IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i2p177-d1314021.html
   My bibliography  Save this article

Proximal Analytic Center Cutting Plane Algorithms for Variational Inequalities and Nash Economic Equilibrium

Author

Listed:
  • Renying Zeng

    (Mathematics Department, Saskatchewan Polytechnic, Saskatoon, SK S7K 3R5, Canada)

Abstract

In this study, we proposed proximal analytic center cutting plane algorithms for solving variational inequalities whose domains are normal regions. Our algorithms stop with a solution of the variational inequality after a finite number of iterations, or we may find a sequence that converges to the solution of the variational inequality. We introduced the definition of the Nash economic equilibrium solution over a normal region and proved a sufficient condition for our Nash economic solution. An example of Nash equilibrium over a normal region is also provided. Our proximal analytic center cutting plane algorithms are constructive proofs of our Nash equilibrium problems.

Suggested Citation

  • Renying Zeng, 2024. "Proximal Analytic Center Cutting Plane Algorithms for Variational Inequalities and Nash Economic Equilibrium," Mathematics, MDPI, vol. 12(2), pages 1-10, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:177-:d:1314021
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/2/177/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/2/177/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. GOFFIN, Jean-Louis & VIAL, Jean-Philippe, 1990. "Cutting planes and column generation techniques with the projective algorithm," LIDAM Reprints CORE 918, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Jie Shen & Li-Ping Pang, 2012. "A Proximal Analytic Center Cutting Plane Algorithm for Solving Variational Inequality Problems," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-10, December.
    Full references (including those not matched with items on IDEAS)

    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. Enrico Bettiol & Lucas Létocart & Francesco Rinaldi & Emiliano Traversi, 2020. "A conjugate direction based simplicial decomposition framework for solving a specific class of dense convex quadratic programs," Computational Optimization and Applications, Springer, vol. 75(2), pages 321-360, March.
    2. Issmail Elhallaoui & Daniel Villeneuve & François Soumis & Guy Desaulniers, 2005. "Dynamic Aggregation of Set-Partitioning Constraints in Column Generation," Operations Research, INFORMS, vol. 53(4), pages 632-645, August.

    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:gam:jmathe:v:12:y:2024:i:2:p:177-:d:1314021. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.