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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2507.12729 |
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| _version_ | 1866912488235204608 |
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| author | Dunbar, Alex Newman, Elizabeth |
| author_facet | Dunbar, Alex Newman, Elizabeth |
| contents | The $\star_M$-family of tensor-tensor products is a framework which generalizes many properties from linear algebra to third order tensors. Here, we investigate positive semidefiniteness and semidefinite programming under the $\star_M$-product. Critical to our investigation is a connection between the choice of matrix M in the $\star_M$-product and the representation theory of an underlying group action. Using this framework, third order tensors equipped with the $\star_M$-product are a natural setting for the study of invariant semidefinite programs. As applications of the M-SDP framework, we provide a characterization of certain nonnegative quadratic forms and solve low-rank tensor completion problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12729 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor-Tensor Products, Group Representations, and Semidefinite Programming Dunbar, Alex Newman, Elizabeth Optimization and Control Computer Vision and Pattern Recognition Numerical Analysis Representation Theory 90C22, 15A69, 65F99 The $\star_M$-family of tensor-tensor products is a framework which generalizes many properties from linear algebra to third order tensors. Here, we investigate positive semidefiniteness and semidefinite programming under the $\star_M$-product. Critical to our investigation is a connection between the choice of matrix M in the $\star_M$-product and the representation theory of an underlying group action. Using this framework, third order tensors equipped with the $\star_M$-product are a natural setting for the study of invariant semidefinite programs. As applications of the M-SDP framework, we provide a characterization of certain nonnegative quadratic forms and solve low-rank tensor completion problems. |
| title | Tensor-Tensor Products, Group Representations, and Semidefinite Programming |
| topic | Optimization and Control Computer Vision and Pattern Recognition Numerical Analysis Representation Theory 90C22, 15A69, 65F99 |
| url | https://arxiv.org/abs/2507.12729 |