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Exploiting Sparsity in Complex Polynomial Optimization

Author

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  • Jie Wang

    (Academy of Mathematics and Systems Science, CAS)

  • Victor Magron

    (Laboratory for Analysis and Architecture of Systems, CNRS)

Abstract

In this paper, we study the sparsity-adapted complex moment-Hermitian sum of squares (moment-HSOS) hierarchy for complex polynomial optimization problems, where the sparsity includes correlative sparsity and term sparsity. We compare the strengths of the sparsity-adapted complex moment-HSOS hierarchy with the sparsity-adapted real moment-SOS hierarchy on either randomly generated complex polynomial optimization problems or the AC optimal power flow problem. The results of numerical experiments show that the sparsity-adapted complex moment-HSOS hierarchy provides a trade-off between the computational cost and the quality of obtained bounds for large-scale complex polynomial optimization problems.

Suggested Citation

  • Jie Wang & Victor Magron, 2022. "Exploiting Sparsity in Complex Polynomial Optimization," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 335-359, January.
    • Handle: RePEc:spr:joptap:v:192:y:2022:i:1:d:10.1007_s10957-021-01975-z
    DOI: 10.1007/s10957-021-01975-z
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    References listed on IDEAS

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    1. Dan Bienstock & Mauro Escobar & Claudio Gentile & Leo Liberti, 2020. "Mathematical programming formulations for the alternating current optimal power flow problem," 4OR, Springer, vol. 18(3), pages 249-292, September.
    2. Jie Wang & Victor Magron, 2021. "Exploiting term sparsity in noncommutative polynomial optimization," Computational Optimization and Applications, Springer, vol. 80(2), pages 483-521, November.
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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. Cheng Lu & Zhibin Deng & Shu-Cherng Fang & Wenxun Xing, 2023. "A New Global Algorithm for Max-Cut Problem with Chordal Sparsity," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 608-638, May.

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