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

2014/01/25 by Hung M. Phan, Phan, Hung M. · 2 citations
Computer Science · Mathematics · #49J52 #49M20 #49M37 #65K05 #65K10 #90C26 #90C30 #Advanced Optimization Algorithms Research #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Optimization and Control (math.OC) #Optimization and Variational Analysis #Primary 49M27 #Secondary 47H09

paper · pdf · doi:10.48550/arxiv.1401.6509

openalex publication_date 2014/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Splitting Algorithms for the Sum of Two Nonlinear Operators
• Monotone Operators and the Proximal Point Algorithm

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