1	(	(	PUNCT
app01-6401	164	2	23	23	NUM
app01-6401	164	3	)	)	PUNCT
app01-6401	164	4	,	,	PUNCT
app01-6401	164	5	we	we	PRON
app01-6401	164	6	have	have	VERB
app01-6401	164	7	c̃r	c̃r	DET
app01-6401	164	8	≤	≤	NUM
app01-6401	164	9	c∗	c∗	PROPN
app01-6401	164	10	≤	≤	NOUN
app01-6401	164	11	ĉr	ĉr	NOUN
app01-6401	164	12	.	.	PUNCT
app01-6401	165	1	(	(	PUNCT
app01-6401	165	2	34	34	NUM
app01-6401	165	3	)	)	PUNCT
app01-6401	165	4	a	a	DET
app01-6401	165	5	globally	globally	ADV
app01-6401	165	6	optimal	optimal	ADJ
app01-6401	165	7	solution	solution	NOUN
app01-6401	165	8	to	to	ADP
app01-6401	165	9	(	(	PUNCT
app01-6401	165	10	27	27	NUM
app01-6401	165	11	)	)	PUNCT
app01-6401	165	12	is	be	AUX
app01-6401	165	13	found	find	VERB
app01-6401	165	14	if	if	SCONJ
app01-6401	165	15	there	there	PRON
app01-6401	165	16	is	be	VERB
app01-6401	165	17	no	no	DET
app01-6401	165	18	gap	gap	NOUN
app01-6401	165	19	,	,	PUNCT
app01-6401	165	20	ĉr	ĉr	NOUN
app01-6401	165	21	−	−	PROPN
app01-6401	166	1	c̃r	c̃r	INTJ
app01-6401	166	2	−→	−→	NOUN
app01-6401	166	3	0	0	NUM
app01-6401	166	4	.	.	PUNCT
app01-6401	167	1	(	(	PUNCT
app01-6401	167	2	35	35	NUM
app01-6401	167	3	)	)	PUNCT
app01-6401	167	4	note	note	NOUN
app01-6401	167	5	that	that	SCONJ
app01-6401	167	6	(	(	PUNCT
app01-6401	167	7	35	35	NUM
app01-6401	167	8	)	)	PUNCT
app01-6401	167	9	is	be	AUX
app01-6401	167	10	substantially	substantially	ADV
app01-6401	167	11	simpler	simple	ADJ
app01-6401	167	12	to	to	PART
app01-6401	167	13	check	check	VERB
app01-6401	167	14	than	than	ADP
app01-6401	167	15	(	(	PUNCT
app01-6401	167	16	33	33	NUM
app01-6401	167	17	)	)	PUNCT
app01-6401	167	18	.	.	PUNCT
app01-6401	168	1	if	if	SCONJ
app01-6401	168	2	(	(	PUNCT
app01-6401	168	3	35	35	NUM
app01-6401	168	4	)	)	PUNCT
app01-6401	168	5	is	be	AUX
app01-6401	168	6	not	not	PART
app01-6401	168	7	satisfied	satisfied	ADJ
app01-6401	168	8	in	in	ADP
app01-6401	168	9	the	the	DET
app01-6401	168	10	(	(	PUNCT
app01-6401	168	11	current	current	ADJ
app01-6401	168	12	)	)	PUNCT
app01-6401	168	13	relaxation	relaxation	NOUN
app01-6401	168	14	order	order	NOUN
app01-6401	168	15	r	r	NOUN
app01-6401	168	16	,	,	PUNCT
app01-6401	168	17	we	we	PRON
app01-6401	168	18	have	have	VERB
app01-6401	168	19	at	at	ADP
app01-6401	168	20	least	least	ADJ
app01-6401	168	21	the	the	DET
app01-6401	168	22	quality	quality	NOUN
app01-6401	168	23	measure	measure	NOUN
app01-6401	168	24	for	for	ADP
app01-6401	168	25	the	the	DET
app01-6401	168	26	current	current	ADJ
app01-6401	168	27	solution	solution	NOUN
app01-6401	168	28	in	in	ADP
app01-6401	168	29	hand	hand	NOUN
app01-6401	168	30	.	.	PUNCT
app01-6401	169	1	3	3	X
app01-6401	169	2	.	.	X
app01-6401	169	3	sample	sample	NOUN
app01-6401	169	4	problems	problem	NOUN
app01-6401	169	5	in	in	ADP
app01-6401	169	6	this	this	DET
app01-6401	169	7	section	section	NOUN
app01-6401	169	8	,	,	PUNCT
app01-6401	169	9	we	we	PRON
app01-6401	169	10	describe	describe	VERB
app01-6401	169	11	and	and	CCONJ
app01-6401	169	12	solve	solve	VERB
app01-6401	169	13	three	three	NUM
app01-6401	169	14	rather	rather	ADV
app01-6401	169	15	small	small	ADV
app01-6401	169	16	-	-	PUNCT
app01-6401	169	17	scaled	scale	VERB
app01-6401	169	18	structural	structural	ADJ
app01-6401	169	19	optimization	optimization	NOUN
app01-6401	169	20	problems	problem	NOUN
app01-6401	169	21	,	,	PUNCT
app01-6401	169	22	and	and	CCONJ
app01-6401	169	23	compare	compare	VERB
app01-6401	169	24	the	the	DET
app01-6401	169	25	four	four	NUM
app01-6401	169	26	optimization	optimization	NOUN
app01-6401	169	27	approaches	approach	NOUN
app01-6401	169	28	.	.	PUNCT
app01-6401	170	1	3.1	3.1	NUM
app01-6401	170	2	.	.	PUNCT
app01-6401	170	3	cantilever	cantilever	NOUN
app01-6401	170	4	beam	beam	NOUN
app01-6401	170	5	consider	consider	VERB
app01-6401	170	6	a	a	DET
app01-6401	170	7	(	(	PUNCT
app01-6401	170	8	simple	simple	ADJ
app01-6401	170	9	)	)	PUNCT
app01-6401	170	10	cantilever	cantilever	NOUN
app01-6401	170	11	beam	beam	NOUN
app01-6401	170	12	design	design	NOUN
app01-6401	170	13	problem	problem	NOUN
app01-6401	170	14	,	,	PUNCT
app01-6401	170	15	as	as	SCONJ
app01-6401	170	16	shown	show	VERB
app01-6401	170	17	in	in	ADP
app01-6401	170	18	fig	fig	NOUN
app01-6401	170	19	.	.	PUNCT
app01-6401	171	1	1a	1a	PROPN
app01-6401	171	2	.	.	PUNCT
app01-6401	172	1	the	the	DET
app01-6401	172	2	beam	beam	NOUN
app01-6401	172	3	is	be	AUX
app01-6401	172	4	discretized	discretize	VERB
app01-6401	172	5	into	into	ADP
app01-6401	172	6	ne	ne	PROPN
app01-6401	172	7	finite	finite	ADJ
app01-6401	172	8	elements	element	NOUN
app01-6401	172	9	of	of	ADP
app01-6401	172	10	equal	equal	ADJ
app01-6401	172	11	lengths	length	NOUN
app01-6401	172	12	,	,	PUNCT
app01-6401	172	13	each	each	PRON
app01-6401	172	14	of	of	ADP
app01-6401	172	15	them	they	PRON
app01-6401	172	16	assigned	assign	VERB
app01-6401	172	17	a	a	DET
app01-6401	172	18	prismatic	prismatic	ADJ
app01-6401	172	19	square	square	ADJ
app01-6401	172	20	cross	cross	NOUN
app01-6401	172	21	-	-	NOUN
app01-6401	172	22	section	section	NOUN
app01-6401	172	23	.	.	PUNCT
app01-6401	173	1	the	the	DET
app01-6401	173	2	beam	beam	NOUN
app01-6401	173	3	is	be	AUX
app01-6401	173	4	loaded	load	VERB
app01-6401	173	5	with	with	ADP
app01-6401	173	6	a	a	DET
app01-6401	173	7	skew	skew	ADJ
app01-6401	173	8	force	force	NOUN
app01-6401	173	9	at	at	ADP
app01-6401	173	10	its	its	PRON
app01-6401	173	11	tip	tip	NOUN
app01-6401	173	12	.	.	PUNCT
app01-6401	174	1	further	far	ADV
app01-6401	174	2	,	,	PUNCT
app01-6401	174	3	we	we	PRON
app01-6401	174	4	assume	assume	VERB
app01-6401	174	5	(	(	PUNCT
app01-6401	174	6	dimensionless	dimensionless	NOUN
app01-6401	174	7	)	)	PUNCT
app01-6401	174	8	e	e	NOUN
app01-6401	174	9	=	=	SYM
app01-6401	174	10	1	1	NUM
app01-6401	174	11	and	and	CCONJ
app01-6401	174	12	v	v	NOUN
app01-6401	174	13	=	=	SYM
app01-6401	174	14	0.1	0.1	NUM
app01-6401	174	15	.	.	PUNCT
app01-6401	175	1	it	it	PRON
app01-6401	175	2	can	can	AUX
app01-6401	175	3	be	be	AUX
app01-6401	175	4	seen	see	VERB
app01-6401	175	5	from	from	ADP
app01-6401	175	6	table	table	NOUN
app01-6401	175	7	1	1	NUM
app01-6401	175	8	that	that	SCONJ
app01-6401	175	9	the	the	DET
app01-6401	175	10	problem	problem	NOUN
app01-6401	175	11	is	be	AUX
app01-6401	175	12	relatively	relatively	ADV
app01-6401	175	13	“	"	PUNCT
app01-6401	175	14	easy	easy	ADJ
app01-6401	175	15	”	"	PUNCT
app01-6401	175	16	to	to	PART
app01-6401	175	17	solve	solve	VERB
app01-6401	175	18	,	,	PUNCT
app01-6401	175	19	as	as	SCONJ
app01-6401	175	20	all	all	PRON
app01-6401	175	21	of	of	ADP
app01-6401	175	22	the	the	DET
app01-6401	175	23	tested	test	VERB
app01-6401	175	24	algorithms	algorithm	NOUN
app01-6401	175	25	converge	converge	VERB
app01-6401	175	26	to	to	ADP
app01-6401	175	27	the	the	DET
app01-6401	175	28	unique	unique	ADJ
app01-6401	175	29	global	global	ADJ
app01-6401	175	30	optima	optima	NOUN
app01-6401	175	31	(	(	PUNCT
app01-6401	175	32	shown	show	VERB
app01-6401	175	33	in	in	ADP
app01-6401	175	34	1b–1e	1b–1e	PROPN
app01-6401	175	35	)	)	PUNCT
app01-6401	175	36	,	,	PUNCT
app01-6401	175	37	proved	prove	VERB
app01-6401	175	38	by	by	ADP
app01-6401	175	39	the	the	DET
app01-6401	175	40	po	po	PROPN
app01-6401	175	41	approach	approach	NOUN
app01-6401	175	42	(	(	PUNCT
app01-6401	175	43	figs	fig	NOUN
app01-6401	175	44	.	.	PUNCT
app01-6401	176	1	1h–1j	1h–1j	NOUN
app01-6401	176	2	)	)	PUNCT
app01-6401	176	3	.	.	PUNCT
app01-6401	177	1	in	in	ADP
app01-6401	177	2	fact	fact	NOUN
app01-6401	177	3	,	,	PUNCT
app01-6401	177	4	we	we	PRON
app01-6401	177	5	include	include	VERB
app01-6401	177	6	this	this	DET
app01-6401	177	7	optimization	optimization	NOUN
app01-6401	177	8	problem	problem	NOUN
app01-6401	177	9	mainly	mainly	ADV
app01-6401	177	10	to	to	PART
app01-6401	177	11	show	show	VERB
app01-6401	177	12	that	that	SCONJ
app01-6401	177	13	po	po	PROPN
app01-6401	177	14	scales	scale	VERB
app01-6401	177	15	unambiguously	unambiguously	ADV
app01-6401	177	16	worse	bad	ADJ
app01-6401	177	17	with	with	ADP
app01-6401	177	18	the	the	DET
app01-6401	177	19	problem	problem	NOUN
app01-6401	177	20	dimension	dimension	NOUN
app01-6401	177	21	than	than	ADP
app01-6401	177	22	the	the	DET
app01-6401	177	23	other	other	ADJ
app01-6401	177	24	methods	method	NOUN
app01-6401	177	25	,	,	PUNCT
app01-6401	177	26	and	and	CCONJ
app01-6401	177	27	that	that	SCONJ
app01-6401	177	28	the	the	DET
app01-6401	177	29	optimality	optimality	NOUN
app01-6401	177	30	criteria	criterion	NOUN
app01-6401	177	31	(	(	PUNCT
app01-6401	177	32	oc	oc	NOUN
app01-6401	177	33	)	)	PUNCT
app01-6401	177	34	method	method	NOUN
app01-6401	177	35	is	be	AUX
app01-6401	177	36	the	the	DET
app01-6401	177	37	fastest	fast	ADJ
app01-6401	177	38	one	one	NOUN
app01-6401	177	39	.	.	PUNCT
app01-6401	178	1	using	use	VERB
app01-6401	178	2	oc	oc	NOUN
app01-6401	178	3	,	,	PUNCT
app01-6401	178	4	we	we	PRON
app01-6401	178	5	can	can	AUX
app01-6401	178	6	optimize	optimize	VERB
app01-6401	178	7	the	the	DET
app01-6401	178	8	discretizations	discretization	NOUN
app01-6401	178	9	of	of	ADP
app01-6401	178	10	150	150	NUM
app01-6401	178	11	or	or	CCONJ
app01-6401	178	12	300	300	NUM
app01-6401	178	13	elements	element	NOUN
app01-6401	178	14	in	in	ADP
app01-6401	178	15	0.4	0.4	NUM
app01-6401	178	16	and	and	CCONJ
app01-6401	178	17	0.8	0.8	NUM
app01-6401	178	18	seconds	second	NOUN
app01-6401	178	19	(	(	PUNCT
app01-6401	178	20	figs	fig	NOUN
app01-6401	178	21	.	.	PUNCT
app01-6401	179	1	1f	1f	PROPN
app01-6401	179	2	and	and	CCONJ
app01-6401	179	3	1h	1h	NUM
app01-6401	179	4	)	)	PUNCT
app01-6401	179	5	.	.	PUNCT
app01-6401	180	1	121	121	NUM
app01-6401	180	2	m.	m.	NOUN
app01-6401	180	3	tyburec	tyburec	NOUN
app01-6401	180	4	,	,	PUNCT
app01-6401	180	5	j.	j.	PROPN
app01-6401	180	6	zeman	zeman	PROPN
app01-6401	180	7	,	,	PUNCT
app01-6401	180	8	m.	m.	NOUN
app01-6401	180	9	kružík	kružík	PROPN
app01-6401	180	10	,	,	PUNCT
app01-6401	180	11	d.	d.	PROPN
app01-6401	180	12	henrion	henrion	PROPN
app01-6401	180	13	acta	acta	PROPN
app01-6401	180	14	polytechnica	polytechnica	PROPN
app01-6401	180	15	ctu	ctu	NOUN
app01-6401	180	16	proceedings	proceeding	NOUN
app01-6401	180	17	t	t	VERB
app01-6401	181	1	[	[	X
app01-6401	181	2	s	s	X
