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arXiv · 1903.00184

Proximal algorithms for constrained composite optimization, with applications to solving low-rank SDPs

Yu Bai·John Duchi·Song Mei
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Abstract

We study a family of (potentially non-convex) constrained optimization problems with convex composite structure. Through a novel analysis of non-smooth geometry, we show that proximal-type algorithms applied to exact penalty formulations of such problems exhibit local linear convergence under a quadratic growth condition, which the compositional structure we consider ensures. The main application of our results is to low-rank semidefinite optimization with Burer-Monteiro factorizations. We precisely identify the conditions for quadratic growth in the factorized problem via structures in the semidefinite problem, which could be of independent interest for understanding matrix factorization.

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Yu Bai, John Duchi, Song Mei. 2019-03-01. Proximal algorithms for constrained composite optimization, with applications to solving low-rank SDPs. https://arxiv.org/abs/1903.00184

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