The analytic criterion of strict copositivity for a 4th-order 3-dimensional tensor
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910695397785600 |
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| author | Sheng, Mingjun Song, Yisheng |
| author_facet | Sheng, Mingjun Song, Yisheng |
| contents | This paper focuses on the strict copositivity analysis of 4th-order 3-dimensional symmetric tensors. A necessary and sufficient condition is provided for the strict copositivity of a fourth-order symmetric tensor. Subsequently, building upon this conclusion, we discuss the strict copositivity of fourth-order three-dimensional symmetric tensors with its entries $\pm 1, 0$, and further build their necessary and sufficient conditions. Utilizing these theorems, we can effectively verify the strict copositivity of a general fourth-order three-dimensional symmetric tensors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07596 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The analytic criterion of strict copositivity for a 4th-order 3-dimensional tensor Sheng, Mingjun Song, Yisheng Optimization and Control This paper focuses on the strict copositivity analysis of 4th-order 3-dimensional symmetric tensors. A necessary and sufficient condition is provided for the strict copositivity of a fourth-order symmetric tensor. Subsequently, building upon this conclusion, we discuss the strict copositivity of fourth-order three-dimensional symmetric tensors with its entries $\pm 1, 0$, and further build their necessary and sufficient conditions. Utilizing these theorems, we can effectively verify the strict copositivity of a general fourth-order three-dimensional symmetric tensors. |
| title | The analytic criterion of strict copositivity for a 4th-order 3-dimensional tensor |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2411.07596 |