Linear Convergence of the Douglas-Rachford Method for Two Closed Sets
arXiv:1401.65092.4100 citationsh-index: 20
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Provides theoretical convergence guarantees for the Douglas-Rachford method in nonconvex settings, benefiting optimization researchers.
The paper proves local R-linear convergence of the Douglas-Rachford method for two closed (possibly nonconvex) sets under regularity conditions, and global linear convergence in convex settings, recovering recent results.
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.