Benign landscape for Burer-Monteiro factorizations of MaxCut-type semidefinite programs - Archive ouverte HAL
Preprints, Working Papers, ... Year : 2024

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

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 Z 2 -synchronization problems.
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hal-04797879 , version 1 (22-11-2024)

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Faniriana Rakoto Endor, Irène Waldspurger. Benign landscape for Burer-Monteiro factorizations of MaxCut-type semidefinite programs. 2024. ⟨hal-04797879⟩
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