Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28414

Authors: Quan, Jan, Patrinos, Panagiotis

Institution: KU Leuven

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Fonds Wetenschappelijk Onderzoek

Award: Shedding Light on the Optimization of Machine Learning Models: A Novel Paradigm Based on Generalized Convexity.

OpenAlex ID: W7223145782

Cites: 8

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Related to: 10