IDEAS home Printed from
   My bibliography  Save this paper

Global quadratic optimization via conic relaxation


  • NESTEROV, Yurii

    () (Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium)


We present a convex conic relaxation for a problem of maximizing an indefinite quadratic form over a set of convex constraints on the squared variables. We show that for all these problems we get at least 12/37-relative accuracy of the approximation. In the second part of the paper we derive the conic relaxation by another approach based on the second order optimality conditions. We show that for lp-balls, p>=2, intersected by a linear subspace, it is possible to guarantee (1- 2/p)-relative accuracy of the solution. As a consequence, we prove (1 - 1/eln-n)-relative accuracy of the conic relaxation for an indefinite quadratic maximization problem over an n-dimensional unit box with homogeneous linear equality constraints. We discuss the implications of the results for the discussion around the question P = NP.

Suggested Citation

  • NESTEROV, Yurii, 1998. "Global quadratic optimization via conic relaxation," CORE Discussion Papers 1998060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:1998060

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. NESTEROV, Yurii, 1997. "Quality of semidefinite relaxation for nonconvex quadratic optimization," CORE Discussion Papers 1997019, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. NESTEROV, Yurii, 1997. "Semidefinite relaxation and nonconvex quadratic optimization," CORE Discussion Papers 1997044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. NESTEROV, Yurii, 1999. "Global quadratic optimization on the sets with simplex structure," CORE Discussion Papers 1999015, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    More about this item


    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:cor:louvco:1998060. 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: (Alain GILLIS). 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.