{
  "abstract": "We consider a network of finitely many agents aiming to cooperatively solve a convex-concave min-max problem combining nonsmooth terms with a smooth saddle function whose partial gradients are only locally Lipschitz continuous. Without requiring prior knowledge of the local Lipschitz moduli of the partial gradients, we propose a distributed proximal-reflected-gradient algorithm which incorporates a distributed backtracking procedure to adjust the stepsizes at each iteration. The algorithm is derived by reformulating the min-max problem as a composite monotone inclusion involving the sum of a maximally monotone operator, a linearly composed maximally monotone operator, and a single-valued locally Lipschitz continuous monotone operator. To solve this inclusion, we introduce a novel primal-dual forward-reflected splitting method with linesearch and establish its convergence using a Lyapunov-based analysis. In addition, when specialised to the min-max formulation, we derive an $\\mathcal{O}(1/N)$ ergodic convergence rate for a consensus-penalised gap function. Finally, applying this splitting framework with mixing matrices yields our distributed method for consensus min-max optimisation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23518",
  "author_total": 4,
  "authors": [
    {
      "name": "Felipe Atenas"
    },
    {
      "name": "Minh N. Dao"
    },
    {
      "name": "Matthew K. Tam"
    },
    {
      "name": "David Torregrosa-Belén"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b25gkg8qbx2cf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23518",
  "fulltext_url": null,
  "id": "b25gkg8qbx2cf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23518",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1705|Distributed Control Multi-Agent Systems"
    ]
  ],
  "openalex": "W7222961338",
  "pdf_url": "https://arxiv.org/pdf/2610.23518",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b25gkg8qbx2cf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23518",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23518"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Primal-dual forward-reflected splitting with linesearch for distributed min-max problems under local Lipschitz smoothness",
  "title_text": "Primal-dual forward-reflected splitting with linesearch for distributed min-max problems under local Lipschitz smoothness",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/b25gkg8qbx2cf",
  "venue": "arXiv",
  "versions": []
}