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A semismooth Newton method for a class of semilinear optimal control problems with box and volume constraints

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  • Samuel Amstutz
  • Antoine Laurain

Abstract

In this paper we consider optimal control problems subject to a semilinear elliptic state equation together with the control constraints 0≤u≤1 and ∫u=m. Optimality conditions for this problem are derived and reformulated as a nonlinear, nonsmooth equation which is solved using a semismooth Newton method. A regularization of the nonsmooth equation is necessary to obtain the superlinear convergence of the semismooth Newton method. We prove that the solutions of the regularized problems converge to a solution of the original problem and a path-following technique is used to ensure a constant decrease rate of the residual. We show that, in certain situations, the optimal controls take 0–1 values, which amounts to solving a topology optimization problem with volume constraint. Copyright Springer Science+Business Media New York 2013

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  • Samuel Amstutz & Antoine Laurain, 2013. "A semismooth Newton method for a class of semilinear optimal control problems with box and volume constraints," Computational Optimization and Applications, Springer, vol. 56(2), pages 369-403, October.
    • Handle: RePEc:spr:coopap:v:56:y:2013:i:2:p:369-403
    DOI: 10.1007/s10589-013-9555-6
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    References listed on IDEAS

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    1. Georg Stadler, 2009. "Elliptic optimal control problems with L 1 -control cost and applications for the placement of control devices," Computational Optimization and Applications, Springer, vol. 44(2), pages 159-181, November.
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