IDEAS home Printed from https://ideas.repec.org/a/hin/jnlmpe/7175385.html
   My bibliography  Save this article

Uniqueness of the Minimal -Norm Solution to the Monotone Linear Complementarity Problem

Author

Listed:
  • Ting Zhang
  • Xiaoqin Jiang

Abstract

The linear complementarity problem (LCP) has wide applications in economic equilibrium, operations research, and so on, which attracted a lot of interest of experts. Finding the sparsest solution to the LCP has real applications in the field of portfolio selection and bimatrix game. Motivated by the approach developed in compressive sensing, we may try to solve an -minimization problem to obtain the sparsest solution to the LCP, where an important theoretical problem is to investigate uniqueness of the solution to the concerned -minimization problem. In this paper, we investigate the problem of finding the minimal -norm solution to the monotone LCP and propose a sufficient and necessary condition for the uniqueness of the minimal -norm solution to the monotone LCP, which provides an important theoretical basis for finding the sparsest solution to the monotone LCP via solving the corresponding -minimization problem. Furthermore, several examples are given to confirm our theoretical finding.

Suggested Citation

  • Ting Zhang & Xiaoqin Jiang, 2017. "Uniqueness of the Minimal -Norm Solution to the Monotone Linear Complementarity Problem," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-8, January.
    • Handle: RePEc:hin:jnlmpe:7175385
    DOI: 10.1155/2017/7175385
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/MPE/2017/7175385.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/MPE/2017/7175385.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2017/7175385?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
    ---><---

    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:hin:jnlmpe:7175385. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.