About: Primal Interior-Point Method for Minimization of Generalized Minimax Functions

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In this paper, we propose a primal interior-point method for large sparse generalized minimax optimization. After a short introduction, where the problem is stated, we introduce the basic equations of the Newton method applied to the KKT conditions and propose a primal interior-point method. Next we describe the basic algorithm and give more details concerning its implementation covering numerical differentiation, variable metric updates, and a barrier parameter decrease. Using standard weak assumptions, we prove that this algorithm is globally convergent if a bounded barrier is used. Then, using stronger assumptions, we prove that it is globally convergent also for the logarithmic barrier. Finally, we present results of computational experiments confirming the efficiency of the primal interior point method for special cases of generalized minimax problems. In this paper, we propose a primal interior-point method for large sparse generalized minimax optimization. After a short introduction, where the problem is stated, we introduce the basic equations of the Newton method applied to the KKT conditions and propose a primal interior-point method. Next we describe the basic algorithm and give more details concerning its implementation covering numerical differentiation, variable metric updates, and a barrier parameter decrease. Using standard weak assumptions, we prove that this algorithm is globally convergent if a bounded barrier is used. Then, using stronger assumptions, we prove that it is globally convergent also for the logarithmic barrier. Finally, we present results of computational experiments confirming the efficiency of the primal interior point method for special cases of generalized minimax problems. (en)
Title	Primal Interior-Point Method for Minimization of Generalized Minimax Functions Primal Interior-Point Method for Minimization of Generalized Minimax Functions (en)
skos:prefLabel	Primal Interior-Point Method for Minimization of Generalized Minimax Functions Primal Interior-Point Method for Minimization of Generalized Minimax Functions (en)
skos:notation	RIV/67985807:_____/10:00347293!RIV11-GA0-67985807
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	4
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Matonoha, Ctirad 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	281671
http://linked.open...ai/riv/idVysledku	RIV/67985807:_____/10:00347293
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	unconstrained optimization; large-scale optimization; nonsmooth optimization; generalized minimax optimization; interior-point methods; modified Newton methods; variable metric methods; global convergence; computational experiments (en)
http://linked.open.../riv/klicoveSlovo	unconstrained optimization variable metric methods computational experiments generalized minimax optimization interior-point methods large-scale optimization modified Newton methods nonsmooth optimization global convergence
http://linked.open...odStatuVydavatele	CZ - Česká republika
http://linked.open...ontrolniKodProRIV	[D63A2C0EECD5]
http://linked.open...i/riv/nazevZdroje	Kybernetika
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	3 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (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	2010
http://linked.open...v/svazekPeriodika	46
http://linked.open...iv/tvurceVysledku	Matonoha, Ctirad Vlček, Jan Lukšan, Ladislav
http://linked.open...ain/vavai/riv/wos	000284562000008
http://linked.open...n/vavai/riv/zamer	Informatika pro informační společnost: modely, algoritmy, aplikace
issn	0023-5954
number of pages	25 (xsd:int)
is http://linked.open...avai/riv/vysledek of	Primal Interior-Point Method for Minimization of Generalized Minimax Functions Primal Interior-Point Method for Minimization of Generalized Minimax Functions Primal Interior-Point Method for Minimization of Generalized Minimax Functions

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