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Regularization for semilinear elliptic optimal control problems with pointwise state and control constraints

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Abstract

In this paper a class of semilinear elliptic optimal control problem with pointwise state and control constraints is studied. We show that sufficient second order optimality conditions for regularized problems with small regularization parameter can be obtained from a second order sufficient condition assumed for the unregularized problem. Moreover, error estimates with respect to the regularization parameter are derived.

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Authors and Affiliations

  1. Weierstrass Institute for Applied Mathematics and Stochastics, Nonlinear Optimization and Inverse Problems, Mohrenstrasse 39, 10117, Berlin, Germany

    Klaus Krumbiegel

  2. Fakultät II–Mathematik und Naturwissenschaften, Technische Universität Berlin, Str. des 17.Juni 136, 10623, Berlin, Germany

    Ira Neitzel

  3. Department of Mathematics, Universität Duisburg-Essen, Forsthausweg 2, 47057, Duisburg, Germany

    Arnd Rösch

Authors
  1. Klaus Krumbiegel
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  2. Ira Neitzel
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  3. Arnd Rösch
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Correspondence to Klaus Krumbiegel.

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Krumbiegel, K., Neitzel, I. & Rösch, A. Regularization for semilinear elliptic optimal control problems with pointwise state and control constraints. Comput Optim Appl 52, 181–207 (2012). https://doi.org/10.1007/s10589-010-9357-z

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  • DOI: https://doi.org/10.1007/s10589-010-9357-z

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