app01-6401	181	3	]	]	X
app01-6401	181	4	ĉ	ĉ	X
app01-6401	181	5	c̃	c̃	PROPN
app01-6401	181	6	a1	a1	NOUN
app01-6401	181	7	fmincon	fmincon	VERB
app01-6401	181	8	0.7	0.7	NUM
app01-6401	181	9	107.50	107.50	NUM
app01-6401	181	10	0.100	0.100	NUM
app01-6401	181	11	oc	oc	ADP
app01-6401	181	12	0.1	0.1	NUM
app01-6401	181	13	107.50	107.50	NUM
app01-6401	181	14	0.100	0.100	NUM
app01-6401	181	15	nsdp	nsdp	NOUN
app01-6401	181	16	0.2	0.2	NUM
app01-6401	181	17	107.50	107.50	NUM
app01-6401	181	18	0.100	0.100	NUM
app01-6401	181	19	po(1	po(1	NOUN
app01-6401	181	20	)	)	PUNCT
app01-6401	181	21	0.3	0.3	NUM
app01-6401	181	22	107.50	107.50	NUM
app01-6401	181	23	107.50	107.50	NUM
app01-6401	181	24	0.100	0.100	NUM
app01-6401	181	25	(	(	PUNCT
app01-6401	181	26	a	a	NOUN
app01-6401	181	27	)	)	PUNCT
app01-6401	181	28	1	1	NUM
app01-6401	181	29	element	element	NOUN
app01-6401	181	30	t	t	NOUN
app01-6401	182	1	[	[	X
app01-6401	182	2	s	s	X
app01-6401	182	3	]	]	X
app01-6401	182	4	ĉ	ĉ	X
app01-6401	182	5	c̃	c̃	PROPN
app01-6401	182	6	a1	a1	NOUN
app01-6401	182	7	a2	a2	PROPN
app01-6401	182	8	a3	a3	NOUN
app01-6401	182	9	fmincon	fmincon	VERB
app01-6401	182	10	0.6	0.6	NUM
app01-6401	182	11	80.30	80.30	NUM
app01-6401	182	12	0.142	0.142	NUM
app01-6401	182	13	0.102	0.102	NUM
app01-6401	182	14	0.056	0.056	NUM
app01-6401	182	15	oc	oc	ADP
app01-6401	182	16	0.1	0.1	NUM
app01-6401	182	17	80.30	80.30	NUM
app01-6401	182	18	0.142	0.142	NUM
app01-6401	182	19	0.102	0.102	NUM
app01-6401	182	20	0.056	0.056	NUM
app01-6401	182	21	nsdp	nsdp	ADJ
app01-6401	183	1	0.3	0.3	NUM
app01-6401	183	2	80.30	80.30	NUM
app01-6401	183	3	0.142	0.142	NUM
app01-6401	183	4	0.102	0.102	NUM
app01-6401	183	5	0.056	0.056	NUM
app01-6401	183	6	po(1	po(1	NOUN
app01-6401	183	7	)	)	PUNCT
app01-6401	183	8	0.3	0.3	NUM
app01-6401	183	9	80.72	80.72	NUM
app01-6401	183	10	35.81	35.81	NUM
app01-6401	183	11	0.147	0.147	NUM
app01-6401	183	12	0.097	0.097	NUM
app01-6401	183	13	0.056	0.056	NUM
app01-6401	183	14	po(2	po(2	NOUN
app01-6401	183	15	)	)	PUNCT
app01-6401	183	16	0.3	0.3	NUM
app01-6401	183	17	80.30	80.30	NUM
app01-6401	183	18	80.30	80.30	NUM
app01-6401	183	19	0.142	0.142	NUM
app01-6401	183	20	0.102	0.102	NUM
app01-6401	183	21	0.056	0.056	NUM
app01-6401	183	22	(	(	PUNCT
app01-6401	183	23	b	b	NOUN
app01-6401	183	24	)	)	PUNCT
app01-6401	183	25	3	3	NUM
app01-6401	183	26	elements	element	NOUN
app01-6401	183	27	t	t	X
app01-6401	184	1	[	[	X
app01-6401	184	2	s	s	X
app01-6401	184	3	]	]	X
app01-6401	184	4	ĉ	ĉ	X
app01-6401	184	5	c̃	c̃	PROPN
app01-6401	184	6	a1	a1	NOUN
app01-6401	184	7	a2	a2	PROPN
app01-6401	184	8	a3	a3	PROPN
app01-6401	184	9	a4	a4	PROPN
app01-6401	184	10	a5	a5	PROPN
app01-6401	184	11	fmincon	fmincon	VERB
app01-6401	184	12	0.4	0.4	NUM
app01-6401	184	13	77.19	77.19	NUM
app01-6401	184	14	0.151	0.151	NUM
app01-6401	184	15	0.128	0.128	NUM
app01-6401	184	16	0.103	0.103	NUM
app01-6401	184	17	0.075	0.075	NUM
app01-6401	184	18	0.043	0.043	NUM
app01-6401	184	19	oc	oc	ADP
app01-6401	184	20	0.1	0.1	NUM
app01-6401	184	21	77.19	77.19	NUM
app01-6401	184	22	0.151	0.151	NUM
app01-6401	184	23	0.128	0.128	NUM
app01-6401	184	24	0.103	0.103	NUM
app01-6401	184	25	0.075	0.075	NUM
app01-6401	184	26	0.043	0.043	NUM
app01-6401	184	27	nsdp	nsdp	NOUN
app01-6401	184	28	0.5	0.5	NUM
app01-6401	184	29	77.19	77.19	NUM
app01-6401	184	30	0.151	0.151	NUM
app01-6401	184	31	0.128	0.128	NUM
app01-6401	184	32	0.103	0.103	NUM
app01-6401	184	33	0.075	0.075	NUM
app01-6401	184	34	0.043	0.043	NUM
app01-6401	184	35	po(1	po(1	NOUN
app01-6401	184	36	)	)	PUNCT
app01-6401	184	37	0.3	0.3	NUM
app01-6401	184	38	79.09	79.09	NUM
app01-6401	184	39	24.72	24.72	NUM
app01-6401	184	40	0.151	0.151	NUM
app01-6401	184	41	0.123	0.123	NUM
app01-6401	184	42	0.096	0.096	NUM
app01-6401	184	43	0.073	0.073	NUM
app01-6401	184	44	0.058	0.058	NUM
app01-6401	184	45	po(2	po(2	NOUN
app01-6401	184	46	)	)	PUNCT
app01-6401	184	47	0.7	0.7	NUM
app01-6401	184	48	77.37	77.37	NUM
app01-6401	184	49	76.34	76.34	NUM
app01-6401	184	50	0.154	0.154	NUM
app01-6401	184	51	0.131	0.131	NUM
app01-6401	184	52	0.103	0.103	NUM
app01-6401	184	53	0.072	0.072	NUM
app01-6401	184	54	0.040	0.040	NUM
app01-6401	184	55	po(3	po(3	NOUN
app01-6401	184	56	)	)	PUNCT
app01-6401	184	57	26.8	26.8	NUM
app01-6401	184	58	77.19	77.19	NUM
app01-6401	184	59	77.19	77.19	NUM
app01-6401	184	60	0.151	0.151	NUM
app01-6401	184	61	0.128	0.128	NUM
app01-6401	184	62	0.103	0.103	NUM
app01-6401	184	63	0.075	0.075	NUM
app01-6401	184	64	0.043	0.043	NUM
app01-6401	184	65	(	(	PUNCT
app01-6401	184	66	c	c	NOUN
app01-6401	184	67	)	)	PUNCT
app01-6401	184	68	5	5	NUM
app01-6401	184	69	elements	element	NOUN
app01-6401	184	70	t	t	X
app01-6401	185	1	[	[	X
app01-6401	185	2	s	s	X
app01-6401	185	3	]	]	X
app01-6401	185	4	ĉ	ĉ	X
app01-6401	185	5	c̃	c̃	PROPN
app01-6401	185	6	a1	a1	NOUN
app01-6401	185	7	a2	a2	PROPN
app01-6401	185	8	a3	a3	PROPN
app01-6401	185	9	a4	a4	PROPN
app01-6401	185	10	a5	a5	PROPN
app01-6401	185	11	a6	a6	PROPN
app01-6401	185	12	a7	a7	PROPN
app01-6401	185	13	fmincon	fmincon	VERB
app01-6401	185	14	0.5	0.5	NUM
app01-6401	185	15	76.23	76.23	NUM
app01-6401	185	16	0.155	0.155	NUM
app01-6401	185	17	0.139	0.139	NUM
app01-6401	185	18	0.122	0.122	NUM
app01-6401	185	19	0.104	0.104	NUM
app01-6401	185	20	0.084	0.084	NUM
app01-6401	185	21	0.061	0.061	NUM
app01-6401	185	22	0.036	0.036	NUM
app01-6401	185	23	oc	oc	ADP
app01-6401	185	24	0.1	0.1	NUM
app01-6401	185	25	76.23	76.23	NUM
app01-6401	185	26	0.155	0.155	NUM
app01-6401	185	27	0.139	0.139	NUM
app01-6401	185	28	0.122	0.122	NUM
app01-6401	185	29	0.104	0.104	NUM
app01-6401	185	30	0.084	0.084	NUM
app01-6401	185	31	0.061	0.061	NUM
app01-6401	185	32	0.036	0.036	NUM
app01-6401	185	33	nsdp	nsdp	NOUN
app01-6401	185	34	0.4	0.4	NUM
app01-6401	185	35	76.23	76.23	NUM
app01-6401	185	36	0.155	0.155	NUM
app01-6401	185	37	0.139	0.139	NUM
app01-6401	185	38	0.122	0.122	NUM
app01-6401	185	39	0.104	0.104	NUM
app01-6401	185	40	0.084	0.084	NUM
app01-6401	185	41	0.061	0.061	NUM
app01-6401	185	42	0.036	0.036	NUM
app01-6401	185	43	po(1	po(1	NOUN
app01-6401	185	44	)	)	PUNCT
app01-6401	185	45	0.3	0.3	NUM
app01-6401	185	46	79.81	79.81	NUM
app01-6401	185	47	20.00	20.00	NUM
app01-6401	185	48	0.149	0.149	NUM
app01-6401	185	49	0.130	0.130	NUM
app01-6401	185	50	0.112	0.112	NUM
app01-6401	185	51	0.096	0.096	NUM
app01-6401	185	52	0.081	0.081	NUM
app01-6401	185	53	0.069	0.069	NUM
app01-6401	185	54	0.062	0.062	NUM
app01-6401	185	55	po(2	po(2	NOUN
app01-6401	185	56	)	)	PUNCT
app01-6401	185	57	2.5	2.5	NUM
app01-6401	185	58	77.02	77.02	NUM
app01-6401	185	59	71.69	71.69	NUM
app01-6401	185	60	0.166	0.166	NUM
app01-6401	185	61	0.145	0.145	NUM
app01-6401	185	62	0.122	0.122	NUM
app01-6401	185	63	0.099	0.099	NUM
app01-6401	185	64	0.077	0.077	NUM
app01-6401	185	65	0.055	0.055	NUM
app01-6401	185	66	0.036	0.036	NUM
app01-6401	185	67	po(3	po(3	NOUN
app01-6401	185	68	)	)	PUNCT
app01-6401	185	69	550.1	550.1	NUM
app01-6401	185	70	76.23	76.23	NUM
app01-6401	185	71	76.23	76.23	NUM
app01-6401	185	72	0.155	0.155	NUM
app01-6401	185	73	0.139	0.139	NUM
app01-6401	185	74	0.122	0.122	NUM
app01-6401	185	75	0.104	0.104	NUM
app01-6401	185	76	0.084	0.084	NUM
app01-6401	185	77	0.061	0.061	NUM
app01-6401	185	78	0.036	0.036	NUM
app01-6401	185	79	(	(	PUNCT
app01-6401	185	80	d	d	NOUN
app01-6401	185	81	)	)	PUNCT
app01-6401	185	82	7	7	NUM
app01-6401	185	83	elements	element	NOUN
app01-6401	185	84	table	table	NOUN
app01-6401	185	85	1	1	NUM
app01-6401	185	86	.	.	PUNCT
app01-6401	185	87	comparison	comparison	NOUN
app01-6401	185	88	of	of	ADP
app01-6401	185	89	the	the	DET
app01-6401	185	90	four	four	NUM
app01-6401	185	91	optimization	optimization	NOUN
app01-6401	185	92	approaches	approach	NOUN
app01-6401	185	93	on	on	ADP
app01-6401	185	94	the	the	DET
app01-6401	185	95	design	design	NOUN
app01-6401	185	96	of	of	ADP
app01-6401	185	97	the	the	DET
app01-6401	185	98	cantilever	cantilever	NOUN
app01-6401	185	99	beam	beam	NOUN
app01-6401	185	100	problem	problem	NOUN
app01-6401	185	101	.	.	PUNCT
app01-6401	186	1	bold	bold	ADJ
app01-6401	186	2	text	text	NOUN
app01-6401	186	3	denotes	denote	VERB
app01-6401	186	4	the	the	DET
app01-6401	186	5	proven	prove	VERB
app01-6401	186	6	global	global	ADJ
app01-6401	186	7	optimum	optimum	NOUN
app01-6401	186	8	.	.	PUNCT
app01-6401	187	1	1	1	NUM
app01-6401	187	2	ne	ne	PROPN
app01-6401	187	3	1	1	NUM
app01-6401	187	4	ne	ne	PROPN
app01-6401	187	5	1−	1−	NUM
app01-6401	187	6	2	2	NUM
app01-6401	187	7	ne	ne	NOUN
app01-6401	187	8	1	1	NUM
app01-6401	187	9	1	1	NUM
app01-6401	187	10	2	2	NUM
app01-6401	187	11	ne	ne	X
app01-6401	187	12	nn	nn	PROPN
app01-6401	187	13	1	1	NUM
app01-6401	187	14	ne	ne	PROPN
app01-6401	187	15	1	1	NUM
app01-6401	187	16	30	30	NUM
app01-6401	187	17	◦	◦	NOUN
app01-6401	187	18	x	x	SYM
app01-6401	187	19	y	y	NOUN
app01-6401	187	20	(	(	PUNCT
app01-6401	187	21	a	a	NOUN
app01-6401	187	22	)	)	PUNCT
app01-6401	187	23	(	(	PUNCT
app01-6401	187	24	b	b	X
app01-6401	187	25	)	)	PUNCT
app01-6401	187	26	c∗	c∗	NOUN
app01-6401	187	27	=	=	SYM
app01-6401	187	28	107.50	107.50	NUM
app01-6401	187	29	(	(	PUNCT
app01-6401	187	30	c	c	NOUN
app01-6401	187	31	)	)	PUNCT
app01-6401	187	32	c∗	c∗	NOUN
app01-6401	187	33	=	=	PUNCT
app01-6401	187	34	80.30	80.30	NUM
app01-6401	187	35	(	(	PUNCT
app01-6401	187	36	d	d	NOUN
app01-6401	187	37	)	)	PUNCT
app01-6401	187	38	c∗	c∗	NOUN
app01-6401	187	39	=	=	SYM
app01-6401	187	40	77.19	77.19	NUM
app01-6401	187	41	(	(	PUNCT
app01-6401	187	42	e	e	NOUN
app01-6401	187	43	)	)	PUNCT
app01-6401	187	44	c∗	c∗	NOUN
app01-6401	187	45	=	=	SYM
app01-6401	187	46	76.23	76.23	NUM
app01-6401	187	47	(	(	PUNCT
app01-6401	187	48	f	f	X
app01-6401	187	49	)	)	PUNCT
app01-6401	187	50	c	c	NOUN
app01-6401	187	51	=	=	SYM
app01-6401	187	52	75.19	75.19	NUM
app01-6401	187	53	(	(	PUNCT
app01-6401	187	54	g	g	NOUN
app01-6401	187	55	)	)	PUNCT
app01-6401	187	56	c	c	NOUN
app01-6401	187	57	=	=	SYM
app01-6401	187	58	75.19	75.19	NUM
app01-6401	187	59	1	1	NUM
app01-6401	187	60	2	2	NUM
app01-6401	187	61	0	0	NUM
app01-6401	187	62	20	20	NUM
app01-6401	187	63	40	40	NUM
app01-6401	187	64	60	60	NUM
app01-6401	187	65	80	80	NUM
app01-6401	187	66	100	100	NUM
app01-6401	187	67	120	120	NUM
