Local Convergence of Proximal Splitting Methods for Rank Constrained Problems

Code

• github.com/LowRankOpt/LRINorm
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• github.com/LowRankOpt/LRIPy
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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.

Reproductions