Local Convergence of Proximal Splitting Methods for Rank Constrained Problems

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.

To be presented at the 56th IEEE Conference on Decision and Control, Melbourne, Dec 2017

References in corpus (1)

• Forward-backward envelope for the sum of two nonconvex functions: Further properties and nonmonotone line-search algorithms

Cited by in corpus (2)

• Low-rank Optimization with Convex Constraints
• Efficient Proximal Mapping Computation for Unitarily Invariant Low-Rank Inducing Norms