app01-6401	187	68	relaxation	relaxation	NOUN
app01-6401	187	69	order	order	NOUN
app01-6401	187	70	r	r	NOUN
app01-6401	187	71	c	c	NOUN
app01-6401	187	72	om	om	PROPN
app01-6401	187	73	pl	pl	PROPN
app01-6401	187	74	ia	ia	PROPN
app01-6401	187	75	nc	nc	PROPN
app01-6401	187	76	e	e	PROPN
app01-6401	187	77	c	c	PROPN
app01-6401	187	78	ĉr	ĉr	X
app01-6401	187	79	c̃r	c̃r	DET
app01-6401	187	80	c∗	c∗	PROPN
app01-6401	187	81	(	(	PUNCT
app01-6401	187	82	h	h	NOUN
app01-6401	187	83	)	)	PUNCT
app01-6401	187	84	1	1	NUM
app01-6401	187	85	2	2	NUM
app01-6401	187	86	3	3	NUM
app01-6401	187	87	0	0	NUM
app01-6401	187	88	20	20	NUM
app01-6401	187	89	40	40	NUM
app01-6401	187	90	60	60	NUM
app01-6401	187	91	80	80	NUM
app01-6401	187	92	100	100	NUM
app01-6401	187	93	120	120	NUM
app01-6401	187	94	relaxation	relaxation	NOUN
app01-6401	187	95	order	order	NOUN
app01-6401	187	96	r	r	NOUN
app01-6401	187	97	c	c	NOUN
app01-6401	187	98	om	om	PROPN
app01-6401	187	99	pl	pl	PROPN
app01-6401	187	100	ia	ia	PROPN
app01-6401	187	101	nc	nc	PROPN
app01-6401	187	102	e	e	PROPN
app01-6401	187	103	c	c	PROPN
app01-6401	187	104	ĉr	ĉr	X
app01-6401	187	105	c̃r	c̃r	DET
app01-6401	187	106	c∗	c∗	PROPN
app01-6401	187	107	(	(	PUNCT
app01-6401	187	108	i	i	NOUN
app01-6401	187	109	)	)	PUNCT
app01-6401	187	110	1	1	NUM
app01-6401	187	111	2	2	NUM
app01-6401	187	112	3	3	NUM
app01-6401	187	113	0	0	NUM
app01-6401	187	114	20	20	NUM
app01-6401	187	115	40	40	NUM
app01-6401	187	116	60	60	NUM
app01-6401	187	117	80	80	NUM
app01-6401	187	118	100	100	NUM
app01-6401	187	119	120	120	NUM
app01-6401	187	120	relaxation	relaxation	NOUN
app01-6401	187	121	order	order	NOUN
app01-6401	187	122	r	r	NOUN
app01-6401	187	123	c	c	NOUN
app01-6401	187	124	om	om	PROPN
app01-6401	187	125	pl	pl	PROPN
app01-6401	187	126	ia	ia	PROPN
app01-6401	187	127	nc	nc	PROPN
app01-6401	187	128	e	e	PROPN
app01-6401	187	129	c	c	PROPN
app01-6401	187	130	ĉr	ĉr	X
app01-6401	187	131	c̃r	c̃r	PRON
app01-6401	187	132	c∗	c∗	PROPN
app01-6401	187	133	(	(	PUNCT
app01-6401	187	134	j	j	NOUN
app01-6401	187	135	)	)	PUNCT
app01-6401	187	136	figure	figure	NOUN
app01-6401	187	137	1	1	NUM
app01-6401	187	138	.	.	PUNCT
app01-6401	187	139	cantilever	cantilever	NOUN
app01-6401	187	140	beam	beam	NOUN
app01-6401	187	141	design	design	NOUN
app01-6401	187	142	problem	problem	NOUN
app01-6401	187	143	.	.	PUNCT
app01-6401	188	1	(	(	PUNCT
app01-6401	188	2	a	a	X
app01-6401	188	3	)	)	PUNCT
app01-6401	188	4	shows	show	VERB
app01-6401	188	5	the	the	DET
app01-6401	188	6	design	design	NOUN
app01-6401	188	7	domain	domain	NOUN
app01-6401	188	8	,	,	PUNCT
app01-6401	188	9	(	(	PUNCT
app01-6401	188	10	b)–(e	b)–(e	X
app01-6401	188	11	)	)	PUNCT
app01-6401	188	12	are	be	AUX
app01-6401	188	13	the	the	DET
app01-6401	188	14	optimal	optimal	ADJ
app01-6401	188	15	topologies	topology	NOUN
app01-6401	188	16	for	for	ADP
app01-6401	188	17	1	1	NUM
app01-6401	188	18	,	,	PUNCT
app01-6401	188	19	3	3	NUM
app01-6401	188	20	,	,	PUNCT
app01-6401	188	21	5	5	NUM
app01-6401	188	22	,	,	PUNCT
app01-6401	188	23	and	and	CCONJ
app01-6401	188	24	7	7	NUM
app01-6401	188	25	elements	element	NOUN
app01-6401	188	26	;	;	PUNCT
app01-6401	188	27	(	(	PUNCT
app01-6401	189	1	f	f	X
app01-6401	189	2	)	)	PUNCT
app01-6401	189	3	and	and	CCONJ
app01-6401	189	4	(	(	PUNCT
app01-6401	189	5	g	g	NOUN
app01-6401	189	6	)	)	PUNCT
app01-6401	189	7	display	display	NOUN
app01-6401	189	8	optimized	optimize	VERB
app01-6401	189	9	topologies	topology	NOUN
app01-6401	189	10	computed	compute	VERB
app01-6401	189	11	by	by	ADP
app01-6401	189	12	oc	oc	NOUN
app01-6401	189	13	with	with	ADP
app01-6401	189	14	discretization	discretization	NOUN
app01-6401	189	15	by	by	ADP
app01-6401	189	16	150	150	NUM
app01-6401	189	17	and	and	CCONJ
app01-6401	189	18	300	300	NUM
app01-6401	189	19	elements	element	NOUN
app01-6401	189	20	.	.	PUNCT
app01-6401	190	1	figures	figure	NOUN
app01-6401	190	2	(	(	PUNCT
app01-6401	190	3	h)–(j	h)–(j	X
app01-6401	190	4	)	)	PUNCT
app01-6401	190	5	show	show	VERB
app01-6401	190	6	the	the	DET
app01-6401	190	7	convergance	convergance	NOUN
app01-6401	190	8	of	of	ADP
app01-6401	190	9	po	po	PROPN
app01-6401	190	10	for	for	ADP
app01-6401	190	11	3	3	NUM
app01-6401	190	12	,	,	PUNCT
app01-6401	190	13	5	5	NUM
app01-6401	190	14	,	,	PUNCT
app01-6401	190	15	and	and	CCONJ
app01-6401	190	16	7	7	NUM
app01-6401	190	17	elements	element	NOUN
app01-6401	190	18	.	.	PUNCT
app01-6401	191	1	122	122	NUM
app01-6401	191	2	vol	vol	NOUN
app01-6401	191	3	.	.	PUNCT
app01-6401	192	1	26/2020	26/2020	NUM
app01-6401	192	2	on	on	ADP
app01-6401	192	3	optimum	optimum	ADJ
app01-6401	192	4	design	design	NOUN
app01-6401	192	5	of	of	ADP
app01-6401	192	6	frame	frame	NOUN
app01-6401	192	7	structures	structure	NOUN
app01-6401	192	8	1	1	NUM
app01-6401	192	9	2	2	NUM
app01-6401	192	10	x	x	SYM
app01-6401	192	11	y	y	NOUN
app01-6401	192	12	1	1	NUM
app01-6401	192	13	1	1	NUM
app01-6401	192	14	1	1	NUM
app01-6401	192	15	1	1	NUM
app01-6401	192	16	2	2	NUM
app01-6401	192	17	3	3	NUM
app01-6401	192	18	4	4	NUM
app01-6401	192	19	5	5	NUM
app01-6401	192	20	6	6	NUM
app01-6401	192	21	7	7	NUM
app01-6401	192	22	8	8	NUM
app01-6401	192	23	9	9	NUM
app01-6401	192	24	10	10	NUM
app01-6401	192	25	1	1	NUM
app01-6401	192	26	2	2	NUM
app01-6401	192	27	3	3	NUM
app01-6401	192	28	4	4	NUM
app01-6401	192	29	5	5	NUM
app01-6401	192	30	6	6	NUM
app01-6401	192	31	(	(	PUNCT
app01-6401	192	32	a	a	NOUN
app01-6401	192	33	)	)	PUNCT
app01-6401	192	34	(	(	PUNCT
app01-6401	192	35	b	b	X
app01-6401	192	36	)	)	PUNCT
app01-6401	192	37	c	c	NOUN
app01-6401	192	38	=	=	SYM
app01-6401	192	39	1042.20	1042.20	NUM
app01-6401	192	40	(	(	PUNCT
app01-6401	192	41	c	c	NOUN
app01-6401	192	42	)	)	PUNCT
app01-6401	192	43	c∗	c∗	NOUN
app01-6401	192	44	=	=	NOUN
app01-6401	193	1	959.32	959.32	NUM
app01-6401	193	2	1	1	NUM
app01-6401	193	3	2	2	NUM
app01-6401	193	4	0	0	NUM
app01-6401	193	5	500	500	NUM
app01-6401	193	6	1,000	1,000	NUM
app01-6401	193	7	1,500	1,500	NUM
app01-6401	193	8	2,000	2,000	NUM
app01-6401	193	9	relaxation	relaxation	NOUN
app01-6401	193	10	order	order	NOUN
app01-6401	193	11	r	r	NOUN
app01-6401	193	12	c	c	NOUN
app01-6401	193	13	om	om	PROPN
app01-6401	193	14	pl	pl	PROPN
app01-6401	193	15	ia	ia	PROPN
app01-6401	193	16	nc	nc	PROPN
app01-6401	193	17	e	e	PROPN
app01-6401	193	18	c	c	PROPN
app01-6401	193	19	ĉr	ĉr	X
app01-6401	193	20	c̃r	c̃r	PRON
app01-6401	193	21	c∗	c∗	PROPN
app01-6401	193	22	(	(	PUNCT
app01-6401	193	23	d	d	NOUN
app01-6401	193	24	)	)	PUNCT
app01-6401	193	25	figure	figure	NOUN
app01-6401	193	26	2	2	NUM
app01-6401	193	27	.	.	NOUN
app01-6401	193	28	10	10	NUM
app01-6401	193	29	-	-	PUNCT
app01-6401	193	30	beam	beam	NOUN
app01-6401	193	31	structure	structure	NOUN
app01-6401	193	32	design	design	NOUN
app01-6401	193	33	problem	problem	NOUN
app01-6401	193	34	.	.	PUNCT
app01-6401	194	1	(	(	PUNCT
app01-6401	194	2	a	a	X
app01-6401	194	3	)	)	PUNCT
app01-6401	194	4	shows	show	VERB
app01-6401	194	5	the	the	DET
app01-6401	194	6	design	design	NOUN
app01-6401	194	7	domain	domain	NOUN
app01-6401	194	8	.	.	PUNCT
app01-6401	195	1	while	while	SCONJ
app01-6401	195	2	all	all	DET
app01-6401	195	3	the	the	DET
app01-6401	195	4	tested	test	VERB
app01-6401	195	5	local	local	ADJ
app01-6401	195	6	optimization	optimization	NOUN
app01-6401	195	7	algorithms	algorithm	NOUN
app01-6401	195	8	converged	converge	VERB
app01-6401	195	9	to	to	ADP
app01-6401	195	10	the	the	DET
app01-6401	195	11	topology	topology	NOUN
app01-6401	195	12	in	in	ADP
app01-6401	195	13	(	(	PUNCT
app01-6401	195	14	b	b	NOUN
app01-6401	195	15	)	)	PUNCT
app01-6401	195	16	,	,	PUNCT
app01-6401	195	17	the	the	DET
app01-6401	195	18	global	global	ADJ
app01-6401	195	19	optimum	optimum	ADJ
app01-6401	195	20	design	design	NOUN
app01-6401	195	21	(	(	PUNCT
app01-6401	195	22	c	c	NOUN
app01-6401	195	23	)	)	PUNCT
app01-6401	195	24	obtained	obtain	VERB
app01-6401	195	25	by	by	ADP
app01-6401	195	26	po	po	PROPN
app01-6401	195	27	possesses	possess	VERB
app01-6401	195	28	a	a	DET
app01-6401	195	29	clearly	clearly	ADV
app01-6401	195	30	different	different	ADJ
app01-6401	195	31	topology	topology	NOUN
app01-6401	195	32	.	.	PUNCT
app01-6401	196	1	figure	figure	NOUN
app01-6401	196	2	(	(	PUNCT
app01-6401	196	3	d	d	NOUN
app01-6401	196	4	)	)	PUNCT
app01-6401	196	5	shows	show	VERB
app01-6401	196	6	the	the	DET
app01-6401	196	7	convergence	convergence	NOUN
app01-6401	196	8	of	of	ADP
app01-6401	196	9	po	po	PROPN
app01-6401	196	10	.	.	PUNCT
app01-6401	197	1	t	t	PROPN
app01-6401	198	1	[	[	X
app01-6401	198	2	s	s	X
app01-6401	198	3	]	]	X
app01-6401	198	4	ĉ	ĉ	NOUN
app01-6401	198	5	c̃	c̃	PROPN
app01-6401	198	6	a1	a1	NOUN
app01-6401	198	7	a3	a3	NOUN
app01-6401	198	8	a4	a4	PROPN
app01-6401	198	9	a5	a5	PROPN
app01-6401	198	10	a6	a6	NOUN
app01-6401	198	11	a7	a7	PROPN
app01-6401	198	12	a8	a8	PROPN
app01-6401	198	13	a9	a9	PROPN
app01-6401	198	14	a10	a10	NOUN
app01-6401	198	15	fmincon	fmincon	VERB
app01-6401	198	16	1.0	1.0	NUM
app01-6401	198	17	1042.14	1042.14	NUM
app01-6401	198	18	0.144	0.144	NUM
app01-6401	198	19	0.040	0.040	NUM
app01-6401	198	20	0.018	0.018	NUM
app01-6401	198	21	0.000	0.000	NUM
app01-6401	198	22	0.003	0.003	NUM
app01-6401	198	23	0.000	0.000	NUM
app01-6401	198	24	0.210	0.210	NUM
app01-6401	198	25	0.039	0.039	NUM
app01-6401	198	26	0.038	0.038	NUM
app01-6401	198	27	oc	oc	ADP
app01-6401	198	28	0.6	0.6	NUM
app01-6401	198	29	1042.33	1042.33	NUM
app01-6401	198	30	0.146	0.146	NUM
app01-6401	198	31	0.039	0.039	NUM
app01-6401	198	32	0.017	0.017	NUM
app01-6401	198	33	0.000	0.000	NUM
app01-6401	198	34	0.002	0.002	NUM
app01-6401	198	35	0.000	0.000	NUM
app01-6401	198	36	0.212	0.212	NUM
app01-6401	198	37	0.039	0.039	NUM
app01-6401	198	38	0.037	0.037	NUM
app01-6401	198	39	nsdp	nsdp	NOUN
app01-6401	198	40	1.0	1.0	NUM
app01-6401	198	41	1042.20	1042.20	NUM
app01-6401	198	42	0.144	0.144	NUM
app01-6401	198	43	0.040	0.040	NUM
app01-6401	198	44	0.018	0.018	NUM
app01-6401	198	45	0.000	0.000	NUM
app01-6401	198	46	0.003	0.003	NUM
app01-6401	198	47	0.000	0.000	NUM
app01-6401	198	48	0.210	0.210	NUM
app01-6401	198	49	0.039	0.039	NUM
app01-6401	198	50	0.038	0.038	NUM
app01-6401	198	51	po(1	po(1	NOUN
app01-6401	198	52	)	)	PUNCT
