Low-Rank Mirror-Prox for Nonsmooth and Low-Rank Matrix Optimization Problems. (arXiv:2206.11523v1 [math.OC])

Web: http://arxiv.org/abs/2206.11523

Low-rank and nonsmooth matrix optimization problems capture many fundamental
tasks in statistics and machine learning. While significant progress has been
made in recent years in developing efficient methods for \textit{smooth}
low-rank optimization problems that avoid maintaining high-rank matrices and
computing expensive high-rank SVDs, advances for nonsmooth problems have been
slow paced. In this paper we consider standard convex relaxations for such
problems. Mainly, we prove that under a \textit{strict complementarity}
condition and under the relatively mild assumption that the nonsmooth …

arxiv math optimization