{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28414",
  "author_total": 2,
  "authors": [
    {
      "name": "Jan Quan"
    },
    {
      "name": "Panagiotis Patrinos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9971er77sf8g4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28414",
  "fulltext_url": null,
  "id": "9971er77sf8g4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28414",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7223145782",
  "pdf_url": "https://arxiv.org/pdf/2610.28414",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9971er77sf8g4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28414",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28414"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Convex Feasibility Problem for Which Douglas-Rachford Converges Only Weakly",
  "title_text": "A Convex Feasibility Problem for Which Douglas-Rachford Converges Only Weakly",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/9971er77sf8g4",
  "venue": "arXiv",
  "versions": []
}