IDEAS home Printed from https://ideas.repec.org/h/spr/lnechp/978-3-540-85646-7_2.html
   My bibliography  Save this book chapter

The Attainment of the Solution of the Dual Program in Vertices for Vectorial Linear Programs

In: Multiobjective Programming and Goal Programming

Author

Listed:
  • Frank Heyde
  • Andreas Löhne
  • Christiane Tammer

    (Martin-Luther-University Halle Halle-Wittenberg)

Abstract

This article is a continuation of Löhne A, Tammer C (2007: A new approach to duality in vector optimization. Optimization 56(1–2):221–239) [14]. We developed in [14] a duality theory for convex vector optimization problems, which is different from other approaches in the literature. The main idea is to embed the image space Rq of the objective function into an appropriate complete lattice, which is a subset of the power set of Rq. This leads to a duality theory which is very analogous to that of scalar convex problems. We applied these results to linear problems and showed duality assertions. However, in [14] we could not answer the question, whether the supremum of the dual linear program is attained in vertices of the dual feasible set. We show in this paper that this is, in general, not true but, it is true under additional assumptions.

Suggested Citation

  • Frank Heyde & Andreas Löhne & Christiane Tammer, 2009. "The Attainment of the Solution of the Dual Program in Vertices for Vectorial Linear Programs," Lecture Notes in Economics and Mathematical Systems, in: Vincent Barichard & Matthias Ehrgott & Xavier Gandibleux & Vincent T'Kindt (ed.), Multiobjective Programming and Goal Programming, pages 13-24, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-85646-7_2
    DOI: 10.1007/978-3-540-85646-7_2
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    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:spr:lnechp:978-3-540-85646-7_2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.