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A graphic structure based branch-and-bound algorithm for complex quadratic optimization and applications to magnitude least-square problem

Author

Listed:
  • Cheng Lu

    (North China Electric Power University)

  • Jitao Ma

    (North China Electric Power University)

  • Zhibin Deng

    (University of Chinese Academy of Sciences)

  • Wenxun Xing

    (Tsinghua University)

Abstract

In this paper, we propose a semidefinite relaxation based branch-and-bound algorithm to the unit-modulus constrained complex quadratic programming problem, which has broad applications in signal processing and wireless communications. Our research is motivated from the potential application of the magnitude least-square problem, which possesses the so-called block-arrow sparsity pattern. We discuss how to reduce the worst-case complexity of the proposed branch-and-bound algorithm by exploiting this special sparsity pattern. Numerical results are presented to show the effectiveness of the proposed algorithm.

Suggested Citation

  • Cheng Lu & Jitao Ma & Zhibin Deng & Wenxun Xing, 2024. "A graphic structure based branch-and-bound algorithm for complex quadratic optimization and applications to magnitude least-square problem," Journal of Global Optimization, Springer, vol. 88(1), pages 115-137, January.
    • Handle: RePEc:spr:jglopt:v:88:y:2024:i:1:d:10.1007_s10898-023-01305-9
    DOI: 10.1007/s10898-023-01305-9
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    References listed on IDEAS

    as
    1. Godai Azuma & Mituhiro Fukuda & Sunyoung Kim & Makoto Yamashita, 2022. "Exact SDP relaxations of quadratically constrained quadratic programs with forest structures," Journal of Global Optimization, Springer, vol. 82(2), pages 243-262, February.
    2. Cheng Lu & Zhibin Deng & Wei-Qiang Zhang & Shu-Cherng Fang, 2018. "Argument division based branch-and-bound algorithm for unit-modulus constrained complex quadratic programming," Journal of Global Optimization, Springer, vol. 70(1), pages 171-187, January.
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