Linear convergence of the Douglas–Rachford method for two closed sets

By Hung M. Phan. 2014

100 citations recorded by the source corpus.

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

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/530db9c58a198ce01e13500403ce5c3455d0761c

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In Computational Theory and Mathematics

1. Scott B. Lindstrom
2. Brailey Sims
3. Pontus Giselsson

In Geometry and Topology

1. Pontus Giselsson
2. Scott B. Lindstrom
3. Brailey Sims

In Numerical Analysis

1. Pontus Giselsson
2. Scott B. Lindstrom
3. Brailey Sims

Citations in the corpus

• Linear and strong convergence of algorithms involving averaged nonexpansive operators (2014, unknown): “Our next two results are essentially contained in [26], where even nonconvex settings were considered.”
• Tight global linear convergence rate bounds for Douglas–Rachford splitting (2015, background): “The works in [19, 20, 10, 4, 30] concern local linear convergence under different assumptions.”
• SURVEY: SIXTY YEARS OF DOUGLAS–RACHFORD (2018, background): “359 S. B. Lindstrom and B. Sims [28] Theorem 3.8 Affine reduction for generalized DR sequences (Dao and Phan, 2016 [67, Theorem 5.25]).”