IDEAS home Printed from https://ideas.repec.org/a/bla/mathna/v291y2018i8-9p1191-1207.html
   My bibliography  Save this article

Steepest†descent proximal point algorithms for a class of variational inequalities in Banach spaces

Author

Listed:
  • Nguyen Buong

Abstract

In this paper, we present a new approach to the problem of finding a common zero for a system of m†accretive mappings in a uniformly convex Banach space with a uniformly Gâteaux differentiable norm. We propose an implicit iteration method and two explicit ones, based on compositions of resolvents with the steepest†descent method. We show that our results contain some iterative methods in literature as special cases. An extension of the Xu's regularization method for the proximal point algorithm from Hilbert spaces onto Banach ones under simple conditions of convergence and a new variant for the method of alternating resolvents are obtained. Numerical experiments are given to affirm efficiency of the methods.

Suggested Citation

  • Nguyen Buong, 2018. "Steepest†descent proximal point algorithms for a class of variational inequalities in Banach spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 291(8-9), pages 1191-1207, June.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:8-9:p:1191-1207
    DOI: 10.1002/mana.201600240
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/mana.201600240
    Download Restriction: no
    File URL: https://libkey.io/10.1002/mana.201600240?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
    ---><---

    Citations

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


    Cited by:

    1. Nguyen Buong & Nguyen Duong Nguyen & Nguyen Thi Quynh Anh, 2024. "An Inertial Iterative Regularization Method for a Class of Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 649-667, August.

    More about this item

    Statistics

    Access and download statistics

    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:bla:mathna:v:291:y:2018:i:8-9:p:1191-1207. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0025-584X .

    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.