About: Coarse-convex-compactification approach to numerical solution of nonconvex variational problems

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	A numerical method for a (possibly non-convex) scalar variational problem is proposed. This method allows for computation of the Young-measure solution of the generalized relaxed version of the original problem and applies to those cases with polynomial functionals. The Young measures involved in the relaxed problem can be represented by their algebraic moments and also a finite-element mesh is used. Eventually, thus obtained convex semidefinite program can be solved by efficient specialized mathematical-programming solvers. This method is justified by convergence analysis and eventually tested on a 2-dimensional benchmark numerical example. It serves as an example how convex compactification can efficiently be used numerically if enough ``small'', i.e. enough coarse. A numerical method for a (possibly non-convex) scalar variational problem is proposed. This method allows for computation of the Young-measure solution of the generalized relaxed version of the original problem and applies to those cases with polynomial functionals. The Young measures involved in the relaxed problem can be represented by their algebraic moments and also a finite-element mesh is used. Eventually, thus obtained convex semidefinite program can be solved by efficient specialized mathematical-programming solvers. This method is justified by convergence analysis and eventually tested on a 2-dimensional benchmark numerical example. It serves as an example how convex compactification can efficiently be used numerically if enough ``small'', i.e. enough coarse. (en)
Title	Coarse-convex-compactification approach to numerical solution of nonconvex variational problems Coarse-convex-compactification approach to numerical solution of nonconvex variational problems (en)
skos:prefLabel	Coarse-convex-compactification approach to numerical solution of nonconvex variational problems Coarse-convex-compactification approach to numerical solution of nonconvex variational problems (en)
skos:notation	RIV/61388998:_____/10:00351985!RIV11-AV0-61388998
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA1075402), P(LC06052), Z(AV0Z20760514), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Roubíček, 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	Ústav termomechaniky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	251084
http://linked.open...ai/riv/idVysledku	RIV/61388998:_____/10:00351985
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	convex approximations; method of moments; relaxed variational problems (en)
http://linked.open.../riv/klicoveSlovo	method of moments convex approximations relaxed variational problems
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[DEC465AC1D47]
http://linked.open...i/riv/nazevZdroje	Numerical Functional Analysis and Optimization
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	The Nečas Center for Mathematical Modeling Variational analysis in nonsmooth problems of mathematical physics
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	31
http://linked.open...iv/tvurceVysledku	Roubíček, Tomáš Meziat, R. Patino, D.
http://linked.open...ain/vavai/riv/wos	000278663200004
http://linked.open...n/vavai/riv/zamer	Complex dynamical systems in thermodynamics, fluid and solid mechanics Metody moderní matematiky a jejich aplikace
issn	0163-0563
number of pages	23 (xsd:int)
is http://linked.open...avai/riv/vysledek of	Coarse-convex-compactification approach to numerical solution of nonconvex variational problems Coarse-convex-compactification approach to numerical solution of nonconvex variational problems Coarse-convex-compactification approach to numerical solution of nonconvex variational problems

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