app01-6401	198	53	0.3	0.3	NUM
app01-6401	198	54	1429.31	1429.31	NUM
app01-6401	198	55	443.20	443.20	NUM
app01-6401	198	56	0.103	0.103	NUM
app01-6401	198	57	0.082	0.082	NUM
app01-6401	198	58	0.000	0.000	NUM
app01-6401	198	59	0.029	0.029	NUM
app01-6401	198	60	0.000	0.000	NUM
app01-6401	198	61	0.000	0.000	NUM
app01-6401	198	62	0.121	0.121	NUM
app01-6401	198	63	0.095	0.095	NUM
app01-6401	198	64	0.069	0.069	NUM
app01-6401	198	65	po(2	po(2	NOUN
app01-6401	198	66	)	)	PUNCT
app01-6401	198	67	5.2	5.2	NUM
app01-6401	198	68	959.32	959.32	NUM
app01-6401	198	69	959.31	959.31	NUM
app01-6401	198	70	0.070	0.070	NUM
app01-6401	198	71	0.186	0.186	NUM
app01-6401	198	72	0.000	0.000	NUM
app01-6401	198	73	0.043	0.043	NUM
app01-6401	198	74	0.000	0.000	NUM
app01-6401	198	75	0.098	0.098	NUM
app01-6401	198	76	0.000	0.000	NUM
app01-6401	198	77	0.064	0.064	NUM
app01-6401	198	78	0.000	0.000	NUM
app01-6401	198	79	table	table	NOUN
app01-6401	198	80	2	2	NUM
app01-6401	198	81	.	.	PUNCT
app01-6401	198	82	comparison	comparison	NOUN
app01-6401	198	83	of	of	ADP
app01-6401	198	84	the	the	DET
app01-6401	198	85	four	four	NUM
app01-6401	198	86	optimization	optimization	NOUN
app01-6401	198	87	approaches	approach	NOUN
app01-6401	198	88	on	on	ADP
app01-6401	198	89	the	the	DET
app01-6401	198	90	design	design	NOUN
app01-6401	198	91	of	of	ADP
app01-6401	198	92	10	10	NUM
app01-6401	198	93	-	-	PUNCT
app01-6401	198	94	beam	beam	NOUN
app01-6401	198	95	structure	structure	NOUN
app01-6401	198	96	.	.	PUNCT
app01-6401	199	1	bold	bold	ADJ
app01-6401	199	2	text	text	NOUN
app01-6401	199	3	denotes	denote	NOUN
app01-6401	199	4	proven	prove	VERB
app01-6401	199	5	global	global	ADJ
app01-6401	199	6	optimum	optimum	NOUN
app01-6401	199	7	.	.	PUNCT
app01-6401	200	1	the	the	DET
app01-6401	200	2	cross	cross	ADJ
app01-6401	200	3	-	-	ADJ
app01-6401	200	4	sectional	sectional	ADJ
app01-6401	200	5	area	area	NOUN
app01-6401	200	6	a2	a2	PROPN
app01-6401	200	7	is	be	AUX
app01-6401	200	8	zero	zero	NUM
app01-6401	200	9	in	in	ADP
app01-6401	200	10	all	all	DET
app01-6401	200	11	test	test	NOUN
app01-6401	200	12	cases	case	NOUN
app01-6401	200	13	.	.	PUNCT
app01-6401	201	1	1	1	NUM
app01-6401	201	2	2	2	NUM
app01-6401	201	3	3	3	NUM
app01-6401	201	4	4	4	NUM
app01-6401	201	5	5	5	NUM
app01-6401	201	6	1	1	NUM
app01-6401	201	7	1	1	NUM
app01-6401	201	8	2	2	NUM
app01-6401	201	9	3	3	NUM
app01-6401	201	10	4	4	NUM
app01-6401	201	11	5	5	NUM
app01-6401	201	12	6	6	NUM
app01-6401	201	13	2	2	NUM
app01-6401	201	14	2	2	NUM
app01-6401	201	15	2	2	NUM
app01-6401	201	16	2	2	NUM
app01-6401	201	17	2	2	NUM
app01-6401	201	18	10	10	NUM
app01-6401	201	19	(	(	PUNCT
app01-6401	201	20	a	a	NOUN
app01-6401	201	21	)	)	PUNCT
app01-6401	201	22	tp	tp	ADP
app01-6401	201	23	5tp	5tp	NOUN
app01-6401	201	24	10	10	NUM
app01-6401	201	25	t	t	NOUN
app01-6401	201	26	p	p	X
app01-6401	201	27	(	(	PUNCT
app01-6401	201	28	b	b	NOUN
app01-6401	201	29	)	)	PUNCT
app01-6401	201	30	1	1	NUM
app01-6401	201	31	2	2	NUM
app01-6401	201	32	3	3	NUM
app01-6401	201	33	0	0	NUM
app01-6401	201	34	500	500	NUM
app01-6401	201	35	1,000	1,000	NUM
app01-6401	201	36	1,500	1,500	NUM
app01-6401	201	37	2,000	2,000	NUM
app01-6401	201	38	2,500	2,500	NUM
app01-6401	201	39	relaxation	relaxation	NOUN
app01-6401	201	40	order	order	NOUN
app01-6401	202	1	r	r	NOUN
app01-6401	202	2	c	c	NOUN
app01-6401	202	3	om	om	PROPN
app01-6401	202	4	pl	pl	PROPN
app01-6401	202	5	ia	ia	PROPN
app01-6401	202	6	nc	nc	PROPN
app01-6401	202	7	e	e	PROPN
app01-6401	202	8	c	c	PROPN
app01-6401	202	9	ĉr	ĉr	X
app01-6401	202	10	c̃r	c̃r	PRON
app01-6401	202	11	c∗	c∗	PROPN
app01-6401	202	12	(	(	PUNCT
app01-6401	202	13	c	c	NOUN
app01-6401	202	14	)	)	PUNCT
app01-6401	202	15	figure	figure	NOUN
app01-6401	202	16	3	3	NUM
app01-6401	202	17	.	.	PUNCT
app01-6401	202	18	girder	girder	NOUN
app01-6401	202	19	beam	beam	PROPN
app01-6401	202	20	design	design	NOUN
app01-6401	202	21	problem	problem	NOUN
app01-6401	202	22	.	.	PUNCT
app01-6401	203	1	(	(	PUNCT
app01-6401	203	2	a	a	X
app01-6401	203	3	)	)	PUNCT
app01-6401	203	4	shows	show	VERB
app01-6401	203	5	the	the	DET
app01-6401	203	6	design	design	NOUN
app01-6401	203	7	domain	domain	NOUN
app01-6401	203	8	,	,	PUNCT
app01-6401	203	9	(	(	PUNCT
app01-6401	203	10	b	b	X
app01-6401	203	11	)	)	PUNCT
app01-6401	203	12	the	the	DET
app01-6401	203	13	cross	cross	ADJ
app01-6401	203	14	-	-	ADJ
app01-6401	203	15	sectional	sectional	ADJ
app01-6401	203	16	shape	shape	NOUN
app01-6401	203	17	,	,	PUNCT
app01-6401	203	18	and	and	CCONJ
app01-6401	203	19	(	(	PUNCT
app01-6401	203	20	c	c	X
app01-6401	203	21	)	)	PUNCT
app01-6401	203	22	the	the	DET
app01-6401	203	23	convergence	convergence	NOUN
app01-6401	203	24	of	of	ADP
app01-6401	203	25	polynomial	polynomial	ADJ
app01-6401	203	26	optimization	optimization	NOUN
app01-6401	203	27	.	.	PUNCT
app01-6401	204	1	t	t	X
app01-6401	205	1	[	[	X
app01-6401	205	2	s	s	X
app01-6401	205	3	]	]	X
app01-6401	205	4	ĉ	ĉ	X
app01-6401	205	5	c̃	c̃	PROPN
app01-6401	205	6	a1	a1	NOUN
app01-6401	205	7	a2	a2	PROPN
app01-6401	205	8	a3	a3	PROPN
app01-6401	205	9	a4	a4	PROPN
app01-6401	205	10	a5	a5	PROPN
app01-6401	205	11	fmincon	fmincon	VERB
app01-6401	205	12	0.4	0.4	NUM
app01-6401	205	13	0.394	0.394	NUM
app01-6401	205	14	0.256	0.256	NUM
app01-6401	205	15	0.000	0.000	NUM
app01-6401	205	16	0.003	0.003	NUM
app01-6401	205	17	0.000	0.000	NUM
app01-6401	205	18	oc	oc	ADP
app01-6401	205	19	0.1	0.1	NUM
app01-6401	205	20	1372.25	1372.25	NUM
app01-6401	205	21	0.010	0.010	NUM
app01-6401	205	22	0.017	0.017	NUM
app01-6401	205	23	0.022	0.022	NUM
app01-6401	205	24	0.025	0.025	NUM
app01-6401	205	25	0.026	0.026	NUM
app01-6401	205	26	nsdp	nsdp	NOUN
app01-6401	205	27	2.0	2.0	NUM
app01-6401	205	28	0.000	0.000	NUM
app01-6401	205	29	0.000	0.000	NUM
app01-6401	205	30	0.000	0.000	NUM
app01-6401	205	31	0.000	0.000	NUM
app01-6401	205	32	0.000	0.000	NUM
app01-6401	205	33	po(1	po(1	NOUN
app01-6401	205	34	)	)	PUNCT
app01-6401	205	35	0.2	0.2	NUM
app01-6401	205	36	1456.75	1456.75	NUM
app01-6401	205	37	297.34	297.34	NUM
app01-6401	205	38	0.007	0.007	NUM
app01-6401	205	39	0.015	0.015	NUM
app01-6401	205	40	0.022	0.022	NUM
app01-6401	205	41	0.027	0.027	NUM
app01-6401	205	42	0.029	0.029	NUM
app01-6401	205	43	po(2	po(2	PROPN
app01-6401	205	44	)	)	PUNCT
app01-6401	205	45	1.0	1.0	NUM
app01-6401	205	46	1426.05	1426.05	NUM
app01-6401	205	47	1286.44	1286.44	NUM
app01-6401	205	48	0.007	0.007	NUM
app01-6401	205	49	0.016	0.016	NUM
app01-6401	205	50	0.023	0.023	NUM
app01-6401	205	51	0.026	0.026	NUM
app01-6401	205	52	0.028	0.028	NUM
app01-6401	205	53	po(3	po(3	NOUN
app01-6401	205	54	)	)	PUNCT
app01-6401	205	55	37.7	37.7	NUM
app01-6401	205	56	1372.25	1372.25	NUM
app01-6401	205	57	1372.25	1372.25	NUM
app01-6401	205	58	0.010	0.010	NUM
app01-6401	205	59	0.017	0.017	NUM
app01-6401	205	60	0.022	0.022	NUM
app01-6401	205	61	0.025	0.025	NUM
app01-6401	205	62	0.026	0.026	NUM
app01-6401	205	63	table	table	NOUN
app01-6401	205	64	3	3	NUM
app01-6401	205	65	.	.	PUNCT
app01-6401	205	66	comparison	comparison	NOUN
app01-6401	205	67	of	of	ADP
app01-6401	205	68	the	the	DET
app01-6401	205	69	four	four	NUM
app01-6401	205	70	optimization	optimization	NOUN
app01-6401	205	71	approaches	approach	NOUN
app01-6401	205	72	on	on	ADP
app01-6401	205	73	the	the	DET
app01-6401	205	74	design	design	NOUN
app01-6401	205	75	of	of	ADP
app01-6401	205	76	the	the	DET
app01-6401	205	77	girder	girder	NOUN
app01-6401	205	78	beam	beam	PROPN
app01-6401	205	79	problem	problem	NOUN
app01-6401	205	80	.	.	PUNCT
app01-6401	206	1	bold	bold	ADJ
app01-6401	206	2	text	text	NOUN
app01-6401	206	3	denotes	denote	VERB
app01-6401	206	4	the	the	DET
app01-6401	206	5	proven	prove	VERB
app01-6401	206	6	global	global	ADJ
app01-6401	206	7	optimum	optimum	NOUN
app01-6401	206	8	.	.	PUNCT
app01-6401	207	1	123	123	NUM
app01-6401	207	2	m.	m.	NOUN
app01-6401	207	3	tyburec	tyburec	NOUN
app01-6401	207	4	,	,	PUNCT
app01-6401	207	5	j.	j.	PROPN
app01-6401	207	6	zeman	zeman	PROPN
app01-6401	207	7	,	,	PUNCT
app01-6401	207	8	m.	m.	NOUN
app01-6401	207	9	kružík	kružík	PROPN
app01-6401	207	10	,	,	PUNCT
app01-6401	207	11	d.	d.	PROPN
app01-6401	207	12	henrion	henrion	PROPN
app01-6401	207	13	acta	acta	PROPN
app01-6401	207	14	polytechnica	polytechnica	PROPN
app01-6401	207	15	ctu	ctu	NOUN
app01-6401	207	16	proceedings	proceeding	NOUN
app01-6401	207	17	3.2	3.2	NUM
app01-6401	207	18	.	.	PUNCT
app01-6401	207	19	10	10	NUM
app01-6401	207	20	-	-	PUNCT
app01-6401	207	21	beam	beam	NOUN
app01-6401	207	22	frame	frame	NOUN
app01-6401	207	23	structure	structure	NOUN
app01-6401	207	24	second	second	ADV
app01-6401	207	25	,	,	PUNCT
app01-6401	207	26	we	we	PRON
app01-6401	207	27	consider	consider	VERB
app01-6401	207	28	the	the	DET
app01-6401	207	29	topology	topology	NOUN
app01-6401	207	30	optimization	optimization	NOUN
app01-6401	207	31	problem	problem	NOUN
app01-6401	207	32	of	of	ADP
app01-6401	207	33	designing	design	VERB
app01-6401	207	34	circular	circular	ADJ
app01-6401	207	35	cross	cross	NOUN
app01-6401	207	36	-	-	NOUN
app01-6401	207	37	sections	section	NOUN
app01-6401	207	38	of	of	ADP
app01-6401	207	39	the	the	DET
app01-6401	207	40	10	10	NUM
app01-6401	207	41	-	-	PUNCT
app01-6401	207	42	beam	beam	NOUN
app01-6401	207	43	structure	structure	NOUN
app01-6401	207	44	shown	show	VERB
app01-6401	207	45	in	in	ADP
app01-6401	207	46	fig	fig	NOUN
app01-6401	207	47	.	.	PUNCT
app01-6401	208	1	2a	2a	NUM
app01-6401	208	2	.	.	PUNCT
app01-6401	209	1	this	this	DET
app01-6401	209	2	structure	structure	NOUN
app01-6401	209	3	is	be	AUX
app01-6401	209	4	loaded	load	VERB
app01-6401	209	5	by	by	ADP
app01-6401	209	6	two	two	NUM
app01-6401	209	7	moments	moment	NOUN
app01-6401	209	8	of	of	ADP
app01-6401	209	9	magnitudes	magnitude	NOUN
app01-6401	209	10	1	1	NUM
app01-6401	209	11	and	and	CCONJ
app01-6401	209	12	2	2	NUM
app01-6401	209	13	,	,	PUNCT
app01-6401	209	14	placed	place	VERB
app01-6401	209	15	at	at	ADP
app01-6401	209	16	the	the	DET
app01-6401	209	17	nodes	node	NOUN
app01-6401	209	18	2	2	NUM
app01-6401	209	19	and	and	CCONJ
app01-6401	209	20	3	3	NUM
app01-6401	209	21	,	,	PUNCT
app01-6401	209	22	respectively	respectively	ADV
app01-6401	209	23	.	.	PUNCT
