IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v204y2025i3d10.1007_s10957-024-02574-4.html
   My bibliography  Save this article

A Progressive Decoupling Algorithm for Minimizing the Difference of Convex and Weakly Convex Functions

Author

Listed:
  • Welington de Oliveira

    (Mines Paris, Université PSL, Centre de Mathématiques Appliquées (CMA))

  • João Carlos de Oliveira Souza

    (Federal University of Piauí)

Abstract

Commonly, decomposition and splitting techniques for optimization problems strongly depend on convexity. Implementable splitting methods for nonconvex and nonsmooth optimization problems are scarce and often lack convergence guarantees. Among the few exceptions is the Progressive Decoupling Algorithm (PDA), which has local convergence should convexity be elicitable. In this work, we furnish PDA with a descent test and extend the method to accommodate a broad class of nonsmooth optimization problems with non-elicitable convexity. More precisely, we focus on the problem of minimizing the difference of convex and weakly convex functions over a linear subspace. This framework covers, in particular, a family of stochastic programs with nonconvex recourse and statistical estimation problems for supervised learning.

Suggested Citation

  • Welington de Oliveira & João Carlos de Oliveira Souza, 2025. "A Progressive Decoupling Algorithm for Minimizing the Difference of Convex and Weakly Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 204(3), pages 1-24, March.
    • Handle: RePEc:spr:joptap:v:204:y:2025:i:3:d:10.1007_s10957-024-02574-4
    DOI: 10.1007/s10957-024-02574-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-024-02574-4
    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/s10957-024-02574-4?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:joptap:v:204:y:2025:i:3:d:10.1007_s10957-024-02574-4. 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.