IDEAS home Printed from https://ideas.repec.org/a/ids/ijmore/v26y2023i1p96-110.html
   My bibliography  Save this article

An algorithm for solving a min-max problem by adaptive method

Author

Listed:
  • Aghiles Azizen
  • Kahina Louadj
  • Mohamed Aidene

Abstract

Min-max problems occupies an important place in linear programming (LP), as it addresses a large number of optimisation problems, in various fields of science. In this study, an algorithm using adaptive method is proposed for solving the min-max problem in linear programming. It consists on finding the maximum of the minimum of a function (where the essential constraints are in equality and the direct constraints are bounded) in a minimum execution time. A solving algorithm is built using the principle of the adaptive method and it is based on the concept of the support matrix of the problem. Necessary and sufficient conditions for the optimality of a support feasible solution are established and sub-optimality criterion is derived. This algorithm allows to solve directly the considered problem, without modifying it and avoids the drawbacks of the increase in the number of the variables and the constraints, thus, improve the convergence speed of the method. Its performance is tested on a numerical example.

Suggested Citation

  • Aghiles Azizen & Kahina Louadj & Mohamed Aidene, 2023. "An algorithm for solving a min-max problem by adaptive method," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 26(1), pages 96-110.
    • Handle: RePEc:ids:ijmore:v:26:y:2023:i:1:p:96-110
    as

    Download full text from publisher

    File URL: http://www.inderscience.com/link.php?id=133718
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:ids:ijmore:v:26:y:2023:i:1:p:96-110. 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: Sarah Parker (email available below). General contact details of provider: http://www.inderscience.com/browse/index.php?journalID=320 .

    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.