Work

Benign landscape for Burer-Monteiro factorizations of MaxCut-type semidefinite programs

Year: 2024

Type: preprint

Abstract: We consider MaxCut-type semidefinite programs (SDP) which admit a low rank solution. To numerically leverage the low rank hypothesis, a standard algorithmic approach is the Burer-Monteiro factorization, which allows to significantly reduce the dimensionality of the problem at the cost of its convexity. We give a sharp condition on the conditioning of the Laplacian matrix associated with the SDP under which any second-order critical point of the non-convex problem is a global minimizer. By applying our theorem, we improve on recent results about the correctness of the Burer-Monteiro approach on $\mathbb{Z}_2$-synchronization problems and the Kuramoto model.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2411.03103

Authors: Endor, Faniriana Rakoto, Waldspurger, Irène

Institutions: Centre National de la Recherche Scientifique, Centre de Recherche en Mathématiques de la Décision, Université Paris Dauphine-PSL

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Award: PaRis Artificial Intelligence Research InstitutE

OpenAlex ID: W4404395899

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