Local Convergence of Proximal Splitting Methods for Rank Constrained Problems
Optimization and Control
2018-11-12 v1 Machine Learning
Machine Learning
Abstract
We analyze the local convergence of proximal splitting algorithms to solve optimization problems that are convex besides a rank constraint. For this, we show conditions under which the proximal operator of a function involving the rank constraint is locally identical to the proximal operator of its convex envelope, hence implying local convergence. The conditions imply that the non-convex algorithms locally converge to a solution whenever a convex relaxation involving the convex envelope can be expected to solve the non-convex problem.
Cite
@article{arxiv.1710.04248,
title = {Local Convergence of Proximal Splitting Methods for Rank Constrained Problems},
author = {Christian Grussler and Pontus Giselsson},
journal= {arXiv preprint arXiv:1710.04248},
year = {2018}
}
Comments
To be presented at the 56th IEEE Conference on Decision and Control, Melbourne, Dec 2017