IDEAS home Printed from https://ideas.repec.org/a/inm/ormoor/v50y2025i2p993-1018.html
   My bibliography  Save this article

Efficiency of Stochastic Coordinate Proximal Gradient Methods on Nonseparable Composite Optimization

Author

Listed:
  • Ion Necoara

    (Automatic Control and Systems Engineering Department, University Politehnica Bucharest, 060042 Bucharest, Romania; and Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, 050711 Bucharest, Romania)

  • Flavia Chorobura

    (Automatic Control and Systems Engineering Department, University Politehnica Bucharest, 060042 Bucharest, Romania)

Abstract

This paper deals with composite optimization problems having the objective function formed as the sum of two terms; one has a Lipschitz continuous gradient along random subspaces and may be nonconvex, and the second term is simple and differentiable but possibly nonconvex and nonseparable. Under these settings, we design a stochastic coordinate proximal gradient method that takes into account the nonseparable composite form of the objective function. This algorithm achieves scalability by constructing at each iteration a local approximation model of the whole nonseparable objective function along a random subspace with user-determined dimension. We outline efficient techniques for selecting the random subspace, yielding an implementation that has low cost per iteration, also achieving fast convergence rates. We present a probabilistic worst case complexity analysis for our stochastic coordinate proximal gradient method in convex and nonconvex settings; in particular, we prove high-probability bounds on the number of iterations before a given optimality is achieved. Extensive numerical results also confirm the efficiency of our algorithm.

Suggested Citation

  • Ion Necoara & Flavia Chorobura, 2025. "Efficiency of Stochastic Coordinate Proximal Gradient Methods on Nonseparable Composite Optimization," Mathematics of Operations Research, INFORMS, vol. 50(2), pages 993-1018, May.
  • Handle: RePEc:inm:ormoor:v:50:y:2025:i:2:p:993-1018
    DOI: 10.1287/moor.2023.0044
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/moor.2023.0044
    Download Restriction: no

    File URL: https://libkey.io/10.1287/moor.2023.0044?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
    ---><---

    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:inm:ormoor:v:50:y:2025:i:2:p:993-1018. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.