About: An optimal algorithm and superrelaxation for minimization of a quadratic function subject to separable convex constraints with applications

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About: An optimal algorithm and superrelaxation for minimization of a quadratic function subject to separable convex constraints with applications Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We propose a modification of our MPGP algorithm for the solution of bound constrained quadratic programming problems so that it can be used for minimization of a strictly convex quadratic function subject to separable convex constraints. Our active set based algorithm explores the faces by conjugate gradients and changes the active sets and active variables by gradient projections, possibly with the superrelaxation steplength. The error estimate in terms of extreme eigenvalues guarantees that if a class of minimization problems has the spectrum of the Hessian matrix in a given positive interval, then the algorithm can find and recognize an approximate solution of any particular problem in a number of iterations that is uniformly bounded. We also show how to use the algorithm for the solution of separable and equality constraints. The power of our algorithm and its optimality are demonstrated on the solution of a problem of two cantilever beams in mutual contact with Tresca friction discretized by almost twelve millions nodal variables. We propose a modification of our MPGP algorithm for the solution of bound constrained quadratic programming problems so that it can be used for minimization of a strictly convex quadratic function subject to separable convex constraints. Our active set based algorithm explores the faces by conjugate gradients and changes the active sets and active variables by gradient projections, possibly with the superrelaxation steplength. The error estimate in terms of extreme eigenvalues guarantees that if a class of minimization problems has the spectrum of the Hessian matrix in a given positive interval, then the algorithm can find and recognize an approximate solution of any particular problem in a number of iterations that is uniformly bounded. We also show how to use the algorithm for the solution of separable and equality constraints. The power of our algorithm and its optimality are demonstrated on the solution of a problem of two cantilever beams in mutual contact with Tresca friction discretized by almost twelve millions nodal variables. (en)
Title	An optimal algorithm and superrelaxation for minimization of a quadratic function subject to separable convex constraints with applications An optimal algorithm and superrelaxation for minimization of a quadratic function subject to separable convex constraints with applications (en)
skos:prefLabel	An optimal algorithm and superrelaxation for minimization of a quadratic function subject to separable convex constraints with applications An optimal algorithm and superrelaxation for minimization of a quadratic function subject to separable convex constraints with applications (en)
skos:notation	RIV/61989100:27740/12:86085078!RIV13-MSM-27740___
http://linked.open...avai/predkladatel	IT4Innovations
http://linked.open...avai/riv/aktivita	S Z
http://linked.open...avai/riv/aktivity	S, Z(MSM6198910027)
http://linked.open...iv/cisloPeriodika	1-2
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Dostál, Zdeněk Kozubek, Tomáš
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	Vysoká škola báňská - Technická univerzita Ostrava / IT4Innovations
http://linked.open...dnocenehoVysledku	122015
http://linked.open...ai/riv/idVysledku	RIV/61989100:27740/12:86085078
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Rate of convergence; Spherical constraints; QPQC with separable constraints (en)
http://linked.open.../riv/klicoveSlovo	QPQC with separable constraints Spherical constraints Rate of convergence
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[09B9EA82A4F6]
http://linked.open...i/riv/nazevZdroje	Mathematical Programming
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...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	135
http://linked.open...iv/tvurceVysledku	Dostál, Zdeněk Kozubek, Tomáš
http://linked.open...ain/vavai/riv/wos	000308647100007
http://linked.open...n/vavai/riv/zamer	Výpočetně náročné počítačové simulace a optimalizace
issn	0025-5610
number of pages	26 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/s10107-011-0454-2
http://localhost/t...ganizacniJednotka	27740
is http://linked.open...avai/riv/vysledek of	An optimal algorithm and superrelaxation for minimization of a quadratic function subject to separable convex constraints with applications

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