arXiv:2610.40872v1 Announce Type: new Abstract: In this work, we study Burer-Monteiro factorizations of semidefinite programs with unit diagonal constraints. For a real symmetric cost matrix whose rank-width over $\mathbb{R}$ is at most $k$, we prove that every non-flat second-order stationary point of the factorized problem is globally optimal whenever the factorization rank is at least $2k$, independently of the matrix size.
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