Locally Optimal Eigenvectors of Regular Simplex Tensors
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917592255430656 |
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| author | Wang, Lei |
| author_facet | Wang, Lei |
| contents | Identifying locally optimal solutions is an important issue given an optimization model. In this paper, we focus on a special class of symmetric tensors termed regular simplex tensors, which is a newly-emerging concept, and investigate its local optimality of the related constrained nonconvex optimization model. This is proceeded by checking the first-order and second-order necessary condition sequentially. Some interesting directions concerning the regular simplex tensors, including the robust eigenpairs checking and other potential issues, are discussed in the end for future work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_00274 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Locally Optimal Eigenvectors of Regular Simplex Tensors Wang, Lei Optimization and Control Statistics Theory 15A69, 90C26 Identifying locally optimal solutions is an important issue given an optimization model. In this paper, we focus on a special class of symmetric tensors termed regular simplex tensors, which is a newly-emerging concept, and investigate its local optimality of the related constrained nonconvex optimization model. This is proceeded by checking the first-order and second-order necessary condition sequentially. Some interesting directions concerning the regular simplex tensors, including the robust eigenpairs checking and other potential issues, are discussed in the end for future work. |
| title | Locally Optimal Eigenvectors of Regular Simplex Tensors |
| topic | Optimization and Control Statistics Theory 15A69, 90C26 |
| url | https://arxiv.org/abs/2303.00274 |