app01-6401	210	1	note	note	VERB
app01-6401	210	2	that	that	SCONJ
app01-6401	210	3	there	there	PRON
app01-6401	210	4	is	be	VERB
app01-6401	210	5	no	no	DET
app01-6401	210	6	intersection	intersection	NOUN
app01-6401	210	7	between	between	ADP
app01-6401	210	8	the	the	DET
app01-6401	210	9	elements	element	NOUN
app01-6401	210	10	3	3	NUM
app01-6401	210	11	and	and	CCONJ
app01-6401	210	12	4	4	NUM
app01-6401	210	13	,	,	PUNCT
app01-6401	210	14	and	and	CCONJ
app01-6401	210	15	between	between	ADP
app01-6401	210	16	6	6	NUM
app01-6401	210	17	and	and	CCONJ
app01-6401	210	18	7	7	NUM
app01-6401	210	19	.	.	PUNCT
app01-6401	211	1	we	we	PRON
app01-6401	211	2	assume	assume	VERB
app01-6401	211	3	the	the	DET
app01-6401	211	4	young	young	ADJ
app01-6401	211	5	modulus	modulus	NOUN
app01-6401	211	6	e	e	NOUN
app01-6401	211	7	=	=	SYM
app01-6401	211	8	1	1	NUM
app01-6401	211	9	and	and	CCONJ
app01-6401	211	10	the	the	DET
app01-6401	211	11	volume	volume	NOUN
app01-6401	211	12	bound	bind	VERB
app01-6401	211	13	v	v	ADP
app01-6401	211	14	=	=	SYM
app01-6401	211	15	0.5	0.5	NUM
app01-6401	211	16	.	.	PUNCT
app01-6401	211	17	evaluating	evaluate	VERB
app01-6401	211	18	the	the	DET
app01-6401	211	19	four	four	NUM
app01-6401	211	20	optimization	optimization	NOUN
app01-6401	211	21	methods	method	NOUN
app01-6401	211	22	,	,	PUNCT
app01-6401	211	23	table	table	NOUN
app01-6401	211	24	2	2	NUM
app01-6401	211	25	,	,	PUNCT
app01-6401	211	26	we	we	PRON
app01-6401	211	27	see	see	VERB
app01-6401	211	28	that	that	SCONJ
app01-6401	211	29	while	while	SCONJ
app01-6401	211	30	the	the	DET
app01-6401	211	31	local	local	ADJ
app01-6401	211	32	optimization	optimization	NOUN
app01-6401	211	33	methods	method	NOUN
app01-6401	211	34	converged	converge	VERB
app01-6401	211	35	to	to	ADP
app01-6401	211	36	nearby	nearby	ADJ
app01-6401	211	37	local	local	ADJ
app01-6401	211	38	minima	minima	NOUN
app01-6401	211	39	of	of	ADP
app01-6401	211	40	topologies	topology	NOUN
app01-6401	211	41	shown	show	VERB
app01-6401	211	42	in	in	ADP
app01-6401	211	43	fig	fig	NOUN
app01-6401	211	44	.	.	PUNCT
app01-6401	212	1	2b	2b	NOUN
app01-6401	212	2	,	,	PUNCT
app01-6401	212	3	po	po	PROPN
app01-6401	212	4	found	find	VERB
app01-6401	212	5	the	the	DET
app01-6401	212	6	global	global	ADJ
app01-6401	212	7	optimum	optimum	NOUN
app01-6401	212	8	of	of	ADP
app01-6401	212	9	a	a	DET
app01-6401	212	10	clearly	clearly	ADV
app01-6401	212	11	different	different	ADJ
app01-6401	212	12	topology	topology	NOUN
app01-6401	212	13	,	,	PUNCT
app01-6401	212	14	fig	fig	NOUN
app01-6401	212	15	.	.	PUNCT
app01-6401	213	1	2c	2c	NOUN
app01-6401	213	2	.	.	PUNCT
app01-6401	214	1	moreover	moreover	ADV
app01-6401	214	2	,	,	PUNCT
app01-6401	214	3	the	the	DET
app01-6401	214	4	global	global	ADJ
app01-6401	214	5	optimum	optimum	NOUN
app01-6401	214	6	possesses	possess	VERB
app01-6401	214	7	the	the	DET
app01-6401	214	8	compliance	compliance	NOUN
app01-6401	214	9	lower	lower	ADV
app01-6401	214	10	by	by	ADP
app01-6401	214	11	8	8	NUM
app01-6401	214	12	%	%	NOUN
app01-6401	214	13	,	,	PUNCT
app01-6401	214	14	which	which	PRON
app01-6401	214	15	was	be	AUX
app01-6401	214	16	reached	reach	VERB
app01-6401	214	17	in	in	ADP
app01-6401	214	18	the	the	DET
app01-6401	214	19	second	second	ADJ
app01-6401	214	20	relaxation	relaxation	NOUN
app01-6401	214	21	,	,	PUNCT
app01-6401	214	22	fig	fig	NOUN
app01-6401	214	23	.	.	PUNCT
app01-6401	215	1	2d	2d	NOUN
app01-6401	215	2	.	.	PUNCT
app01-6401	216	1	3.3	3.3	NUM
app01-6401	216	2	.	.	PUNCT
app01-6401	217	1	i	i	PRON
app01-6401	217	2	-	-	PUNCT
app01-6401	217	3	shaped	shape	VERB
app01-6401	217	4	girder	girder	NOUN
app01-6401	217	5	with	with	ADP
app01-6401	217	6	self	self	NOUN
app01-6401	217	7	-	-	PUNCT
app01-6401	217	8	weight	weight	NOUN
app01-6401	217	9	last	last	NOUN
app01-6401	217	10	,	,	PUNCT
app01-6401	217	11	we	we	PRON
app01-6401	217	12	consider	consider	VERB
app01-6401	217	13	a	a	DET
app01-6401	217	14	simply	simply	ADV
app01-6401	217	15	-	-	PUNCT
app01-6401	217	16	supported	support	VERB
app01-6401	217	17	i	i	NOUN
app01-6401	217	18	-	-	PUNCT
app01-6401	217	19	shaped	shape	VERB
app01-6401	217	20	girder	girder	NOUN
app01-6401	217	21	beam	beam	NOUN
app01-6401	217	22	of	of	ADP
app01-6401	217	23	the	the	DET
app01-6401	217	24	span	span	NOUN
app01-6401	217	25	20	20	NUM
app01-6401	217	26	,	,	PUNCT
app01-6401	217	27	loaded	load	VERB
app01-6401	217	28	by	by	ADP
app01-6401	217	29	a	a	DET
app01-6401	217	30	uniform	uniform	ADJ
app01-6401	217	31	load	load	NOUN
app01-6401	217	32	1	1	NUM
app01-6401	217	33	and	and	CCONJ
app01-6401	217	34	self	self	NOUN
app01-6401	217	35	-	-	PUNCT
app01-6401	217	36	weight	weight	NOUN
app01-6401	217	37	.	.	PUNCT
app01-6401	218	1	due	due	ADP
app01-6401	218	2	to	to	ADP
app01-6401	218	3	the	the	DET
app01-6401	218	4	problem	problem	NOUN
app01-6401	218	5	symmetry	symmetry	NOUN
app01-6401	218	6	,	,	PUNCT
app01-6401	218	7	we	we	PRON
app01-6401	218	8	consider	consider	VERB
app01-6401	218	9	only	only	ADV
app01-6401	218	10	one	one	NUM
app01-6401	218	11	half	half	NOUN
app01-6401	218	12	of	of	ADP
app01-6401	218	13	the	the	DET
app01-6401	218	14	problem	problem	NOUN
app01-6401	218	15	,	,	PUNCT
app01-6401	218	16	fig	fig	NOUN
app01-6401	218	17	.	.	PUNCT
app01-6401	219	1	3a	3a	NUM
app01-6401	219	2	,	,	PUNCT
app01-6401	219	3	and	and	CCONJ
app01-6401	219	4	discretize	discretize	VERB
app01-6401	219	5	it	it	PRON
app01-6401	219	6	using	use	VERB
app01-6401	219	7	5	5	NUM
app01-6401	219	8	finite	finite	ADJ
app01-6401	219	9	elements	element	NOUN
app01-6401	219	10	of	of	ADP
app01-6401	219	11	equal	equal	ADJ
app01-6401	219	12	length	length	NOUN
app01-6401	219	13	.	.	PUNCT
app01-6401	220	1	this	this	DET
app01-6401	220	2	(	(	PUNCT
app01-6401	220	3	half	half	NOUN
app01-6401	220	4	of	of	ADP
app01-6401	220	5	the	the	DET
app01-6401	220	6	)	)	PUNCT
app01-6401	220	7	girder	girder	NOUN
app01-6401	220	8	beam	beam	NOUN
app01-6401	220	9	is	be	AUX
app01-6401	220	10	allowed	allow	VERB
app01-6401	220	11	to	to	PART
app01-6401	220	12	utilize	utilize	VERB
app01-6401	220	13	at	at	ADP
app01-6401	220	14	most	most	ADJ
app01-6401	220	15	v	v	NOUN
app01-6401	220	16	=	=	SYM
app01-6401	220	17	0.2	0.2	NUM
app01-6401	220	18	material	material	NOUN
app01-6401	220	19	of	of	ADP
app01-6401	220	20	the	the	DET
app01-6401	220	21	young	young	ADJ
app01-6401	220	22	modulus	modulus	NOUN
app01-6401	220	23	e	e	NOUN
app01-6401	220	24	=	=	SYM
app01-6401	220	25	104	104	NUM
app01-6401	220	26	and	and	CCONJ
app01-6401	220	27	of	of	ADP
app01-6401	220	28	density	density	NOUN
app01-6401	220	29	ρ	ρ	PROPN
app01-6401	221	1	=	=	SYM
app01-6401	221	2	3	3	X
app01-6401	221	3	.	.	PUNCT
app01-6401	222	1	the	the	DET
app01-6401	222	2	beam	beam	PROPN
app01-6401	222	3	cross	cross	NOUN
app01-6401	222	4	-	-	NOUN
app01-6401	222	5	sections	section	NOUN
app01-6401	222	6	are	be	AUX
app01-6401	222	7	parameterized	parameterize	VERB
app01-6401	222	8	by	by	ADP
app01-6401	222	9	the	the	DET
app01-6401	222	10	parameter	parameter	NOUN
app01-6401	222	11	tp	tp	PROPN
app01-6401	222	12	,	,	PUNCT
app01-6401	222	13	which	which	PRON
app01-6401	222	14	denotes	denote	VERB
app01-6401	222	15	the	the	DET
app01-6401	222	16	thicknesses	thickness	NOUN
app01-6401	222	17	of	of	ADP
app01-6401	222	18	the	the	DET
app01-6401	222	19	flanges	flange	NOUN
app01-6401	222	20	and	and	CCONJ
app01-6401	222	21	web	web	NOUN
app01-6401	222	22	.	.	PUNCT
app01-6401	223	1	the	the	DET
app01-6401	223	2	cross	cross	ADJ
app01-6401	223	3	-	-	ADJ
app01-6401	223	4	sectional	sectional	ADJ
app01-6401	223	5	area	area	NOUN
app01-6401	223	6	equals	equal	VERB
app01-6401	223	7	a(tp	a(tp	PROPN
app01-6401	223	8	)	)	PUNCT
app01-6401	223	9	=	=	SYM
app01-6401	224	1	18t2p	18t2p	X
app01-6401	224	2	.	.	PUNCT
app01-6401	225	1	we	we	PRON
app01-6401	225	2	assume	assume	VERB
app01-6401	225	3	that	that	SCONJ
app01-6401	225	4	the	the	DET
app01-6401	225	5	upper	upper	ADJ
app01-6401	225	6	surfaces	surface	NOUN
app01-6401	225	7	of	of	ADP
app01-6401	225	8	the	the	DET
app01-6401	225	9	top	top	ADJ
app01-6401	225	10	flanges	flange	NOUN
app01-6401	225	11	are	be	AUX
app01-6401	225	12	aligned	align	VERB
app01-6401	225	13	,	,	PUNCT
app01-6401	225	14	so	so	SCONJ
app01-6401	225	15	that	that	SCONJ
app01-6401	225	16	we	we	PRON
app01-6401	225	17	have	have	VERB
app01-6401	225	18	i(tp	i(tp	VERB
app01-6401	225	19	)	)	PUNCT
app01-6401	225	20	=	=	PUNCT
app01-6401	226	1	696t4p	696t4p	NUM
app01-6401	226	2	=	=	SYM
app01-6401	226	3	58/27a(tp)2	58/27a(tp)2	PROPN
app01-6401	226	4	.	.	PUNCT
app01-6401	227	1	consequently	consequently	ADV
app01-6401	227	2	,	,	PUNCT
app01-6401	227	3	we	we	PRON
app01-6401	227	4	optimize	optimize	VERB
app01-6401	227	5	ai	ai	VERB
app01-6401	227	6	of	of	ADP
app01-6401	227	7	individual	individual	ADJ
app01-6401	227	8	elements	element	NOUN
app01-6401	227	9	,	,	PUNCT
app01-6401	227	10	rather	rather	ADV
app01-6401	227	11	than	than	ADP
app01-6401	227	12	tp	tp	PROPN
app01-6401	227	13	.	.	PUNCT
app01-6401	227	14	table	table	NOUN
app01-6401	227	15	3	3	NUM
app01-6401	227	16	reveals	reveal	VERB
app01-6401	227	17	that	that	SCONJ
app01-6401	227	18	for	for	ADP
app01-6401	227	19	this	this	DET
app01-6401	227	20	specific	specific	ADJ
app01-6401	227	21	problem	problem	NOUN
app01-6401	227	22	the	the	DET
app01-6401	227	23	oc	oc	NOUN
app01-6401	227	24	converged	converge	VERB
app01-6401	227	25	to	to	ADP
app01-6401	227	26	the	the	DET
app01-6401	227	27	global	global	ADJ
app01-6401	227	28	optimum	optimum	NOUN
app01-6401	227	29	.	.	PUNCT
app01-6401	228	1	on	on	ADP
app01-6401	228	2	the	the	DET
app01-6401	228	3	other	other	ADJ
app01-6401	228	4	hand	hand	NOUN
app01-6401	228	5	,	,	PUNCT
app01-6401	228	6	the	the	DET
app01-6401	228	7	fmincon	fmincon	NOUN
app01-6401	228	8	and	and	CCONJ
app01-6401	228	9	non	non	ADJ
app01-6401	228	10	-	-	ADJ
app01-6401	228	11	linear	linear	ADJ
app01-6401	228	12	semidefinite	semidefinite	NOUN
app01-6401	228	13	programming	programming	NOUN
app01-6401	228	14	approaches	approach	NOUN
app01-6401	228	15	converged	converge	VERB
app01-6401	228	16	to	to	ADP
app01-6401	228	17	an	an	DET
app01-6401	228	18	infeasible	infeasible	ADJ
app01-6401	228	19	point	point	NOUN
app01-6401	228	20	.	.	PUNCT
