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Argument division based branch-and-bound algorithm for unit-modulus constrained complex quadratic programming

Author

Listed:
  • Cheng Lu

    (North China Electric Power University)

  • Zhibin Deng

    (Chinese Academy of Sciences)

  • Wei-Qiang Zhang

    (Tsinghua University)

  • Shu-Cherng Fang

    (North Carolina State University)

Abstract

This paper proposes a branch-and-bound algorithm for solving the unit-modulus constrained complex quadratic programming problems (CQPP). We study the convex hull of a unit-modulus complex variable with argument constraints, derive new valid linear inequalities from the convex hull, construct an improved semidefinite relaxation of CQPP, and then design an efficient algorithm for solving CQPP globally. The proposed algorithm branches on the sets of argument constraints and derives new valid inequalities from the partitioned sets of arguments. Numerical results are included to support the effectiveness of the proposed algorithm for finding a global solution to CQPP.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:70:y:2018:i:1:d:10.1007_s10898-017-0551-8
    DOI: 10.1007/s10898-017-0551-8
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    Citations

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    Cited by:

    1. Sinjorgo, Lennart & Sotirov, Renata & Anjos, M.F., 2024. "Cuts and semidefinite liftings for the complex cut polytope," Other publications TiSEM e99ba505-f4f2-4b3c-a6b5-2, Tilburg University, School of Economics and Management.
    2. Yingzhe Xu & Cheng Lu & Zhibin Deng & Ya-Feng Liu, 2023. "New semidefinite relaxations for a class of complex quadratic programming problems," Journal of Global Optimization, Springer, vol. 87(1), pages 255-275, September.

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