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Outcome-space branch-and-bound outer approximation algorithm for a class of non-convex quadratic programming problems

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Abstract

The quadratically constrained quadratic programming problem often appears in various fields such as engineering practice, management science and network communication. This paper mainly considers a non-convex quadratic programming problem with convex quadratic constraints. Firstly, the objective function of the problem is reconstructed into a form composed of only one convex function and several linear functions by using the eigenvalue decomposition technique of matrix. Then the reconstructed problem is converted to the equivalent problem with simple concave quadratic objective function in the outcome space by introducing appropriate auxiliary variables, and its feasible domain is convex. Based on the branch-and-bound framework which can guarantee the global optimality of the solution, a global optimization algorithm for solving the equivalent problem is proposed, which integrates the effective relaxation process and the branching process related to the outer approximation technique. Finally, the effectiveness and feasibility of the algorithm are illustrated by numerical experiments.

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Acknowledgements

This research is supported by the National Natural Science Foundation of China under Grant (11961001), the Construction Project of first-class subjects in Ningxia higher Education(NXYLXK2017B09) and the Major proprietary funded project of North Minzu University(ZDZX201901).

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Authors and Affiliations

  1. School of Civil and Hydraulic Engineering, Ningxia University, Yinchuan, 750021, People’s Republic of China

    Bo Zhang

  2. School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, People’s Republic of China

    Bo Zhang & Xia Liu

  3. Ningxia Province Key Laboratory of Intelligent Information and Data Processing, North Minzu University, Yinchuan, 750021, People’s Republic of China

    YueLin Gao

  4. School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, People’s Republic of China

    YueLin Gao & XiaoLi Huang

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  1. Bo Zhang
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  2. YueLin Gao
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  3. Xia Liu
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  4. XiaoLi Huang
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Correspondence to YueLin Gao.

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Zhang, B., Gao, Y., Liu, X. et al. Outcome-space branch-and-bound outer approximation algorithm for a class of non-convex quadratic programming problems. J Glob Optim 86, 61–92 (2023). https://doi.org/10.1007/s10898-022-01255-8

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  • DOI: https://doi.org/10.1007/s10898-022-01255-8

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