IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v67y2017i1d10.1007_s10589-016-9885-2.html
   My bibliography  Save this article

Error estimates for integral constraint regularization of state-constrained elliptic control problems

Author

Listed:
  • B. Jadamba

    (Rochester Institute of Technology)

  • A. Khan

    (Rochester Institute of Technology)

  • M. Sama

    (E.T.S.I.I. Universidad Nacional de Educación a Distancia)

Abstract

In this paper, we study new aspects of the integral contraint regularization of state-constrained elliptic control problems (Jadamba et al. in Syst Control Lett 61(6):707–713, 2012). Besides giving new results on the regularity and the convergence of the regularized controls and associated Lagrange multipliers, the main objective of this paper is to give abstract error estimates for the regularization error. We also consider a discretization of the regularized problems and derive numerical estimates which are uniform with respect to the regularization parameter and the discretization parameter. As an application of these results, we prove that this discretization is indeed a full discretization of the original problem defined in terms of a problem with finitely many integral constraints. Detailed numerical results justifying the theoretical findings as well as a comparison of our work with the existing literature is also given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:67:y:2017:i:1:d:10.1007_s10589-016-9885-2
    DOI: 10.1007/s10589-016-9885-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-016-9885-2
    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/s10589-016-9885-2?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. Dmitriy Leykekhman & Dominik Meidner & Boris Vexler, 2013. "Optimal error estimates for finite element discretization of elliptic optimal control problems with finitely many pointwise state constraints," Computational Optimization and Applications, Springer, vol. 55(3), pages 769-802, July.
    4. Eduardo Casas & Mariano Mateos, 2012. "Numerical approximation of elliptic control problems with finitely many pointwise constraints," Computational Optimization and Applications, Springer, vol. 51(3), pages 1319-1343, April.
    5. Michael Hinze & Anton Schiela, 2011. "Discretization of interior point methods for state constrained elliptic optimal control problems: optimal error estimates and parameter adjustment," Computational Optimization and Applications, Springer, vol. 48(3), pages 581-600, April.
    6. K. Krumbiegel & A. Rösch, 2009. "A virtual control concept for state constrained optimal control problems," Computational Optimization and Applications, Springer, vol. 43(2), pages 213-233, June.
    7. Bienvenido Jiménez & Vicente Novo & Miguel Sama, 2013. "An extension of the Basic Constraint Qualification to nonconvex vector optimization problems," Journal of Global Optimization, Springer, vol. 56(4), pages 1755-1771, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lidia Huerga & Baasansuren Jadamba & Miguel Sama, 2019. "An Extension of the Kaliszewski Cone to Non-polyhedral Pointed Cones in Infinite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 437-455, May.
    2. 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).

    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. 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.
    2. 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.
    3. Mariano Mateos & Ira Neitzel, 2016. "Dirichlet control of elliptic state constrained problems," Computational Optimization and Applications, Springer, vol. 63(3), pages 825-853, April.
    4. 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.
    5. 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.
    6. 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.
    7. César Gutiérrez & Rubén López & Vicente Novo, 2014. "Existence and Boundedness of Solutions in Infinite-Dimensional Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 515-547, August.
    8. Dmitriy Leykekhman & Dominik Meidner & Boris Vexler, 2013. "Optimal error estimates for finite element discretization of elliptic optimal control problems with finitely many pointwise state constraints," Computational Optimization and Applications, Springer, vol. 55(3), pages 769-802, July.
    9. 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.
    10. Dante Kalise & Karl Kunisch & Zhiping Rao, 2017. "Infinite Horizon Sparse Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 481-517, February.
    11. 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).
    12. 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.
    13. Francesco Ludovici & Ira Neitzel & Winnifried Wollner, 2018. "A Priori Error Estimates for State-Constrained Semilinear Parabolic Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 317-348, August.
    14. Gerd Wachsmuth, 2015. "Mathematical Programs with Complementarity Constraints in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 480-507, August.

    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:67:y:2017:i:1:d:10.1007_s10589-016-9885-2. 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.