Adaptive approximation algorithm for relaxed optimization problems

0410721 - UTIA-B 20010190 RIV CH eng C - Konferenční příspěvek (zahraniční konf.)
Roubíček, Tomáš - Kružík, Martin
Adaptive approximation algorithm for relaxed optimization problems.
Basel: Birkhäuser, 2001. In: Proceedings of the Conference Fast Solution of Discretized Optimization Problems. - (Hoffmann, K.; Hoppe, R.; Schultz, V.), s. 242-254
[Fast Solution of Discretized Optimization Problems. Berlin (DE), 12.06.2000-14.06.2000]
Grant CEP: GA AV ČR IAA1075005; GA ČR GA201/00/0768
Výzkumný záměr: AV0Z1075907
Klíčová slova: Young measures * DiPerna-Majda measures * approximation
Kód oboru RIV: BA - Obecná matematika

Nonconvex optimization problems need a relaxation to handle effectively fast oscillation (and possibly also concentration) effects. This uses Young measures or their generalizations. Approximation of the relaxed problem can then be made by various ways, but computationally the most effective way appears to use adaptively a maximum principle (if it forms also a sufficient optimality condition) with the Hamiltonian guessed approximately from a previous iteration, e.g. from a coarser mesh.
Trvalý link: http://hdl.handle.net/11104/0130809