IDEAS home Printed from https://ideas.repec.org/a/hin/jnljam/423040.html
   My bibliography  Save this article

A New Gap Function for Vector Variational Inequalities with an Application

Author

Listed:
  • Hui-qiang Ma
  • Nan-jing Huang
  • Meng Wu
  • Donal O'Regan

Abstract

We consider a vector variational inequality in a finite-dimensional space. A new gap function is proposed, and an equivalent optimization problem for the vector variational inequality is also provided. Under some suitable conditions, we prove that the gap function is directionally differentiable and that any point satisfying the first-order necessary optimality condition for the equivalent optimization problem solves the vector variational inequality. As an application, we use the new gap function to reformulate a stochastic vector variational inequality as a deterministic optimization problem. We solve this optimization problem by employing the sample average approximation method. The convergence of optimal solutions of the approximation problems is also investigated.

Suggested Citation

  • Hui-qiang Ma & Nan-jing Huang & Meng Wu & Donal O'Regan, 2013. "A New Gap Function for Vector Variational Inequalities with an Application," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-8, June.
    • Handle: RePEc:hin:jnljam:423040
    DOI: 10.1155/2013/423040
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/JAM/2013/423040.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/JAM/2013/423040.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/423040?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:jnljam:423040. 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.