IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v77y2020i3d10.1007_s10589-020-00223-w.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-020-00223-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-020-00223-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. B. Jadamba & A. Khan & M. Sama, 2017. "Error estimates for integral constraint regularization of state-constrained elliptic control problems," Computational Optimization and Applications, Springer, vol. 67(1), pages 39-71, May.
    3. 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.
    4. A. Rösch & K. G. Siebert & S. Steinig, 2017. "Reliable a posteriori error estimation for state-constrained optimal control," Computational Optimization and Applications, Springer, vol. 68(1), pages 121-162, September.
    5. Moritz Keuthen & Michael Ulbrich, 2015. "Moreau–Yosida regularization in shape optimization with geometric constraints," Computational Optimization and Applications, Springer, vol. 62(1), pages 181-216, September.
    6. 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.
    7. Martin Seydenschwanz, 2015. "Convergence results for the discrete regularization of linear-quadratic control problems with bang–bang solutions," Computational Optimization and Applications, Springer, vol. 61(3), pages 731-760, July.
    8. Hamdullah Yücel & Peter Benner, 2015. "Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations," Computational Optimization and Applications, Springer, vol. 62(1), pages 291-321, September.
    9. Wang, Fangyuan & Chen, Chuanjun & Zhou, Zhaojie, 2024. "Integral constraint regularization method for fractional optimal control problem with pointwise state constraint," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    10. Bui Trong Kien & Arnd Rösch & Nguyen Hai Son & Nguyen Van Tuyen, 2023. "FEM for Semilinear Elliptic Optimal Control with Nonlinear and Mixed Constraints," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 130-173, April.
    11. 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.
    12. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:77:y:2020:i:3:d:10.1007_s10589-020-00223-w. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.