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

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    0351985 - ÚT 2011 RIV US eng J - Journal Article
    Meziat, R. - Roubíček, Tomáš - Patino, D.
    Coarse-convex-compactification approach to numerical solution of nonconvex variational problems.
    Numerical Functional Analysis and Optimization. Roč. 31, č. 4 (2010), s. 460-488. ISSN 0163-0563. E-ISSN 1532-2467
    Grant - others:GA MŠk(CZ) LC06052
    Program: LC
    Institutional research plan: CEZ:AV0Z20760514
    Keywords : convex approximations * method of moments * relaxed variational problems
    Subject RIV: BA - General Mathematics
    Impact factor: 0.687, year: 2010
    http://www.informaworld.com/smpp/content~db=all~content=a922886514~frm=titlelink

    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.
    Permanent Link: http://hdl.handle.net/11104/0191602

     
     
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