app01-6401	229	1	polynomial	polynomial	ADJ
app01-6401	229	2	optimization	optimization	NOUN
app01-6401	229	3	exhibited	exhibit	VERB
app01-6401	229	4	convergence	convergence	NOUN
app01-6401	229	5	to	to	ADP
app01-6401	229	6	the	the	DET
app01-6401	229	7	global	global	ADJ
app01-6401	229	8	optimum	optimum	NOUN
app01-6401	229	9	in	in	ADP
app01-6401	229	10	three	three	NUM
app01-6401	229	11	relaxations	relaxation	NOUN
app01-6401	229	12	,	,	PUNCT
app01-6401	229	13	fig	fig	NOUN
app01-6401	229	14	.	.	PUNCT
app01-6401	230	1	3c	3c	NUM
app01-6401	230	2	.	.	PUNCT
app01-6401	231	1	notice	notice	NOUN
app01-6401	231	2	,	,	PUNCT
app01-6401	231	3	moreover	moreover	ADV
app01-6401	231	4	,	,	PUNCT
app01-6401	231	5	that	that	SCONJ
app01-6401	231	6	the	the	DET
app01-6401	231	7	designs	design	NOUN
app01-6401	231	8	found	find	VERB
app01-6401	231	9	for	for	ADP
app01-6401	231	10	r	r	NOUN
app01-6401	231	11	=	=	SYM
app01-6401	231	12	{	{	PUNCT
app01-6401	231	13	1	1	NUM
app01-6401	231	14	,	,	PUNCT
app01-6401	231	15	2	2	NUM
app01-6401	231	16	}	}	PUNCT
app01-6401	231	17	were	be	AUX
app01-6401	231	18	of	of	ADP
app01-6401	231	19	very	very	ADV
app01-6401	231	20	high	high	ADJ
app01-6401	231	21	qualities	quality	NOUN
app01-6401	231	22	.	.	PUNCT
app01-6401	232	1	4	4	X
app01-6401	232	2	.	.	X
app01-6401	232	3	conclusions	conclusion	NOUN
app01-6401	232	4	in	in	ADP
app01-6401	232	5	this	this	DET
app01-6401	232	6	contribution	contribution	NOUN
app01-6401	232	7	,	,	PUNCT
app01-6401	232	8	we	we	PRON
app01-6401	232	9	investigated	investigate	VERB
app01-6401	232	10	four	four	NUM
app01-6401	232	11	topology	topology	NOUN
app01-6401	232	12	optimization	optimization	NOUN
app01-6401	232	13	techniques	technique	NOUN
app01-6401	232	14	for	for	ADP
app01-6401	232	15	the	the	DET
app01-6401	232	16	design	design	NOUN
app01-6401	232	17	of	of	ADP
app01-6401	232	18	frame	frame	NOUN
app01-6401	232	19	structures	structure	NOUN
app01-6401	232	20	with	with	ADP
app01-6401	232	21	a	a	DET
app01-6401	232	22	given	give	VERB
app01-6401	232	23	aspect	aspect	NOUN
app01-6401	232	24	-	-	PUNCT
app01-6401	232	25	ratios	ratio	NOUN
app01-6401	232	26	all	all	DET
app01-6401	232	27	components	component	NOUN
app01-6401	232	28	of	of	ADP
app01-6401	232	29	their	their	PRON
app01-6401	232	30	cross	cross	NOUN
app01-6401	232	31	-	-	NOUN
app01-6401	232	32	sections	section	NOUN
app01-6401	232	33	.	.	PUNCT
app01-6401	233	1	three	three	NUM
app01-6401	233	2	of	of	ADP
app01-6401	233	3	the	the	DET
app01-6401	233	4	optimization	optimization	NOUN
app01-6401	233	5	techniques	technique	NOUN
app01-6401	233	6	—	—	PUNCT
app01-6401	233	7	general	general	ADJ
app01-6401	233	8	non	non	ADJ
app01-6401	233	9	-	-	ADJ
app01-6401	233	10	linear	linear	ADJ
app01-6401	233	11	formulation	formulation	NOUN
app01-6401	233	12	solved	solve	VERB
app01-6401	233	13	by	by	ADP
app01-6401	233	14	the	the	DET
app01-6401	233	15	fmincon	fmincon	PROPN
app01-6401	233	16	solver	solver	NOUN
app01-6401	233	17	,	,	PUNCT
app01-6401	233	18	optimality	optimality	NOUN
app01-6401	233	19	criteria	criterion	NOUN
app01-6401	233	20	,	,	PUNCT
app01-6401	233	21	and	and	CCONJ
app01-6401	233	22	non	non	ADJ
app01-6401	233	23	-	-	ADJ
app01-6401	233	24	linear	linear	ADJ
app01-6401	233	25	semidefinite	semidefinite	NOUN
app01-6401	233	26	programming	programming	NOUN
app01-6401	233	27	—	—	PUNCT
app01-6401	233	28	provide	provide	VERB
app01-6401	233	29	a	a	DET
app01-6401	233	30	local	local	ADJ
app01-6401	233	31	solution	solution	NOUN
app01-6401	233	32	to	to	ADP
app01-6401	233	33	the	the	DET
app01-6401	233	34	considered	consider	VERB
app01-6401	233	35	optimization	optimization	NOUN
app01-6401	233	36	problem	problem	NOUN
app01-6401	233	37	,	,	PUNCT
app01-6401	233	38	and	and	CCONJ
app01-6401	233	39	in	in	ADP
app01-6401	233	40	turn	turn	NOUN
app01-6401	233	41	converge	converge	VERB
app01-6401	233	42	to	to	ADP
app01-6401	233	43	a	a	DET
app01-6401	233	44	local	local	ADJ
app01-6401	233	45	optimum	optimum	NOUN
app01-6401	233	46	in	in	ADP
app01-6401	233	47	general	general	ADJ
app01-6401	233	48	.	.	PUNCT
app01-6401	234	1	unfortunately	unfortunately	ADV
app01-6401	234	2	,	,	PUNCT
app01-6401	234	3	the	the	DET
app01-6401	234	4	nsdp	nsdp	ADJ
app01-6401	234	5	and	and	CCONJ
app01-6401	234	6	fmincon	fmincon	NOUN
app01-6401	234	7	techniques	technique	NOUN
app01-6401	234	8	also	also	ADV
app01-6401	234	9	converged	converge	VERB
app01-6401	234	10	to	to	PART
app01-6401	234	11	infeasible	infeasible	ADJ
app01-6401	234	12	points	point	NOUN
app01-6401	234	13	.	.	PUNCT
app01-6401	235	1	from	from	ADP
app01-6401	235	2	the	the	DET
app01-6401	235	3	local	local	ADJ
app01-6401	235	4	optimization	optimization	NOUN
app01-6401	235	5	approaches	approach	NOUN
app01-6401	235	6	,	,	PUNCT
app01-6401	235	7	the	the	DET
app01-6401	235	8	optimality	optimality	NOUN
app01-6401	235	9	criteria	criterion	NOUN
app01-6401	235	10	method	method	NOUN
app01-6401	235	11	seems	seem	VERB
app01-6401	235	12	to	to	PART
app01-6401	235	13	be	be	AUX
app01-6401	235	14	the	the	DET
app01-6401	235	15	most	most	ADV
app01-6401	235	16	efficient	efficient	ADJ
app01-6401	235	17	one	one	NUM
app01-6401	235	18	.	.	PUNCT
app01-6401	236	1	on	on	ADP
app01-6401	236	2	the	the	DET
app01-6401	236	3	other	other	ADJ
app01-6401	236	4	hand	hand	NOUN
app01-6401	236	5	,	,	PUNCT
app01-6401	236	6	the	the	DET
app01-6401	236	7	last	last	ADJ
app01-6401	236	8	technique	technique	NOUN
app01-6401	236	9	—	—	PUNCT
app01-6401	236	10	polynomial	polynomial	ADJ
app01-6401	236	11	optimization	optimization	NOUN
app01-6401	236	12	—	—	PUNCT
app01-6401	236	13	allows	allow	VERB
app01-6401	236	14	to	to	PART
app01-6401	236	15	solve	solve	VERB
app01-6401	236	16	the	the	DET
app01-6401	236	17	problem	problem	NOUN
app01-6401	236	18	to	to	PART
app01-6401	236	19	proven	prove	VERB
app01-6401	236	20	global	global	ADJ
app01-6401	236	21	optimality	optimality	NOUN
app01-6401	236	22	,	,	PUNCT
app01-6401	236	23	while	while	SCONJ
app01-6401	236	24	generating	generate	VERB
app01-6401	236	25	both	both	CCONJ
app01-6401	236	26	lower	low	ADJ
app01-6401	236	27	and	and	CCONJ
app01-6401	236	28	upper	upper	ADJ
app01-6401	236	29	bounds	bound	NOUN
app01-6401	236	30	in	in	ADP
app01-6401	236	31	each	each	PRON
app01-6401	236	32	of	of	ADP
app01-6401	236	33	the	the	DET
app01-6401	236	34	relaxation	relaxation	NOUN
app01-6401	236	35	order	order	NOUN
app01-6401	236	36	.	.	PUNCT
app01-6401	237	1	compared	compare	VERB
app01-6401	237	2	to	to	ADP
app01-6401	237	3	the	the	DET
app01-6401	237	4	local	local	ADJ
app01-6401	237	5	approaches	approach	NOUN
app01-6401	237	6	,	,	PUNCT
app01-6401	237	7	the	the	DET
app01-6401	237	8	designs	design	NOUN
app01-6401	237	9	obtained	obtain	VERB
app01-6401	237	10	in	in	ADP
app01-6401	237	11	lower	low	ADJ
app01-6401	237	12	relaxation	relaxation	NOUN
app01-6401	237	13	orders	order	NOUN
app01-6401	237	14	are	be	AUX
app01-6401	237	15	of	of	ADP
app01-6401	237	16	a	a	DET
app01-6401	237	17	known	know	VERB
app01-6401	237	18	quality	quality	NOUN
app01-6401	237	19	with	with	ADP
app01-6401	237	20	respect	respect	NOUN
app01-6401	237	21	to	to	ADP
app01-6401	237	22	the	the	DET
app01-6401	237	23	optimum	optimum	NOUN
app01-6401	237	24	.	.	PUNCT
app01-6401	238	1	however	however	ADV
app01-6401	238	2	,	,	PUNCT
app01-6401	238	3	finding	find	VERB
app01-6401	238	4	a	a	DET
app01-6401	238	5	proven	prove	VERB
app01-6401	238	6	global	global	ADJ
app01-6401	238	7	optimum	optimum	NOUN
app01-6401	238	8	requires	require	VERB
app01-6401	238	9	a	a	DET
app01-6401	238	10	considerably	considerably	ADV
app01-6401	238	11	higher	high	ADJ
app01-6401	238	12	computational	computational	ADJ
app01-6401	238	13	resources	resource	NOUN
app01-6401	238	14	than	than	ADP
app01-6401	238	15	solving	solve	VERB
app01-6401	238	16	the	the	DET
app01-6401	238	17	local	local	ADJ
app01-6401	238	18	optimization	optimization	NOUN
app01-6401	238	19	formulations	formulation	NOUN
app01-6401	238	20	.	.	PUNCT
app01-6401	239	1	in	in	ADP
app01-6401	239	2	all	all	DET
app01-6401	239	3	the	the	DET
app01-6401	239	4	test	test	NOUN
app01-6401	239	5	cases	case	NOUN
app01-6401	239	6	,	,	PUNCT
app01-6401	239	7	the	the	DET
app01-6401	239	8	convergence	convergence	NOUN
app01-6401	239	9	of	of	ADP
app01-6401	239	10	the	the	DET
app01-6401	239	11	po	po	PROPN
app01-6401	239	12	hierarchy	hierarchy	NOUN
app01-6401	239	13	was	be	AUX
app01-6401	239	14	finite	finite	ADJ
app01-6401	239	15	.	.	PUNCT
app01-6401	239	16	list	list	NOUN
app01-6401	239	17	of	of	ADP
app01-6401	239	18	symbols	symbol	NOUN
app01-6401	239	19	0	0	NUM
app01-6401	239	20	column	column	NOUN
app01-6401	239	21	vector	vector	NOUN
app01-6401	239	22	or	or	CCONJ
app01-6401	239	23	matrix	matrix	NOUN
app01-6401	239	24	of	of	ADP
app01-6401	239	25	all	all	DET
app01-6401	239	26	zeros	zero	NOUN
app01-6401	239	27	1	1	NUM
app01-6401	239	28	column	column	NOUN
app01-6401	239	29	vector	vector	NOUN
app01-6401	239	30	or	or	CCONJ
app01-6401	239	31	matrix	matrix	NOUN
app01-6401	239	32	of	of	ADP
app01-6401	239	33	all	all	DET
app01-6401	239	34	ones	one	NOUN
app01-6401	239	35	a	a	DET
app01-6401	239	36	cross	cross	ADJ
app01-6401	239	37	-	-	ADJ
app01-6401	239	38	sectional	sectional	ADJ
app01-6401	239	39	areas	area	NOUN
app01-6401	239	40	column	column	NOUN
app01-6401	239	41	vector	vector	PROPN
app01-6401	239	42	asc	asc	PROPN
app01-6401	239	43	scaled	scale	VERB
app01-6401	239	44	cross	cross	ADJ
app01-6401	239	45	-	-	ADJ
app01-6401	239	46	sectional	sectional	ADJ
app01-6401	239	47	areas	area	NOUN
app01-6401	239	48	column	column	NOUN
app01-6401	239	49	vector	vector	PROPN
app01-6401	239	50	ai	ai	VERB
app01-6401	239	51	cross	cross	ADJ
app01-6401	239	52	-	-	ADJ
app01-6401	239	53	sectional	sectional	ADJ
app01-6401	239	54	area	area	NOUN
app01-6401	239	55	of	of	ADP
app01-6401	239	56	the	the	DET
app01-6401	239	57	element	element	NOUN
app01-6401	239	58	i	i	PROPN
app01-6401	239	59	asc	asc	PROPN
app01-6401	239	60	,	,	PUNCT
app01-6401	239	61	i	i	PRON
app01-6401	239	62	scaled	scale	VERB
app01-6401	239	63	cross	cross	ADJ
app01-6401	239	64	-	-	ADJ
app01-6401	239	65	sectional	sectional	ADJ
app01-6401	239	66	area	area	NOUN
app01-6401	239	67	of	of	ADP
