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T-semidefinite programming relaxation with third-order tensors for constrained polynomial optimization

Author

Listed:
  • Hiroki Marumo

    (Tokyo Institute of Technology)

  • Sunyoung Kim

    (Ewha W. University)

  • Makoto Yamashita

    (Tokyo Institute of Technology)

Abstract

We study T-semidefinite programming (SDP) relaxation for constrained polynomial optimization problems (POPs). T-SDP relaxation for unconstrained POPs was introduced by Zheng et al. (JGO 84:415–440, 2022). In this work, we propose a T-SDP relaxation for POPs with polynomial inequality constraints and show that the resulting T-SDP relaxation formulated with third-order tensors can be transformed into the standard SDP relaxation with block-diagonal structures. The convergence of the T-SDP relaxation to the optimal value of a given constrained POP is established under moderate assumptions as the relaxation level increases. Additionally, the feasibility and optimality of the T-SDP relaxation are discussed. Numerical results illustrate that the proposed T-SDP relaxation enhances numerical efficiency.

Suggested Citation

  • Hiroki Marumo & Sunyoung Kim & Makoto Yamashita, 2024. "T-semidefinite programming relaxation with third-order tensors for constrained polynomial optimization," Computational Optimization and Applications, Springer, vol. 89(1), pages 183-218, September.
    • Handle: RePEc:spr:coopap:v:89:y:2024:i:1:d:10.1007_s10589-024-00582-8
    DOI: 10.1007/s10589-024-00582-8
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    References listed on IDEAS

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    1. Meng-Meng Zheng & Zheng-Hai Huang & Yong Wang, 2021. "T-positive semidefiniteness of third-order symmetric tensors and T-semidefinite programming," Computational Optimization and Applications, Springer, vol. 78(1), pages 239-272, January.
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