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

Hiroki Marumo (), Sunyoung Kim () and Makoto Yamashita ()
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Hiroki Marumo: Tokyo Institute of Technology
Sunyoung Kim: Ewha W. University
Makoto Yamashita: Tokyo Institute of Technology

Computational Optimization and Applications, 2024, vol. 89, issue 1, No 6, 183-218

Abstract: 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.

Keywords: T-SDP relaxation; Constrained polynomial optimization; Third-order tensors; Convergence to the optimal value; Block-diagonal structured SDP relaxation; Numerical efficiency; 90C22; 90C25; 90C26 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-024-00582-8

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