IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v15y1969i9p539-549.html
   My bibliography  Save this article

Dual Programming Problems as Hemi-Games

Author

Listed:
  • Enrique Cansado

    (Director Inter American Statistical Training Center, Santiago, Chile)

Abstract

It is proposed here a new and unifying formal framework for duality in optimization problems, relating more closely programs to games, by means of the concepts of "hemi-games" and "quasi-duality". A new generalization of the idea of La-grange multipliers is also presented. Associated with each programming problem, we consider (through a generalization of the Lagrange's function) one particular game (from the many possible ones) such that our programming problem is one of the two hemi-games of such a game. Each hemi-game can be considered as a programming problem. Then, for each game we have a pair of programming problems: the two hemi-games of the game considered. If the game has a solution, then so does each of the two associated programming problems; and the solution of each one is an optimal strategy for the respective player. This couple of programming problems constitute a pair of dual problems. And each pair of dual problems can be thought out as such a couple of programming problems associated with the two players of a solvable game. Various and seemingly disparate dualities, already considered in the literature, are then exhibited in order to show how they can be obtained from the hemi-game notion proposed. This conceptual framework of duality is not used here for obtaining "new" results, but seems sufficiently interesting in itself.

Suggested Citation

  • Enrique Cansado, 1969. "Dual Programming Problems as Hemi-Games," Management Science, INFORMS, vol. 15(9), pages 539-549, May.
    • Handle: RePEc:inm:ormnsc:v:15:y:1969:i:9:p:539-549
    DOI: 10.1287/mnsc.15.9.539
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.15.9.539
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.15.9.539?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:inm:ormnsc:v:15:y:1969:i:9:p:539-549. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.