app01-6401	239	68	the	the	DET
app01-6401	239	69	element	element	NOUN
app01-6401	239	70	i	i	PRON
app01-6401	239	71	âr	âr	VERB
app01-6401	239	72	optimized	optimize	VERB
app01-6401	239	73	cross	cross	ADJ
app01-6401	239	74	-	-	ADJ
app01-6401	239	75	sectional	sectional	ADJ
app01-6401	239	76	areas	area	NOUN
app01-6401	239	77	at	at	ADP
app01-6401	239	78	the	the	DET
app01-6401	239	79	relaxation	relaxation	NOUN
app01-6401	239	80	r	r	NOUN
app01-6401	239	81	bi	bi	ADJ
app01-6401	239	82	auxiliary	auxiliary	ADJ
app01-6401	239	83	variable	variable	NOUN
app01-6401	239	84	associated	associate	VERB
app01-6401	239	85	with	with	ADP
app01-6401	239	86	the	the	DET
app01-6401	239	87	element	element	NOUN
app01-6401	239	88	i	i	PRON
app01-6401	239	89	br	br	VERB
app01-6401	239	90	polynomial	polynomial	ADJ
app01-6401	239	91	space	space	NOUN
app01-6401	239	92	basis	basis	NOUN
app01-6401	239	93	of	of	ADP
app01-6401	239	94	maximum	maximum	ADJ
app01-6401	239	95	degree	degree	NOUN
app01-6401	239	96	r	r	NOUN
app01-6401	239	97	c	c	NOUN
app01-6401	239	98	compliance	compliance	NOUN
app01-6401	239	99	(	(	PUNCT
app01-6401	239	100	external	external	ADJ
app01-6401	239	101	work	work	NOUN
app01-6401	239	102	)	)	PUNCT
app01-6401	240	1	c̃	c̃	PROPN
app01-6401	240	2	lower	lower	ADV
app01-6401	240	3	bound	bind	VERB
app01-6401	240	4	on	on	ADP
app01-6401	240	5	compliance	compliance	NOUN
app01-6401	240	6	ĉ	ĉ	X
app01-6401	240	7	upper	upper	ADV
app01-6401	240	8	bound	bind	VERB
app01-6401	240	9	on	on	ADP
app01-6401	240	10	compliance	compliance	NOUN
app01-6401	240	11	c∗	c∗	NOUN
app01-6401	240	12	globally	globally	ADV
app01-6401	240	13	optimal	optimal	ADJ
app01-6401	240	14	compliance	compliance	NOUN
app01-6401	240	15	csc	csc	PROPN
app01-6401	240	16	scaled	scale	VERB
app01-6401	240	17	compliance	compliance	NOUN
app01-6401	240	18	ci	ci	NOUN
app01-6401	240	19	,	,	PUNCT
app01-6401	240	20	i	i	PRON
app01-6401	240	21	positive	positive	ADJ
app01-6401	240	22	constant	constant	ADJ
app01-6401	240	23	dj	dj	NOUN
app01-6401	240	24	degree	degree	NOUN
app01-6401	240	25	of	of	ADP
app01-6401	240	26	the	the	DET
app01-6401	240	27	polynomial	polynomial	ADJ
app01-6401	240	28	j	j	PROPN
app01-6401	240	29	e	e	PROPN
app01-6401	240	30	young	young	ADJ
app01-6401	240	31	modulus	modulus	NOUN
app01-6401	240	32	f	f	PROPN
app01-6401	240	33	generalized	generalized	ADJ
app01-6401	240	34	force	force	NOUN
app01-6401	240	35	column	column	NOUN
app01-6401	240	36	vector	vector	NOUN
app01-6401	240	37	fi	fi	NOUN
app01-6401	240	38	generalized	generalized	ADJ
app01-6401	240	39	force	force	NOUN
app01-6401	240	40	column	column	NOUN
app01-6401	240	41	vector	vector	NOUN
app01-6401	240	42	of	of	ADP
app01-6401	240	43	element	element	NOUN
app01-6401	240	44	i	i	PRON
app01-6401	240	45	f̂	f̂	VERB
app01-6401	240	46	generalized	generalized	ADJ
app01-6401	240	47	force	force	NOUN
app01-6401	240	48	column	column	NOUN
app01-6401	240	49	vector	vector	NOUN
app01-6401	240	50	associated	associate	VERB
app01-6401	240	51	with	with	ADP
app01-6401	240	52	k̂	k̂	PROPN
app01-6401	240	53	i	i	PROPN
app01-6401	240	54	element	element	VERB
app01-6401	240	55	index	index	NOUN
app01-6401	240	56	j	j	PROPN
app01-6401	240	57	polynomial	polynomial	PROPN
app01-6401	240	58	index	index	PROPN
app01-6401	240	59	ii	ii	PROPN
app01-6401	240	60	moment	moment	NOUN
app01-6401	240	61	of	of	ADP
app01-6401	240	62	inertia	inertia	NOUN
app01-6401	240	63	of	of	ADP
app01-6401	240	64	the	the	DET
app01-6401	240	65	element	element	NOUN
app01-6401	241	1	i	i	PRON
app01-6401	241	2	i	i	VERB
app01-6401	241	3	identity	identity	NOUN
app01-6401	241	4	matrix	matrix	NOUN
app01-6401	241	5	k	k	NOUN
app01-6401	241	6	iteration	iteration	NOUN
app01-6401	241	7	number	number	NOUN
app01-6401	241	8	k	k	NOUN
app01-6401	241	9	stiffness	stiffness	ADJ
app01-6401	241	10	matrix	matrix	NOUN
app01-6401	241	11	k̂	k̂	X
app01-6401	241	12	positive	positive	ADJ
app01-6401	241	13	definite	definite	ADJ
app01-6401	241	14	principal	principal	ADJ
app01-6401	241	15	submatrix	submatrix	NOUN
app01-6401	241	16	of	of	ADP
app01-6401	241	17	k	k	PROPN
app01-6401	241	18	ki	ki	PROPN
app01-6401	241	19	stiffness	stiffness	NOUN
app01-6401	241	20	matrix	matrix	NOUN
app01-6401	241	21	of	of	ADP
app01-6401	241	22	the	the	DET
app01-6401	241	23	element	element	NOUN
app01-6401	241	24	i	i	NOUN
app01-6401	241	25	l	l	NOUN
app01-6401	241	26	lagrangian	lagrangian	ADJ
app01-6401	241	27	function	function	NOUN
app01-6401	241	28	`	`	PUNCT
app01-6401	241	29	column	column	NOUN
app01-6401	241	30	vector	vector	NOUN
app01-6401	241	31	of	of	ADP
app01-6401	241	32	element	element	NOUN
app01-6401	241	33	lengths	length	NOUN
app01-6401	241	34	`	`	PUNCT
app01-6401	241	35	i	i	PRON
app01-6401	241	36	length	length	VERB
app01-6401	241	37	of	of	ADP
app01-6401	241	38	the	the	DET
app01-6401	241	39	element	element	NOUN
app01-6401	241	40	i	i	NOUN
app01-6401	241	41	m	m	VERB
app01-6401	241	42	index	index	NOUN
app01-6401	241	43	of	of	ADP
app01-6401	241	44	x	x	SYM
app01-6401	241	45	mr	mr	PROPN
app01-6401	241	46	moment	moment	NOUN
app01-6401	241	47	matrix	matrix	NOUN
app01-6401	241	48	of	of	ADP
app01-6401	241	49	the	the	DET
app01-6401	241	50	order	order	NOUN
app01-6401	241	51	r	r	NOUN
app01-6401	241	52	mr−dj	mr−dj	NOUN
app01-6401	241	53	localization	localization	NOUN
app01-6401	241	54	matrix	matrix	NOUN
app01-6401	241	55	of	of	ADP
app01-6401	241	56	the	the	DET
app01-6401	241	57	order	order	NOUN
app01-6401	241	58	r	r	NOUN
app01-6401	241	59	−	−	NOUN
app01-6401	241	60	dj	dj	NOUN
app01-6401	241	61	ne	ne	NOUN
app01-6401	241	62	number	number	NOUN
app01-6401	241	63	of	of	ADP
app01-6401	241	64	elements	element	NOUN
app01-6401	241	65	nn	nn	INTJ
app01-6401	241	66	number	number	NOUN
app01-6401	241	67	of	of	ADP
app01-6401	241	68	nodes	node	NOUN
app01-6401	241	69	pj	pj	PROPN
app01-6401	241	70	polynomial	polynomial	PROPN
app01-6401	241	71	inequality	inequality	PROPN
app01-6401	241	72	pj	pj	PROPN
app01-6401	241	73	polynomial	polynomial	ADJ
app01-6401	241	74	matrix	matrix	NOUN
app01-6401	241	75	inequality	inequality	NOUN
app01-6401	241	76	pα	pα	PROPN
app01-6401	241	77	,	,	PUNCT
app01-6401	241	78	j	j	PROPN
app01-6401	241	79	coefficients	coefficient	NOUN
app01-6401	241	80	of	of	ADP
app01-6401	241	81	linear	linear	ADJ
app01-6401	241	82	combinations	combination	NOUN
app01-6401	241	83	of	of	ADP
app01-6401	241	84	monomials	monomial	NOUN
app01-6401	241	85	r	r	NOUN
app01-6401	241	86	relaxation	relaxation	NOUN
app01-6401	241	87	order	order	NOUN
app01-6401	241	88	,	,	PUNCT
app01-6401	241	89	maximum	maximum	ADJ
app01-6401	241	90	polynomial	polynomial	ADJ
app01-6401	241	91	degree	degree	NOUN
app01-6401	241	92	s	s	PART
app01-6401	241	93	inverse	inverse	NOUN
app01-6401	241	94	of	of	ADP
app01-6401	241	95	c	c	PROPN
app01-6401	241	96	tp	tp	PROPN
app01-6401	241	97	parameter	parameter	PROPN
app01-6401	241	98	,	,	PUNCT
app01-6401	241	99	web	web	NOUN
app01-6401	241	100	and	and	CCONJ
app01-6401	241	101	flanges	flange	VERB
app01-6401	241	102	thickness	thickness	NOUN
app01-6401	241	103	t	t	PROPN
app01-6401	241	104	time	time	NOUN
app01-6401	241	105	u	u	PRON
app01-6401	241	106	generalized	generalized	ADJ
app01-6401	241	107	displacement	displacement	ADJ
app01-6401	241	108	column	column	NOUN
app01-6401	241	109	vector	vector	NOUN
app01-6401	241	110	v	v	PROPN
app01-6401	241	111	column	column	NOUN
app01-6401	241	112	vector	vector	NOUN
app01-6401	241	113	of	of	ADP
app01-6401	241	114	coefficients	coefficient	NOUN
app01-6401	241	115	of	of	ADP
app01-6401	241	116	linear	linear	ADJ
app01-6401	241	117	combination	combination	NOUN
app01-6401	241	118	v	v	ADP
app01-6401	241	119	volume	volume	NOUN
app01-6401	241	120	124	124	NUM
app01-6401	241	121	vol	vol	NOUN
app01-6401	241	122	.	.	PUNCT
app01-6401	242	1	26/2020	26/2020	NUM
app01-6401	242	2	on	on	ADP
app01-6401	242	3	optimum	optimum	ADJ
app01-6401	242	4	design	design	NOUN
app01-6401	242	5	of	of	ADP
app01-6401	242	6	frame	frame	NOUN
app01-6401	242	7	structures	structure	NOUN
app01-6401	242	8	v	v	ADP
app01-6401	242	9	volume	volume	NOUN
app01-6401	242	10	upper	upper	ADJ
app01-6401	242	11	bound	bind	VERB
app01-6401	242	12	x	x	PUNCT
app01-6401	242	13	design	design	NOUN
app01-6401	242	14	variables	variable	NOUN
app01-6401	242	15	column	column	NOUN
app01-6401	242	16	vector	vector	NOUN
app01-6401	242	17	xα	xα	PROPN
app01-6401	242	18	monomial	monomial	PROPN
app01-6401	242	19	indexed	index	VERB
app01-6401	242	20	by	by	ADP
app01-6401	242	21	α	α	PROPN
app01-6401	242	22	yβ	yβ	PROPN
app01-6401	242	23	moment	moment	NOUN
app01-6401	242	24	associated	associate	VERB
app01-6401	242	25	with	with	ADP
app01-6401	242	26	the	the	DET
app01-6401	242	27	basis	basis	NOUN
app01-6401	242	28	br	br	NOUN
app01-6401	242	29	y	y	PROPN
app01-6401	242	30	column	column	PROPN
app01-6401	242	31	vector	vector	NOUN
app01-6401	242	32	of	of	ADP
app01-6401	242	33	moments	moment	NOUN
app01-6401	242	34	y∗	y∗	ADV
app01-6401	242	35	optimal	optimal	ADJ
app01-6401	242	36	column	column	NOUN
app01-6401	242	37	vector	vector	NOUN
app01-6401	242	38	of	of	ADP
app01-6401	242	39	moments	moment	NOUN
app01-6401	242	40	yr	yr	NOUN
app01-6401	242	41	column	column	NOUN
app01-6401	242	42	vector	vector	NOUN
app01-6401	242	43	of	of	ADP
app01-6401	242	44	moments	moment	NOUN
app01-6401	242	45	at	at	ADP
app01-6401	242	46	r	r	NOUN
app01-6401	242	47	-	-	PUNCT
app01-6401	242	48	th	th	VERB
app01-6401	242	49	relaxation	relaxation	NOUN
app01-6401	242	50	α	α	PRON
app01-6401	242	51	vector	vector	NOUN
app01-6401	242	52	of	of	ADP
app01-6401	242	53	integers	integer	NOUN
app01-6401	242	54	β	β	X
app01-6401	242	55	br	br	PROPN
app01-6401	242	56	index	index	PROPN
app01-6401	242	57	η	η	PROPN
app01-6401	242	58	tuning	tuning	NOUN
app01-6401	242	59	parameter	parameter	NOUN
app01-6401	242	60	,	,	PUNCT
app01-6401	242	61	0.3	0.3	NUM
app01-6401	242	62	in	in	ADP
app01-6401	242	63	this	this	DET
app01-6401	242	64	study	study	NOUN
app01-6401	242	65	ζ	ζ	NOUN
app01-6401	242	66	move	move	NOUN
app01-6401	242	67	limit	limit	NOUN
app01-6401	242	68	,	,	PUNCT
app01-6401	242	69	0.2	0.2	NUM
app01-6401	242	70	in	in	ADP
app01-6401	242	71	this	this	DET
