Exploiting Sparsity in Complex Polynomial Optimization
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866916707974512640 |
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| author | Wang, Jie Magron, Victor |
| author_facet | Wang, Jie Magron, Victor |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_12444 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Exploiting Sparsity in Complex Polynomial Optimization Wang, Jie Magron, Victor Optimization and Control 90C23, 14P10, 90C22, 90C26, 12D15 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. |
| title | Exploiting Sparsity in Complex Polynomial Optimization |
| topic | Optimization and Control 90C23, 14P10, 90C22, 90C26, 12D15 |
| url | https://arxiv.org/abs/2103.12444 |