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arXiv · 1710.04248

Local Convergence of Proximal Splitting Methods for Rank Constrained Problems

Christian Grussler·Pontus Giselsson
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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.

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Christian Grussler, Pontus Giselsson. 2017-10-11. Local Convergence of Proximal Splitting Methods for Rank Constrained Problems. https://doi.org/10.1109/cdc.2017.8263743

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