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On the control of an evolutionary equilibrium in micromagnetics

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Optimization with Multivalued Mappings

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 2))

Summary

Optimal control of magnetization in a ferromagnet is formulated as a mathematical program with evolutionary equilibrium constraints. To this purpose, we construct an evolutionary infinite-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 implicit programming technique. The adjoint equations, needed to compute subgradients of the composite objective, are derived using the generalized differential calculus of B. Mordukhovich. We solve two test examples and discuss numerical results.

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Author information

Authors and Affiliations

  1. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vodárenskou věží 4, CZ-182 08, Praha 8, Czech Republic

    Michal Kočvara, Martin Kružík & Jiří V. Outrata

  2. Fakulty of Civil Engineering, Czech Technical University, Thákurova 7, CZ-166 29, Praha 6, Czech Republic

    Martin Kružík

Authors
  1. Michal Kočvara
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  2. Martin Kružík
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  3. Jiří V. Outrata
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Editor information

Editors and Affiliations

  1. TU Bergakademie Freiberg, Germany

    Stephan Dempe

  2. ITESM, Monterrey, Mexico

    Vyacheslav Kalashnikov

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Kočvara, M., Kružík, M., Outrata, J.V. (2006). On the control of an evolutionary equilibrium in micromagnetics. In: Dempe, S., Kalashnikov, V. (eds) Optimization with Multivalued Mappings. Springer Optimization and Its Applications, vol 2. Springer, Boston, MA . https://doi.org/10.1007/0-387-34221-4_8

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