On the convergence rate of the Douglas-Rachford splitting algorithm

Fuente: arXiv
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Main Authors: Abbaszadehpeivasti, Hadi, Zamani, Moslem
Format: Preprint
Published: 2025
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author Abbaszadehpeivasti, Hadi
Zamani, Moslem
author_facet Abbaszadehpeivasti, Hadi
Zamani, Moslem
contents This work is concerned with the convergence rate analysis of the Douglas-Rachford splitting (DRS) method for finding a zero of the sum of two maximally monotone operators. We obtain an exact rate of convergence for the DRS algorithm and demonstrate its sharpness in the setting of convex feasibility problems. Furthermore, we investigate the linear convergence of the DRS algorithm, providing both necessary and sufficient conditions that characterize this behavior. We further examine the performance of the DRS method when applied to convex composite optimization problems. The paper concludes with several conjectures on the convergence behavior of the DRS algorithm for this class of problems.
format Preprint
id arxiv_https___arxiv_org_abs_2509_06676
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On the convergence rate of the Douglas-Rachford splitting algorithm
Abbaszadehpeivasti, Hadi
Zamani, Moslem
Optimization and Control
This work is concerned with the convergence rate analysis of the Douglas-Rachford splitting (DRS) method for finding a zero of the sum of two maximally monotone operators. We obtain an exact rate of convergence for the DRS algorithm and demonstrate its sharpness in the setting of convex feasibility problems. Furthermore, we investigate the linear convergence of the DRS algorithm, providing both necessary and sufficient conditions that characterize this behavior. We further examine the performance of the DRS method when applied to convex composite optimization problems. The paper concludes with several conjectures on the convergence behavior of the DRS algorithm for this class of problems.
title On the convergence rate of the Douglas-Rachford splitting algorithm
topic Optimization and Control
url https://arxiv.org/abs/2509.06676