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

Samuel Amstutz () and Antoine Laurain ()

Computational Optimization and Applications, 2013, vol. 56, issue 2, 369-403

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

Keywords: Optimal control; Topology optimization; Semilinear equation; Semismooth Newton method; Volume constraint (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10589-013-9555-6

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