IDEAS home Printed from https://ideas.repec.org/p/cor/louvco/2002008.html
   My bibliography  Save this paper

On unions and dominants of polytopes

Author

Listed:
  • BALAS, Egon
  • BOCKMAYR, Alexander
  • PISARUK, Nicolai
  • WOLSEY, Laurence

Abstract

A well-known result on unions of polyhedra in the same space gives an extended formulation whose projection is the convex hull of the union. Here in contrast we study the unions of polytopes in different spaces, giving a complete description of the convex hull without additional variables. When the underlying polytopes are monotone, the facets are described explicitly, generalizing results of Hong and Hooker on cardinality rules, and an efficient separation algorithm is proposed. These results are based on an explicit representation of the dominant of a polytope, and an algorithm for the separation problem for the dominant. For non-monotone polytopes, both the dominant and the union are characterized. We also give results on the unions of polymatroids both on disjoint ground sets and on the same ground set generalizing results of Conforti and Laurent.

Suggested Citation

  • BALAS, Egon & BOCKMAYR, Alexander & PISARUK, Nicolai & WOLSEY, Laurence, 2002. "On unions and dominants of polytopes," LIDAM Discussion Papers CORE 2002008, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2002008
    as

    Download full text from publisher

    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2002.html
    Download Restriction: no
    ---><---

    Other versions of this item:

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dan A. Iancu & Marek Petrik & Dharmashankar Subramanian, 2015. "Tight Approximations of Dynamic Risk Measures," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 655-682, March.
    2. Ioannis Mourtos, 2016. "Cardinality constraints and systems of restricted representatives," Journal of Combinatorial Optimization, Springer, vol. 31(3), pages 1061-1089, April.
    3. L. Foulds & B. Toklu & J. Wilson, 2009. "Modelling either-or relations in integer programming," Annals of Operations Research, Springer, vol. 166(1), pages 203-222, February.

    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:cor:louvco:2002008. 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: Alain GILLIS (email available below). General contact details of provider: https://edirc.repec.org/data/coreebe.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.