Benign landscape for Burer-Monteiro factorizations of MaxCut-type semidefinite programs
Optimization and Control
2025-03-27 v2 Computational Complexity
Machine Learning
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 -synchronization problems and the Kuramoto model.
Cite
@article{arxiv.2411.03103,
title = {Benign landscape for Burer-Monteiro factorizations of MaxCut-type semidefinite programs},
author = {Faniriana Rakoto Endor and Irène Waldspurger},
journal= {arXiv preprint arXiv:2411.03103},
year = {2025}
}