Article

Journal of Optimization Theory and Applications

, Volume 151, Issue 2, pp 241-259

Global Optimality Conditions and Optimization Methods for Quadratic Knapsack Problems

  • Z. Y. WuAffiliated withSchool of Information Technology and Mathematical Sciences, University of Ballarat Email author 
  • , Y. J. YangAffiliated withDepartment of Mathematics, Shanghai University
  • , F. S. BaiAffiliated withSchool of Information Technology and Mathematical Sciences, University of Ballarat
  • , M. MammadovAffiliated withSchool of Information Technology and Mathematical Sciences, University of Ballarat

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Abstract

The quadratic knapsack problem (QKP) maximizes a quadratic objective function subject to a binary and linear capacity constraint. Due to its simple structure and challenging difficulty, it has been studied intensively during the last two decades. This paper first presents some global optimality conditions for (QKP), which include necessary conditions and sufficient conditions. Then a local optimization method for (QKP) is developed using the necessary global optimality condition. Finally a global optimization method for (QKP) is proposed based on the sufficient global optimality condition, the local optimization method and an auxiliary function. Several numerical examples are given to illustrate the efficiency of the presented optimization methods.

Keywords

Quadratic knapsack problem Global optimality conditions Local optimization method Global optimization method