IDEAS home Printed from
   My bibliography  Save this article

On reduction of duality gap in quadratic knapsack problems


  • X. Zheng


  • X. Sun


  • D. Li


  • Y. Xu



We investigate in this paper the duality gap between quadratic knapsack problem and its Lagrangian dual or semidefinite programming relaxation. We characterize the duality gap by a distance measure from set {0, 1} n to certain polyhedral set and demonstrate that the duality gap can be reduced by an amount proportional to the square of the distance. We further discuss how to compute the distance measure via cell enumeration method and to derive the corresponding improved upper bound of the problem. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • X. Zheng & X. Sun & D. Li & Y. Xu, 2012. "On reduction of duality gap in quadratic knapsack problems," Journal of Global Optimization, Springer, vol. 54(2), pages 325-339, October.
  • Handle: RePEc:spr:jglopt:v:54:y:2012:i:2:p:325-339
    DOI: 10.1007/s10898-012-9872-9

    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.

    References listed on IDEAS

    1. Michelon, Philippe & Veilleux, Louis, 1996. "Lagrangean methods for the 0-1 Quadratic Knapsack Problem," European Journal of Operational Research, Elsevier, vol. 92(2), pages 326-341, July.
    Full references (including those not matched with items on IDEAS)


    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:2:p:325-339. 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.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with 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.