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Coarse-convex-compactification approach to numerical solution of nonconvex variational problems
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SYSNO ASEP 0351985 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Coarse-convex-compactification approach to numerical solution of nonconvex variational problems Author(s) Meziat, R. (CO)
Roubíček, Tomáš (UT-L) RID, ORCID
Patino, D. (CO)Number of authors 3 Source Title Numerical Functional Analysis and Optimization. - : Taylor & Francis - ISSN 0163-0563
Roč. 31, č. 4 (2010), s. 460-488Number of pages 23 s. Publication form www - www Language eng - English Country US - United States Keywords convex approximations ; method of moments ; relaxed variational problems Subject RIV BA - General Mathematics CEZ AV0Z20760514 - UT-L (2005-2011) UT WOS 000278663200004 DOI 10.1080/01630560903574985 Annotation 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. Workplace Institute of Thermomechanics Contact Marie Kajprová, kajprova@it.cas.cz, Tel.: 266 053 154 ; Jana Lahovská, jaja@it.cas.cz, Tel.: 266 053 823 Year of Publishing 2011
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