Počet záznamů: 1
Coarse-convex-compactification approach to numerical solution of nonconvex variational problems
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