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Improved estimation of duality gap in binary quadratic programming using a weighted distance measure

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  • Xia, Yong
  • Sheu, Ruey-Lin
  • Sun, Xiaoling
  • Li, Duan
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    Abstract

    We present in this paper an improved estimation of duality gap between binary quadratic program and its Lagrangian dual. More specifically, we obtain this improved estimation using a weighted distance measure between the binary set and certain affine subspace. We show that the optimal weights can be computed by solving a semidefinite programming problem. We further establish a necessary and sufficient condition under which the weighted distance measure gives a strictly tighter estimation of the duality gap than the existing estimations.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0377221711009738
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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 218 (2012)
    Issue (Month): 2 ()
    Pages: 351-357

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    Handle: RePEc:eee:ejores:v:218:y:2012:i:2:p:351-357

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    Web page: http://www.elsevier.com/locate/eor

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    Keywords: Quadratic binary programming; Lagrangian duality gap; Semidefinite relaxation; Weighted distance measure; Cell enumeration and hyperplane arrangement;

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    1. Ferrez, J.-A. & Fukuda, K. & Liebling, Th.M., 2005. "Solving the fixed rank convex quadratic maximization in binary variables by a parallel zonotope construction algorithm," European Journal of Operational Research, Elsevier, vol. 166(1), pages 35-50, October.
    2. Alidaee, Bahram & Glover, Fred & Kochenberger, Gary & Wang, Haibo, 2007. "Solving the maximum edge weight clique problem via unconstrained quadratic programming," European Journal of Operational Research, Elsevier, vol. 181(2), pages 592-597, September.
    3. Helmberg, C., 2002. "Semidefinite programming," European Journal of Operational Research, Elsevier, vol. 137(3), pages 461-482, March.
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