On the control of an evolutionary equilibrium in micromagnetics

Michal Kocvara (kocvarautia.cas.cz)
Martin Kruzik (kruzikutia.cas.cz)
Jiri V. Outrata (outratautia.cas.cz)

Abstract: We formulate an optimal control problem of magnetization in a ferromagnet as a mathematical program with evolutionary equilibrium constraints. The evolutionary nature of the 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 the subgradients of the composite objective, are derived using the Mordukhovich's generalized differential calculus. We show the existence of a solution to such program and discuss results of computational experiments.

Keywords: coderivatives, ferromagnetism, hysteresis, implicit programming technique, mathematical programs with equilibrium constraints

Category 1: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Category 2: Applications -- Science and Engineering (Basic Sciences Applications )

Category 3: Complementarity and Variational Inequalities

Citation: IMA Preprint 2026, University of Minnesota, Minneapolis, February 2005

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Entry Submitted: 02/22/2005
Entry Accepted: 02/22/2005
Entry Last Modified: 03/02/2005

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