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Regularity of solutions for an optimal control problem with mixed control-state constraints

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Abstract

A class of optimal control problems for a semilinear elliptic partial differential equation with mixed control-state constraints is considered. Existence results of an optimal control and necessary optimality conditions are stated. Moreover, a projection formula is derived that is equivalent to the necessary optimality conditions. As main result, the Lipschitz continuity of the optimal control is obtained.

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Authors and Affiliations

  1. Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstraße 69, A-4040, Linz, Austria

    Arnd Rösch

  2. Institut für Mathematik, Technische Universität Berlin, Str. des 17. Juni 136, D-10623, Berlin, Germany

    Daniel Wachsmuth

Authors
  1. Arnd Rösch
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  2. Daniel Wachsmuth
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Rösch, A., Wachsmuth, D. Regularity of solutions for an optimal control problem with mixed control-state constraints. TOP 14, 263–278 (2006). https://doi.org/10.1007/BF02837563

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  • DOI: https://doi.org/10.1007/BF02837563

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