Simple Cuts, Simple Landscape: Dimension-Free Rank Bounds for Burer-Monteiro Factorizations via Rank-Width

Hongjin Wu

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arXiv · 2610.40872

Simple Cuts, Simple Landscape: Dimension-Free Rank Bounds for Burer-Monteiro Factorizations via Rank-Width

Hongjin Wu

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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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Hongjin Wu. 2026-10-29. Simple Cuts, Simple Landscape: Dimension-Free Rank Bounds for Burer-Monteiro Factorizations via Rank-Width. https://arxiv.org/abs/2610.40872

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