IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v97y1998i3d10.1023_a1022646327085.html
   My bibliography  Save this article

Convergence Analysis and Applications of the Glowinski–Le Tallec Splitting Method for Finding a Zero of the Sum of Two Maximal Monotone Operators

Author

Listed:
  • S. Haubruge

    (Universitaires, Notre Dame de la Paix)

  • V. H. Nguyen

    (Universitaires, Notre Dame de la Paix)

  • J. J. Strodiot

    (Universitaires, Notre Dame de la Paix)

Abstract

Many problems of convex programming can be reduced to finding a zero of the sum of two maximal monotone operators. For solving this problem, there exists a variety of methods such as the forward–backward method, the Peaceman–Rachford method, the Douglas–Rachford method, and more recently the θ-scheme. This last method has been presented without general convergence analysis by Glowinski and Le Tallec and seems to give good numerical results. The purpose of this paper is first to present convergence results and an estimation of the rate of convergence for this recent method, and then to apply it to variational inequalities and structured convex programming problems to get new parallel decomposition algorithms.

Suggested Citation

  • S. Haubruge & V. H. Nguyen & J. J. Strodiot, 1998. "Convergence Analysis and Applications of the Glowinski–Le Tallec Splitting Method for Finding a Zero of the Sum of Two Maximal Monotone Operators," Journal of Optimization Theory and Applications, Springer, vol. 97(3), pages 645-673, June.
    • Handle: RePEc:spr:joptap:v:97:y:1998:i:3:d:10.1023_a:1022646327085
    DOI: 10.1023/A:1022646327085
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1022646327085
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1022646327085?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. Ciyou Zhu, 1995. "Asymptotic Convergence Analysis of the Forward-Backward Splitting Algorithm," Mathematics of Operations Research, INFORMS, vol. 20(2), pages 449-464, May.
    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. Phan Tu Vuong & Jean Jacques Strodiot, 2018. "The Glowinski–Le Tallec splitting method revisited in the framework of equilibrium problems in Hilbert spaces," Journal of Global Optimization, Springer, vol. 70(2), pages 477-495, February.
    2. Shi Zheng & Wen Zheng & Xia Jin, 2007. "Estimation of ARX parametric model in regional economic systems," Systems Engineering, John Wiley & Sons, vol. 10(4), pages 290-296, December.

    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. Phan Tu Vuong & Jean Jacques Strodiot, 2018. "The Glowinski–Le Tallec splitting method revisited in the framework of equilibrium problems in Hilbert spaces," Journal of Global Optimization, Springer, vol. 70(2), pages 477-495, February.

    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:97:y:1998:i:3:d:10.1023_a:1022646327085. 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.