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

Authors:
Klaus Krumbiegel;Ira Neitzel;Arnd Rösch
Affiliations:
Weierstrass Institute for Applied Mathematics and Stochastics, Nonlinear Optimization and Inverse Problems, Berlin, Germany 10117;Fakultät II---Mathematik und Naturwissenschaften, Technische Universität Berlin, Berlin, Germany 10623;Department of Mathematics, Universität Duisburg-Essen, Duisburg, Germany 47057
Venue:
Computational Optimization and Applications
Year:
2012

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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.