T-semidefinite programming relaxation with third-order tensors for constrained polynomial optimization
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929343132860416 |
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| author | Marumo, Hiroki Kim, Sunyoung Yamashita, Makoto |
| author_facet | Marumo, Hiroki Kim, Sunyoung Yamashita, Makoto |
| contents | We study T-semidefinite programming (SDP) relaxation for constrained polynomial optimization problems (POPs). T-SDP relaxation for unconstrained POPs was introduced by Zheng, Huang and Hu in 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08438 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | T-semidefinite programming relaxation with third-order tensors for constrained polynomial optimization Marumo, Hiroki Kim, Sunyoung Yamashita, Makoto Optimization and Control 90C22, 90C25, 90C26 We study T-semidefinite programming (SDP) relaxation for constrained polynomial optimization problems (POPs). T-SDP relaxation for unconstrained POPs was introduced by Zheng, Huang and Hu in 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. |
| title | T-semidefinite programming relaxation with third-order tensors for constrained polynomial optimization |
| topic | Optimization and Control 90C22, 90C25, 90C26 |
| url | https://arxiv.org/abs/2402.08438 |