PreprintCC BY-NC-ND 4.0arXiv
A Convex Feasibility Problem for Which Douglas-Rachford Converges Only Weakly
Abstract
We provide two closed, convex sets with nonempty intersection and an initial point for which the Douglas-Rachford algorithm converges weakly but not strongly. This resolves an open question as noted earlier by Aragón Artacho, Borwein and Tam (2014, Remark 2.2). Our construction is a simple lift of a recent construction by Bauschke and Tung concerning firmly nonexpansive operators.
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BibTeX
@misc{quan2026convex,
title = {{A Convex Feasibility Problem for Which Douglas-Rachford Converges Only Weakly}},
author = {Jan Quan and Panagiotis Patrinos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28414},
eprint = {2610.28414},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28414},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A Convex Feasibility Problem for Which Douglas-Rachford Converges Only Weakly
AU - Jan Quan
AU - Panagiotis Patrinos
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28414
UR - https://arxiv.org/abs/2610.28414
AB - We provide two closed, convex sets with nonempty intersection and an initial point for which the Douglas-Rachford algorithm converges weakly but not strongly. This resolves an open question as noted earlier by Aragón Artacho, Borwein and Tam (2014, Remark 2.2). Our construction is a simple lift of a recent construction by Bauschke and Tung concerning firmly nonexpansive operators.
ER -