IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v92y2025i2d10.1007_s10589-025-00714-8.html
   My bibliography  Save this article

Improved Gauss-Seidel type and Jacobi type methods for linear complementarity problems

Author

Listed:
  • Wentai Liu

    (Tianjin University)

  • Yong Wang

    (Tianjin University)

  • Zheng-Hai Huang

    (Tianjin University)

Abstract

In this paper, we propose two Gauss-Seidel type methods, i.e., the improved modulus-based Gauss-Seidel method and the improved projected Gauss-Seidel method, to solve linear complementarity problems with Z-matrices, in which the diagonal entries of the system matrices may be non-positive. The monotone convergence of the improved modulus-based Gauss-Seidel method is proved minutely. And by proving the equivalence between the improved projected Gauss-Seidel method and the improved modulus-based Gauss-Seidel method, the same property of the improved projected Gauss-Seidel method is also shown. In addition, we also propose the improved modulus-based Jacobi method and show its monotone convergence. These methods extend the applications of the classical modulus-based matrix splitting methods and the classical projected method for solving linear complementarity problems. Finally, our numerical experiments verify our theoretical results. We also compare the three proposed methods and an existing related method, and the results show the effectiveness of the proposed algorithms.

Suggested Citation

  • Wentai Liu & Yong Wang & Zheng-Hai Huang, 2025. "Improved Gauss-Seidel type and Jacobi type methods for linear complementarity problems," Computational Optimization and Applications, Springer, vol. 92(2), pages 683-708, November.
    • Handle: RePEc:spr:coopap:v:92:y:2025:i:2:d:10.1007_s10589-025-00714-8
    DOI: 10.1007/s10589-025-00714-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-025-00714-8
    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/s10589-025-00714-8?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

    for a different version of it.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:spr:coopap:v:92:y:2025:i:2:d:10.1007_s10589-025-00714-8. 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.