Copositive Matrices with Ordered Off-Diagonal Entries
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917500164243456 |
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| author | Blekherman, Grigoriy Dey, Santanu S. Dunbar, Alex Kocuk, Burak |
| author_facet | Blekherman, Grigoriy Dey, Santanu S. Dunbar, Alex Kocuk, Burak |
| contents | We study copositive matrices which admit a decomposition into a sum of a positive semidefinite matrix and a matrix with nonnegative entries. Our main result shows that if the off-diagonal entries of a copositive matrix are nondecreasing in rows and in columns, then it admits such a decomposition. We apply this result to study optimization of quadratic forms over the standard simplex. As a corollary, we obtain that a natural relaxation of this problem is tight when the objective function is separable, resolving an open question of Dey and Kocuk. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_15970 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Copositive Matrices with Ordered Off-Diagonal Entries Blekherman, Grigoriy Dey, Santanu S. Dunbar, Alex Kocuk, Burak Optimization and Control 90C20, 90C22, 15B48 We study copositive matrices which admit a decomposition into a sum of a positive semidefinite matrix and a matrix with nonnegative entries. Our main result shows that if the off-diagonal entries of a copositive matrix are nondecreasing in rows and in columns, then it admits such a decomposition. We apply this result to study optimization of quadratic forms over the standard simplex. As a corollary, we obtain that a natural relaxation of this problem is tight when the objective function is separable, resolving an open question of Dey and Kocuk. |
| title | Copositive Matrices with Ordered Off-Diagonal Entries |
| topic | Optimization and Control 90C20, 90C22, 15B48 |
| url | https://arxiv.org/abs/2605.15970 |