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On reduction of duality gap in quadratic knapsack problems

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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.

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Authors and Affiliations

  1. School of Economics and Management, Tongji University, Shanghai, 200092, People’s Republic of China

    X. L. Sun & Y. F. Xu

  2. Department of Management Science, School of Management, Fudan University, 670 Guoshun Road, Shanghai, 200433, People’s Republic of China

    X. J. Zheng

  3. Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, NT, Hong Kong

    D. Li

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  1. X. J. Zheng
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  2. X. L. Sun
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  3. D. Li
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  4. Y. F. Xu
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Correspondence to X. L. Sun.

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Zheng, X.J., Sun, X.L., Li, D. et al. On reduction of duality gap in quadratic knapsack problems. J Glob Optim 54, 325–339 (2012). https://doi.org/10.1007/s10898-012-9872-9

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  • DOI: https://doi.org/10.1007/s10898-012-9872-9

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