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An augmented Lagrange method for elliptic state constrained optimal control problems

Author

Listed:
  • Veronika Karl

    (University of Würzburg)

  • Daniel Wachsmuth

    (University of Würzburg)

Abstract

In the present work we apply an augmented Lagrange method to solve pointwise state constrained elliptic optimal control problems. We prove strong convergence of the primal variables as well as weak convergence of the adjoint states and weak-* convergence of the multipliers associated to the state constraint. In addition, we show that the sequence of generated penalty parameters is bounded only in exceptional situations, which is different from classical results in finite-dimensional optimization. In addition, numerical results are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:69:y:2018:i:3:d:10.1007_s10589-017-9965-y
    DOI: 10.1007/s10589-017-9965-y
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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.
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    Cited by:

    1. Caroline Geiersbach & Tim Suchan & Kathrin Welker, 2024. "Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 165-195, October.
    2. Hailing Wang & Changjun Yu & Yongcun Song, 2024. "An Augmented Lagrangian Method for State Constrained Linear Parabolic Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 196-226, October.
    3. Roberto Andreani & Ellen H. Fukuda & Gabriel Haeser & Daiana O. Santos & Leonardo D. Secchin, 2024. "Optimality Conditions for Nonlinear Second-Order Cone Programming and Symmetric Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 1-33, January.
    4. 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.

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