app01-6401	242	72	study	study	NOUN
app01-6401	243	1	ε	ε	PROPN
app01-6401	243	2	small	small	ADJ
app01-6401	243	3	positive	positive	ADJ
app01-6401	243	4	number	number	NOUN
app01-6401	243	5	,	,	PUNCT
app01-6401	243	6	10−6	10−6	NUM
app01-6401	243	7	in	in	ADP
app01-6401	243	8	this	this	DET
app01-6401	243	9	study	study	NOUN
app01-6401	243	10	λ	λ	PROPN
app01-6401	243	11	lagrange	lagrange	NOUN
app01-6401	243	12	multiplier	multipli	ADJ
app01-6401	243	13	column	column	NOUN
app01-6401	243	14	vector	vector	PROPN
app01-6401	243	15	µ	µ	X
app01-6401	243	16	lagrange	lagrange	PROPN
app01-6401	243	17	multiplier	multipli	ADJ
app01-6401	243	18	ν	ν	X
app01-6401	243	19	lagrange	lagrange	NOUN
app01-6401	243	20	multiplier	multipli	ADJ
app01-6401	243	21	column	column	NOUN
app01-6401	243	22	vector	vector	NOUN
app01-6401	243	23	acknowledgements	acknowledgement	VERB
app01-6401	243	24	the	the	DET
app01-6401	243	25	work	work	NOUN
app01-6401	243	26	of	of	ADP
app01-6401	243	27	marek	marek	PROPN
app01-6401	243	28	tyburec	tyburec	NOUN
app01-6401	243	29	was	be	AUX
app01-6401	243	30	supported	support	VERB
app01-6401	243	31	by	by	ADP
app01-6401	243	32	the	the	DET
app01-6401	243	33	grant	grant	PROPN
app01-6401	243	34	agency	agency	NOUN
app01-6401	243	35	of	of	ADP
app01-6401	243	36	the	the	DET
app01-6401	243	37	ctu	ctu	NOUN
app01-6401	243	38	in	in	ADP
app01-6401	243	39	prague	prague	PROPN
app01-6401	243	40	,	,	PUNCT
app01-6401	243	41	sgs19/033	sgs19/033	PROPN
app01-6401	243	42	/	/	SYM
app01-6401	243	43	ohk1/1t/11	ohk1/1t/11	PROPN
app01-6401	243	44	.	.	PUNCT
app01-6401	244	1	martin	martin	PROPN
app01-6401	244	2	kružík	kružík	PROPN
app01-6401	244	3	and	and	CCONJ
app01-6401	244	4	jan	jan	PROPN
app01-6401	244	5	zeman	zeman	PROPN
app01-6401	244	6	acknowledge	acknowledge	VERB
app01-6401	244	7	the	the	DET
app01-6401	244	8	financial	financial	ADJ
app01-6401	244	9	support	support	NOUN
app01-6401	244	10	by	by	ADP
app01-6401	244	11	the	the	DET
app01-6401	244	12	european	european	PROPN
app01-6401	244	13	regional	regional	PROPN
app01-6401	244	14	development	development	PROPN
app01-6401	244	15	fund	fund	NOUN
app01-6401	244	16	through	through	ADP
app01-6401	244	17	the	the	DET
app01-6401	244	18	project	project	NOUN
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app01-6401	245	3	1	1	NUM
app01-6401	245	4	]	]	PUNCT
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app01-6401	245	6	p.	p.	PROPN
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app01-6401	246	2	optimization	optimization	NOUN
app01-6401	246	3	:	:	PUNCT
app01-6401	246	4	theory	theory	NOUN
app01-6401	246	5	,	,	PUNCT
app01-6401	246	6	methods	method	NOUN
app01-6401	246	7	,	,	PUNCT
app01-6401	246	8	and	and	CCONJ
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app01-6401	246	10	.	.	PUNCT
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app01-6401	247	5	berlin	berlin	PROPN
app01-6401	247	6	,	,	PUNCT
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app01-6401	247	8	,	,	PUNCT
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app01-6401	247	10	.	.	PUNCT
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app01-6401	248	4	-	-	PUNCT
app01-6401	248	5	662	662	NUM
app01-6401	248	6	-	-	PUNCT
app01-6401	248	7	05086	05086	NUM
app01-6401	248	8	-	-	PUNCT
app01-6401	248	9	6	6	NUM
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app01-6401	249	3	]	]	PUNCT
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app01-6401	252	3	]	]	X
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app01-6401	252	6	-	-	PROPN
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app01-6401	252	8	,	,	PUNCT
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app01-6401	252	10	nemirovski	nemirovski	PROPN
app01-6401	252	11	.	.	PUNCT
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app01-6401	253	2	on	on	ADP
app01-6401	253	3	modern	modern	ADJ
app01-6401	253	4	convex	convex	NOUN
app01-6401	253	5	optimization	optimization	NOUN
app01-6401	253	6	.	.	PUNCT
app01-6401	254	1	society	society	NOUN
app01-6401	254	2	for	for	ADP
app01-6401	254	3	industrial	industrial	ADJ
app01-6401	254	4	and	and	CCONJ
app01-6401	254	5	applied	applied	ADJ
app01-6401	254	6	mathematics	mathematic	NOUN
app01-6401	254	7	,	,	PUNCT
app01-6401	254	8	2001	2001	NUM
app01-6401	254	9	.	.	PUNCT
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app01-6401	256	10	m.	m.	PROPN
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app01-6401	257	2	structural	structural	ADJ
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app01-6401	257	6	)	)	PUNCT
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app01-6401	257	14	discrete	discrete	ADJ
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app01-6401	258	2	methods	method	NOUN
app01-6401	258	3	in	in	ADP
app01-6401	258	4	applied	applied	ADJ
app01-6401	258	5	mechanics	mechanic	NOUN
app01-6401	258	6	and	and	CCONJ
app01-6401	258	7	engineering	engineering	NOUN
app01-6401	258	8	188(4):743–754	188(4):743–754	NUM
app01-6401	258	9	,	,	PUNCT
app01-6401	258	10	2000	2000	NUM
app01-6401	258	11	.	.	PUNCT
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app01-6401	259	6	-	-	PUNCT
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app01-6401	295	5	löfberg	löfberg	PROPN
app01-6401	295	6	.	.	PUNCT
app01-6401	296	1	yalmip	yalmip	PROPN
app01-6401	296	2	:	:	PUNCT
app01-6401	296	3	a	a	DET
app01-6401	296	4	toolbox	toolbox	NOUN
app01-6401	296	5	for	for	ADP
app01-6401	296	6	modeling	modeling	NOUN
app01-6401	296	7	and	and	CCONJ
app01-6401	296	8	optimization	optimization	NOUN
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app01-6401	296	11	.	.	PUNCT
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app01-6401	297	2	in	in	ADP
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app01-6401	297	4	of	of	ADP
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app01-6401	297	6	cacsd	cacsd	PROPN
app01-6401	297	7	conference	conference	PROPN
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app01-6401	301	8	.	.	PUNCT
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app01-6401	302	6	-	-	PUNCT
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app01-6401	302	8	-	-	PUNCT
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app01-6401	304	8	gloptipoly	gloptipoly	ADJ
app01-6401	304	9	.	.	PUNCT
app01-6401	305	1	lecture	lecture	NOUN
app01-6401	305	2	notes	note	NOUN
app01-6401	305	3	in	in	ADP
app01-6401	305	4	control	control	NOUN
app01-6401	305	5	and	and	CCONJ
app01-6401	305	6	information	information	NOUN
app01-6401	305	7	sciences	science	NOUN
app01-6401	305	8	312:293–310	312:293–310	NUM
app01-6401	305	9	,	,	PUNCT
app01-6401	305	10	2005	2005	NUM
app01-6401	305	11	.	.	PUNCT
app01-6401	306	1	doi:10.1007/10997703_15	doi:10.1007/10997703_15	PROPN
app01-6401	306	2	.	.	NOUN
app01-6401	307	1	125	125	NUM
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app01-6401	307	3	https://doi.org/10.1137/1.9780898718829	https://doi.org/10.1137/1.9780898718829	PROPN
app01-6401	307	4	https://doi.org/10.1016/s0045-7825(99)00359-x	https://doi.org/10.1016/s0045-7825(99)00359-x	VERB
app01-6401	307	5	https://doi.org/10.1007/978-94-009-1161-1	https://doi.org/10.1007/978-94-009-1161-1	PROPN
app01-6401	307	6	1311.5240	1311.5240	NUM
app01-6401	307	7	https://doi.org/10.1017/cbo9781107447226	https://doi.org/10.1017/cbo9781107447226	NOUN
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app01-6401	307	11	https://doi.org/10.1109/tac.2005.863494	https://doi.org/10.1109/tac.2005.863494	NOUN
app01-6401	307	12	https://doi.org/10.1080/10556780802699201	https://doi.org/10.1080/10556780802699201	VERB
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app01-6401	307	14	https://doi.org/10.1007/10997703_15	https://doi.org/10.1007/10997703_15	NOUN
app01-6401	307	15	acta	acta	PROPN
app01-6401	307	16	polytechnica	polytechnica	PROPN
app01-6401	307	17	ctu	ctu	NOUN
app01-6401	307	18	proceedings	proceeding	NOUN
app01-6401	307	19	26:118–126	26:118–126	NUM
app01-6401	307	20	,	,	PUNCT
app01-6401	307	21	2020	2020	NUM
app01-6401	307	22	1	1	NUM
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app01-6401	307	24	2	2	NUM
app01-6401	307	25	solution	solution	NOUN
app01-6401	307	26	techniques	technique	NOUN
app01-6401	307	27	to	to	PART
app01-6401	307	28	frame	frame	VERB
app01-6401	307	29	optimization	optimization	NOUN
app01-6401	307	30	2.1	2.1	NUM
app01-6401	307	31	problem	problem	NOUN
app01-6401	307	32	statement	statement	NOUN
app01-6401	307	33	2.2	2.2	NUM
app01-6401	307	34	optimality	optimality	NOUN
app01-6401	307	35	criteria	criterion	NOUN
app01-6401	307	36	2.3	2.3	NUM
app01-6401	307	37	nonlinear	nonlinear	ADJ
app01-6401	307	38	semidefinite	semidefinite	NOUN
app01-6401	307	39	programming	program	VERB
app01-6401	307	40	2.4	2.4	NUM
app01-6401	307	41	polynomial	polynomial	ADJ
app01-6401	307	42	optimization	optimization	NOUN
app01-6401	307	43	2.4.1	2.4.1	NUM
app01-6401	307	44	solution	solution	NOUN
app01-6401	307	45	process	process	NOUN
app01-6401	307	46	2.4.2	2.4.2	NUM
app01-6401	307	47	recognizing	recognize	VERB
app01-6401	307	48	global	global	ADJ
app01-6401	307	49	optimality	optimality	NOUN
app01-6401	307	50	3	3	NUM
app01-6401	307	51	sample	sample	NOUN
app01-6401	307	52	problems	problem	NOUN
app01-6401	307	53	3.1	3.1	NUM
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app01-6401	307	55	beam	beam	NOUN
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app01-6401	307	57	10	10	NUM
app01-6401	307	58	-	-	PUNCT
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app01-6401	307	60	frame	frame	NOUN
app01-6401	307	61	structure	structure	NOUN
app01-6401	307	62	3.3	3.3	NUM
app01-6401	307	63	i	i	ADV
app01-6401	307	64	-	-	PUNCT
app01-6401	307	65	shaped	shape	VERB
app01-6401	307	66	girder	girder	NOUN
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app01-6401	307	69	-	-	PUNCT
app01-6401	307	70	weight	weight	NOUN
app01-6401	307	71	4	4	NUM
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app01-6401	307	73	list	list	NOUN
app01-6401	307	74	of	of	ADP
app01-6401	307	75	symbols	symbol	NOUN
app01-6401	307	76	acknowledgements	acknowledgement	NOUN
app01-6401	307	77	references	reference	NOUN