IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v57y2003i3p437-448.html
   My bibliography  Save this article

Degeneracy degrees of constraint collections

Author

Listed:
  • Gerard Sierksma
  • Gert A. Tijssen

Abstract

This paper presents an unifying approach to the theory of degeneracy of basic feasible solutions, vertices, faces, and all subsets of polyhedra. It is a generalization of the usual concept of degeneracy defined for basic feasible solutions of an LP-problem. We use the concept of degeneracy degree for arbitrary subsets of ℝ n with respect to linear constraint collections. We discuss the connection with the usual definitions, and establish the relationship between minimal representations of polyhedra and the degeneracy of their faces. We also consider a number of complexity aspects of the problem of determining degeneracy degrees. In the last section we show how our definition of degeneracy can be used to analyze the convergence of interior point methods when the optimal solutions are degenerate. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • Gerard Sierksma & Gert A. Tijssen, 2003. "Degeneracy degrees of constraint collections," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(3), pages 437-448, August.
    • Handle: RePEc:spr:mathme:v:57:y:2003:i:3:p:437-448
    DOI: 10.1007/s001860200259
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s001860200259
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s001860200259?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
    ---><---

    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:spr:mathme:v:57:y:2003:i:3:p:437-448. 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.