IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v20y1972i1p137-142.html
   My bibliography  Save this article

On Refinements of Some Duality Theorems in Linear Programming over Cones

Author

Listed:
  • K. O. Kortanek

    (Carnegie-Mellon University, Pittsburgh, Pennsylvania)

  • A. L. Soyster

    (Carnegie-Mellon University, Pittsburgh, Pennsylvania, and Pennsylvania State University, University Park, Pennsylvania)

Abstract

Recently Schechter (in a Lehigh University report) formulated two dual linear programming problems over closed convex cones in quite general spaces and showed that, if precisely one of the problems is feasible, then the feasible one has infinite value. In this paper we obtain a refinement by using asymptotic duality states as defined by Ben Israel-Charnes-Kortanek and their classification theorem [ Bull. Am. Math. Soc. 74, 318–324 (1969) and 76, 426 (1970)]. The sharpened version shows that in general the feasible-infinite states of the dual problem-pair are not quite as symmetrical as, for example, in the special case of polyhedral cones. Similarly, a sharpened version of Duffin's Theorem 1 [H. W. Kuhn and A. W. Tucker (eds.) Linear Equalities and Related Systems . Princeton University Press, pp. 317–329, 1956] is also developed.

Suggested Citation

  • K. O. Kortanek & A. L. Soyster, 1972. "On Refinements of Some Duality Theorems in Linear Programming over Cones," Operations Research, INFORMS, vol. 20(1), pages 137-142, February.
    • Handle: RePEc:inm:oropre:v:20:y:1972:i:1:p:137-142
    DOI: 10.1287/opre.20.1.137
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.20.1.137
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.20.1.137?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:oropre:v:20:y:1972:i:1:p:137-142. 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.