Počet záznamů: 1

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

  1. 1.
    0351985 - UT-L 2011 RIV US eng J - Článek v odborném periodiku
    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
    Grant ostatní:GA MŠk(CZ) LC06052
    Výzkumný záměr: CEZ:AV0Z20760514
    Klíčová slova: convex approximations * method of moments * relaxed variational problems
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 0.687, rok: 2010

    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.
    Trvalý link: http://hdl.handle.net/11104/0191602