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arXiv · 2610.28414

A Convex Feasibility Problem for Which Douglas-Rachford Converges Only Weakly

Jan Quan·Panagiotis Patrinos
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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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Jan Quan, Panagiotis Patrinos. 2026-10-20. A Convex Feasibility Problem for Which Douglas-Rachford Converges Only Weakly. https://arxiv.org/abs/2610.28414

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