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Global optimality conditions and optimization methods for quadratic integer programming problems

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Abstract

In this paper, we first establish some sufficient and some necessary global optimality conditions for quadratic integer programming problems. Then we present a new local optimization method for quadratic integer programming problems according to its necessary global optimality conditions. A new global optimization method is proposed by combining its sufficient global optimality conditions, local optimization method and an auxiliary function. The numerical examples are also presented to show that the proposed optimization methods for quadratic integer programming problems are very efficient and stable.

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Authors and Affiliations

  1. School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, VIC, 3353, Australia

    Z. Y. Wu

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    G. Q. Li & J. Quan

Authors
  1. Z. Y. Wu
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  2. G. Q. Li
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  3. J. Quan
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Corresponding author

Correspondence to Z. Y. Wu.

Additional information

This research was partially supported by Program for New Century Excellent Talents in University of China, by National Natural Science Foundation of China 10971241, by Australia Research Council Project Grant and by Alexander von Humboldt Foundation.

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Wu, Z.Y., Li, G.Q. & Quan, J. Global optimality conditions and optimization methods for quadratic integer programming problems. J Glob Optim 51, 549–568 (2011). https://doi.org/10.1007/s10898-011-9650-0

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  • DOI: https://doi.org/10.1007/s10898-011-9650-0

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