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

Author

Listed:
  • Bo Zhang

    (Ningxia University
    Ningxia University)

  • YueLin Gao

    (North Minzu University
    North Minzu University)

  • Xia Liu

    (Ningxia University)

  • XiaoLi Huang

    (North Minzu University)

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.

Suggested Citation

  • Bo Zhang & YueLin Gao & Xia Liu & XiaoLi Huang, 2023. "Outcome-space branch-and-bound outer approximation algorithm for a class of non-convex quadratic programming problems," Journal of Global Optimization, Springer, vol. 86(1), pages 61-92, May.
    • Handle: RePEc:spr:jglopt:v:86:y:2023:i:1:d:10.1007_s10898-022-01255-8
    DOI: 10.1007/s10898-022-01255-8
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    References listed on IDEAS

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