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

  • Klaus Krumbiegel
  • Ira Neitzel
  • Arnd Rösch


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.


Optimal control Semilinear elliptic equation State constraints Regularization Virtual control Second order sufficient conditions 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Weierstrass Institute for Applied Mathematics and Stochastics, Nonlinear Optimization and Inverse ProblemsBerlinGermany
  2. 2.Fakultät II–Mathematik und NaturwissenschaftenTechnische Universität BerlinBerlinGermany
  3. 3.Department of MathematicsUniversität Duisburg-EssenDuisburgGermany

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