About: Generalizations of the limited-memory BFGS method based on the quasi-product form of update

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Two families of limited-memory variable metric or quasi-Newton methods for unconstrained minimization based on quasi-product form of update are derived. As for the first family, four variants how to utilize the Strang recurrences for the Broyden class of variable metric updates are investigated; three of them use the same number of stored vectors as the limited- memory BFGS method. Moreover, one of the variants does not require any additional matrix by vector multiplication. The second family uses vectors from the preceding iteration to construct a new class of variable metric updates. Resulting methods again require neither any additional matrix by vector multiplication nor any additional stored vector. Global convergence of four of presented methods is established for convex sufficiently smooth functions. Numerical results indicate that two of the new methods can save computational time substantially for certain problems. Two families of limited-memory variable metric or quasi-Newton methods for unconstrained minimization based on quasi-product form of update are derived. As for the first family, four variants how to utilize the Strang recurrences for the Broyden class of variable metric updates are investigated; three of them use the same number of stored vectors as the limited- memory BFGS method. Moreover, one of the variants does not require any additional matrix by vector multiplication. The second family uses vectors from the preceding iteration to construct a new class of variable metric updates. Resulting methods again require neither any additional matrix by vector multiplication nor any additional stored vector. Global convergence of four of presented methods is established for convex sufficiently smooth functions. Numerical results indicate that two of the new methods can save computational time substantially for certain problems. (en)
Title	Generalizations of the limited-memory BFGS method based on the quasi-product form of update Generalizations of the limited-memory BFGS method based on the quasi-product form of update (en)
skos:prefLabel	Generalizations of the limited-memory BFGS method based on the quasi-product form of update Generalizations of the limited-memory BFGS method based on the quasi-product form of update (en)
skos:notation	RIV/67985807:_____/13:00381640!RIV13-GA0-67985807
http://linked.open...avai/predkladatel	Ústav informatiky AV ČR, v.v.i.
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/09/1957), Z(AV0Z10300504)
http://linked.open...iv/cisloPeriodika	15 March
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Vlček, Jan Lukšan, Ladislav
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav informatiky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	76305
http://linked.open...ai/riv/idVysledku	RIV/67985807:_____/13:00381640
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	unconstrained minimization; variable metric methods; limited-memory methods; Broyden class updates; global convergence; numerical results (en)
http://linked.open.../riv/klicoveSlovo	limited-memory methods numerical results unconstrained minimization variable metric methods Broyden class updates global convergence
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[EEF2642411DE]
http://linked.open...i/riv/nazevZdroje	Journal of Computational and Applied Mathematics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Development of methods for solving large scale nonlinear programming and nonsmooth optimization problems
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	241
http://linked.open...iv/tvurceVysledku	Vlček, Jan Lukšan, Ladislav
http://linked.open...ain/vavai/riv/wos	000312354100008
http://linked.open...n/vavai/riv/zamer	Informatika pro informační společnost: modely, algoritmy, aplikace
issn	0377-0427
number of pages	14 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.cam.2012.09.027

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