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Optimalization with Multivalued Mappings: Theory, Applications and Aldorithms

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    0040521 - ÚTIA 2007 RIV DE eng M - Monography Chapter
    Kočvara, Michal - Kružík, Martin - Outrata, Jiří
    On the control of an evolutionary equilibrium in micromagnetics.
    [K řízení evolučního ekvilibria v mikromagnetismu.]
    Optimalization with Multivalued Mappings: Theory, Applications and Aldorithms. Berlin: Springer, 2006 - (Dempe, S.; Kalashinikov, V.), s. 143-168. Springer Optimization and Its Applications, 2. ISBN 0-387-34220-6
    R&D Projects: GA AV ČR IAA1075402
    Institutional research plan: CEZ:AV0Z10750506
    Keywords : coderivatives * ferromagnetism * hysteresis * implict programming techniques * mathematical programs with equilibrium constraints
    Subject RIV: BA - General Mathematics

    Optimal control of magnetization in a ferromagnet is formulated as a mathematical program with evolutionary equilibrium constrains. To this purpose, we construct an evolutionary infinitive-dimensional model which is discretized both in the space as well as in time variables. The evolutionary nature of this equilibrium is due to the hysteresis behavior of the respective magnetization process. To solve the problem numerically, we adapted the implict programming technique. We solve two test examples.

    Optimální řízení magnetizace ferromagnetu je formulováno jako matematický program s evolučními ekvilibrii. K tomu zkonstruujeme evoluční nekonečne-dimensionální model, který diskretizujeme v čase i prostoru. K numerickému řešení problému používáme implicitní programování. V práci jsou vyřešeny 2 testovací přiklady.
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