On reduction of duality gap in quadratic knapsack problems

X. Zheng (), X. Sun (), D. Li () and Y. Xu ()

Journal of Global Optimization, 2012, vol. 54, issue 2, 325-339

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

Keywords: Quadratic knapsack problem; Lagrangian relaxation; SDP relaxation; Duality gap; Cell enumeration (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10898-012-9872-9

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