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A Lagrange multiplier method for semilinear elliptic state constrained optimal control problems

Author

Listed:
  • Veronika Karl

    (Universität Würzburg)

  • Ira Neitzel

    (Rheinische Friedrich-Wilhelms-Universität Bonn)

  • Daniel Wachsmuth

    (Universität Würzburg)

Abstract

In this paper we apply an augmented Lagrange method to a class of semilinear elliptic optimal control problems with pointwise state constraints. We show strong convergence of subsequences of the primal variables to a local solution of the original problem as well as weak convergence of the adjoint states and weak-* convergence of the multipliers associated to the state constraint. Moreover, we show existence of stationary points in arbitrary small neighborhoods of local solutions of the original problem. Additionally, various numerical results are presented.

Suggested Citation

  • Veronika Karl & Ira Neitzel & Daniel Wachsmuth, 2020. "A Lagrange multiplier method for semilinear elliptic state constrained optimal control problems," Computational Optimization and Applications, Springer, vol. 77(3), pages 831-869, December.
    • Handle: RePEc:spr:coopap:v:77:y:2020:i:3:d:10.1007_s10589-020-00223-w
    DOI: 10.1007/s10589-020-00223-w
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    References listed on IDEAS

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    1. Klaus Krumbiegel & Ira Neitzel & Arnd Rösch, 2012. "Regularization for semilinear elliptic optimal control problems with pointwise state and control constraints," Computational Optimization and Applications, Springer, vol. 52(1), pages 181-207, May.
    2. M. Hinze & C. Meyer, 2010. "Variational discretization of Lavrentiev-regularized state constrained elliptic optimal control problems," Computational Optimization and Applications, Springer, vol. 46(3), pages 487-510, July.
    3. Veronika Karl & Daniel Wachsmuth, 2018. "An augmented Lagrange method for elliptic state constrained optimal control problems," Computational Optimization and Applications, Springer, vol. 69(3), pages 857-880, April.
    4. C. Meyer & I. Yousept, 2009. "Regularization of state-constrained elliptic optimal control problems with nonlocal radiation interface conditions," Computational Optimization and Applications, Springer, vol. 44(2), pages 183-212, November.
    Full references (including those not matched with items on IDEAS)

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