IDEAS home Printed from
   My bibliography  Save this article

A “joint + marginal” heuristic for 0/1 programs


  • Jean Lasserre


  • Tung Thanh



We propose a heuristic for 0/1 programs based on the recent “joint + marginal” approach of the first author for parametric polynomial optimization. The idea is to first consider the n-variable (x 1 , . . . , x n ) problem as a (n − 1)-variable problem (x 2 , . . . , x n ) with the variable x 1 being now a parameter taking value in {0, 1}. One then solves a hierarchy of what we call “joint + marginal” semidefinite relaxations whose duals provide a sequence of polynomial approximations $${x_1\mapsto J_k(x_1)}$$ that converges to the optimal value function J (x 1 ) (as a function of the parameter x 1 ). One considers a fixed index k in the hierarchy and if J k (1) > J k (0) then one decides x 1 = 1 and x 1 =0 otherwise. The quality of the approximation depends on how large k can be chosen (in general, for significant size problems, k=1 is the only choice). One iterates the procedure with now a (n − 2)-variable problem with one parameter $${x_2 \in \{0, 1\}}$$ , etc. Variants are also briefly described as well as some preliminary numerical experiments on the MAXCUT, k-cluster and 0/1 knapsack problems. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Jean Lasserre & Tung Thanh, 2012. "A “joint + marginal” heuristic for 0/1 programs," Journal of Global Optimization, Springer, vol. 54(4), pages 729-744, December.
  • Handle: RePEc:spr:jglopt:v:54:y:2012:i:4:p:729-744
    DOI: 10.1007/s10898-011-9788-9

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item


    0/1 Programs; Semidefinite relaxations;


    Access and download statistics


    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:jglopt:v:54:y:2012:i:4:p:729-744. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.