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arXiv · 2605.15970

Copositive Matrices with Ordered Off-Diagonal Entries

Grigoriy Blekherman·Santanu S. Dey·Alex Dunbar·Burak Kocuk
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Abstract

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.

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Grigoriy Blekherman, Santanu S. Dey, Alex Dunbar, Burak Kocuk. 2026-05-15. Copositive Matrices with Ordered Off-Diagonal Entries. https://arxiv.org/abs/2605.15970

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