IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v61y2015i3p669-688.html
   My bibliography  Save this article

Unifying semidefinite and set-copositive relaxations of binary problems and randomization techniques

Author

Listed:
  • Felix Lieder
  • Fatemeh Rad
  • Florian Jarre

Abstract

A reformulation of quadratically constrained binary programs as duals of set-copositive linear optimization problems is derived using either $$\{0,1\}$$ { 0 , 1 } -formulations or $$\{-1,1\}$$ { - 1 , 1 } -formulations. The latter representation allows an extension of the randomization technique by Goemans and Williamson. An application to the max-clique problem shows that the max-clique problem is equivalent to a linear program over the max-cut polytope with one additional linear constraint. This transformation allows the solution of a semidefinite relaxation of the max-clique problem with about the same computational effort as the semidefinite relaxation of the max-cut problem—independent of the number of edges in the underlying graph. A numerical comparison of this approach to the standard Lovasz number concludes the paper. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Felix Lieder & Fatemeh Rad & Florian Jarre, 2015. "Unifying semidefinite and set-copositive relaxations of binary problems and randomization techniques," Computational Optimization and Applications, Springer, vol. 61(3), pages 669-688, July.
    • Handle: RePEc:spr:coopap:v:61:y:2015:i:3:p:669-688
    DOI: 10.1007/s10589-015-9731-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-015-9731-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-015-9731-y?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.

    Citations

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


    Cited by:

    1. Jose L. Walteros & Austin Buchanan, 2020. "Why Is Maximum Clique Often Easy in Practice?," Operations Research, INFORMS, vol. 68(6), pages 1866-1895, November.
    2. Florian Jarre & Felix Lieder & Ya-Feng Liu & Cheng Lu, 2020. "Set-completely-positive representations and cuts for the max-cut polytope and the unit modulus lifting," Journal of Global Optimization, Springer, vol. 76(4), pages 913-932, April.

    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:coopap:v:61:y:2015:i:3:p:669-688. 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.