On the local convergence of the Douglas-Rachford algorithm

2014/01/23 by Heinz H. Bauschke, Bauschke, H. H., Dominikus Noll +1 · 1 citation
Computer Science · Decision Sciences · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Optimization and Variational Analysis #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.1401.6188

openalex publication_date 2014/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the Douglas-Rachford algorithm to solve the feasibility problem for two closed sets A,B in ℝ^d. We prove its local convergence to a fixed point when A,B are finite unions of convex sets. We also show that for more general nonconvex sets the scheme may fail to converge and start to cycle, and may then even fail to solve the feasibility problem.

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