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On reduction of duality gap in quadratic knapsack problems

Author

Listed:
  • X. Zheng
  • X. Sun
  • D. Li
  • Y. Xu

Abstract

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
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    References listed on IDEAS

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    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.
    2. Alberto Caprara & David Pisinger & Paolo Toth, 1999. "Exact Solution of the Quadratic Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 125-137, May.
    3. C. Helmberg & F. Rendl & R. Weismantel, 2000. "A Semidefinite Programming Approach to the Quadratic Knapsack Problem," Journal of Combinatorial Optimization, Springer, vol. 4(2), pages 197-215, June.
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