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

arXiv: https://arxiv.org/abs/1401.6509 · HTML: https://mlsanity.com/paper/1401.6509/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jan 2014.

## Built on by (most cited first, 1 of 1)

- [Provable Phase Retrieval with Mirror Descent](https://mlsanity.com/paper/2210.09248/) (2022)

## Abstract (arXiv)

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.