IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v158y2013i3d10.1007_s10957-013-0296-6.html
   My bibliography  Save this article

Forward–Backward Penalty Scheme for Constrained Convex Minimization Without Inf-Compactness

Author

Listed:
  • Nahla Noun

    (Université Montpellier 2
    Faculté des Sciences 1 et Ecole Doctorale des Sciences et de Technologie)

  • Juan Peypouquet

    (Universidad Técnica Federico Santa María)

Abstract

In order to solve constrained minimization problems, Attouch et al. propose a forward–backward algorithm that involves an exterior penalization scheme in the forward step. They prove that every sequence generated by the algorithm converges weakly to a solution of the minimization problem if either the objective function or the penalization function corresponding to the feasible set is inf-compact. Unfortunately, this assumption leaves out problems that are not coercive, as well as several interesting applications in infinite-dimensional spaces. The purpose of this short article is to show this convergence result without the inf-compactness assumption.

Suggested Citation

  • Nahla Noun & Juan Peypouquet, 2013. "Forward–Backward Penalty Scheme for Constrained Convex Minimization Without Inf-Compactness," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 787-795, September.
    • Handle: RePEc:spr:joptap:v:158:y:2013:i:3:d:10.1007_s10957-013-0296-6
    DOI: 10.1007/s10957-013-0296-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-013-0296-6
    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/s10957-013-0296-6?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. Juan Peypouquet, 2012. "Coupling the Gradient Method with a General Exterior Penalization Scheme for Convex Minimization," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 123-138, April.
    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. Nimit Nimana & Narin Petrot, 2019. "Generalized forward–backward splitting with penalization for monotone inclusion problems," Journal of Global Optimization, Springer, vol. 73(4), pages 825-847, April.
    2. Sebastian Banert & Radu Ioan Boţ, 2015. "Backward Penalty Schemes for Monotone Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 930-948, September.

    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. Sebastian Banert & Radu Ioan Boţ, 2015. "Backward Penalty Schemes for Monotone Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 930-948, September.
    2. Nimit Nimana & Narin Petrot, 2019. "Generalized forward–backward splitting with penalization for monotone inclusion problems," Journal of Global Optimization, Springer, vol. 73(4), pages 825-847, April.

    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:joptap:v:158:y:2013:i:3:d:10.1007_s10957-013-0296-6. 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.