Copositive Matrices with Ordered Off-Diagonal Entries
最优化与控制
2026-05-18 v1
摘要
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.
引用
@article{arxiv.2605.15970,
title = {Copositive Matrices with Ordered Off-Diagonal Entries},
author = {Grigoriy Blekherman and Santanu S. Dey and Alex Dunbar and Burak Kocuk},
journal= {arXiv preprint arXiv:2605.15970},
year = {2026}
}
备注
17 pages, 2 Figures