arXiv:1401.6509 Abstract | arXiv Analytics

arXiv:1401.6509 [math.OC]Abstract References Reviews Resources

Linear Convergence of the Douglas-Rachford Method for Two Closed Sets

Published 2014-01-25, updated 2014-10-01Version 2

In this paper, we investigate the Douglas-Rachford method for two closed (possibly nonconvex) sets in Euclidean spaces. We show that under certain regularity conditions, the Douglas-Rachford method converges locally with R-linear rate. In convex settings, we prove that the linear convergence is global. Our study recovers recent results on the same topic.

Categories: math.OC, math.NA

Subjects: 49M27, 65K10, 47H09, 49J52, 49M20, 49M37, 65K05, 90C26, 90C30

Keywords: linear convergence, closed sets, set regularity conditions, restricted constraint qualification condition, convex settings

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