IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v90y2024i3d10.1007_s10898-024-01419-8.html
   My bibliography  Save this article

A Two-Step Proximal Point Algorithm for Nonconvex Equilibrium Problems with Applications to Fractional Programming

Author

Listed:
  • Alfredo Iusem

    (Fundação Getúlio Vargas (FGV))

  • Felipe Lara

    (Universidad de Tarapacá)

  • Raúl T. Marcavillaca

    (Universidad de Chile)

  • Le Hai Yen

    (Vietnam Academy of Sciences and Technology (VAST))

Abstract

We present a proximal point type algorithm tailored for tackling pseudomonotone equilibrium problems in a Hilbert space which are not necessarily convex in the second argument of the involved bifunction. Motivated by the extragradient algorithm, we propose a two-step method and we prove that the generated sequence converges strongly to a solution of the nonconvex equilibrium problem under mild assumptions and, also, we establish a linear convergent rate for the iterates. Furthermore, we identify a new class of functions that meet our assumptions, and we provide sufficient conditions for quadratic fractional functions to exhibit strong quasiconvexity. Finally, we perform numerical experiments comparing our algorithm against two alternative methods for classes of nonconvex mixed variational inequalities.

Suggested Citation

  • Alfredo Iusem & Felipe Lara & Raúl T. Marcavillaca & Le Hai Yen, 2024. "A Two-Step Proximal Point Algorithm for Nonconvex Equilibrium Problems with Applications to Fractional Programming," Journal of Global Optimization, Springer, vol. 90(3), pages 755-779, November.
    • Handle: RePEc:spr:jglopt:v:90:y:2024:i:3:d:10.1007_s10898-024-01419-8
    DOI: 10.1007/s10898-024-01419-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-024-01419-8
    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/s10898-024-01419-8?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.

    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:jglopt:v:90:y:2024:i:3:d:10.1007_s10898-024-01419-8. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.