IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v59y2004i2p235-247.html
   My bibliography  Save this article

A conditional gradient method with linear rate of convergence for solving convex linear systems

Author

Listed:
  • Amir Beck
  • Marc Teboulle

Abstract

We consider the problem of finding a point in the intersection of an affine set with a compact convex set, called a convex linear system (CLS). The conditional gradient method is known to exhibit a sublinear rate of convergence. Exploiting the special structure of (CLS), we prove that the conditional gradient method applied to the equivalent minimization formulation of (CLS), converges to a solution at a linear rate, under the sole assumption that Slater’s condition holds for (CLS). The rate of convergence is measured explicitly in terms of the problem’s data and a Slater point. Application to a class of conic linear systems is discussed. Copyright Springer-Verlag 2004

Suggested Citation

  • Amir Beck & Marc Teboulle, 2004. "A conditional gradient method with linear rate of convergence for solving convex linear systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(2), pages 235-247, June.
    • Handle: RePEc:spr:mathme:v:59:y:2004:i:2:p:235-247
    DOI: 10.1007/s001860300327
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s001860300327
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s001860300327?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.

    Citations

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


    Cited by:

    1. R. Díaz Millán & O. P. Ferreira & J. Ugon, 2023. "Approximate Douglas–Rachford algorithm for two-sets convex feasibility problems," Journal of Global Optimization, Springer, vol. 86(3), pages 621-636, July.
    2. R. Díaz Millán & O. P. Ferreira & L. F. Prudente, 2021. "Alternating conditional gradient method for convex feasibility problems," Computational Optimization and Applications, Springer, vol. 80(1), pages 245-269, September.
    3. P. B. Assunção & O. P. Ferreira & L. F. Prudente, 2021. "Conditional gradient method for multiobjective optimization," Computational Optimization and Applications, Springer, vol. 78(3), pages 741-768, April.
    4. O. P. Ferreira & M. Lemes & L. F. Prudente, 2022. "On the inexact scaled gradient projection method," Computational Optimization and Applications, Springer, vol. 81(1), pages 91-125, January.
    5. Deyi Liu & Volkan Cevher & Quoc Tran-Dinh, 2022. "A Newton Frank–Wolfe method for constrained self-concordant minimization," Journal of Global Optimization, Springer, vol. 83(2), pages 273-299, June.

    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:mathme:v:59:y:2004:i:2:p:235-247. 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.