Local Convergence of Proximal Splitting Methods for Rank Constrained Problems

Pontus Giselsson, Christian Grussler

Publication date: 11 October 2017

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.

Has companion code repository: https://github.com/LowRankOpt/LRIPy

Mathematics Subject Classification ID

Large-scale problems in mathematical programming (90C06) Nonconvex programming, global optimization (90C26) Nonlinear programming (90C30) Approximation methods and heuristics in mathematical programming (90C59)

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