{
  "abstract": "The Chambolle-Pock method, also known as the primal-dual hybrid gradient method, is a standard first-order algorithm for convex-concave saddle-point problems and composite convex optimization. We establish weak sequential convergence of its primal-dual iterates in real Hilbert spaces for every $0<\\theta\\leq 1/2$ whenever $\\tau\\sigma\\|L\\|^{2}<4\\theta(2-\\theta)/(1-2\\theta+9\\theta^{2}-4\\theta^{3})$. This extends the weak-convergence theory to a previously unexplored range of extrapolation parameters.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2604.06423",
  "author_total": 1,
  "authors": [
    {
      "name": "Manu Upadhyaya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8ekreb3ttgsw8.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "8ekreb3ttgsw8",
  "issns": [],
  "landing_url": "https://hal.science/hal-05858429v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-oc"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05858429/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8ekreb3ttgsw8.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T12:20:54Z",
      "native_id": "hal-05858429",
      "source": "hal",
      "url": "https://hal.science/hal-05858429v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-oc",
      "subfield": "optimisation-control"
    }
  ],
  "title": "The Chambolle-Pock method converges weakly with $0 < \\theta \\le 1/2$ and $\\tau\\sigma\\|L\\|^{2} < 4\\theta(2-\\theta)/(1 - 2\\theta + 9\\theta^{2} - 4\\theta^{3})$",
  "title_text": "The Chambolle-Pock method converges weakly with 0 < θ ≤ 1/2 and τσ|L|^2 < 4θ(2−θ)/(1 − 2θ + 9θ^2 − 4θ^3)",
  "type": "preprint",
  "updated_at": "2026-11-10T12:20:54Z",
  "url": "https://research.draconitic.com/paper/8ekreb3ttgsw8",
  "venue": "HAL",
  "versions": []
}