{
  "abstract": "This paper introduces a novel second-order dynamical system driven by a forward-backward splitting operator for solving the structured inclusion $0\\in(A+B)(x)$ in a real Hilbert space, where $A$ is a maximal $ρ$-comonotone operator and $B$ is a $ν$-cocoercive operator. The well-posedness of the system is established, and Lyapunov analysis yields accelerated convergence rates of order $o(\\frac{1}{t})$ for the velocity and $o(\\frac{1}{t^2})$ for the forward-backward residual, together with weak convergence of the trajectories to $\\operatorname{zer}(A+B)$. Temporal discretization further leads to a class of double inertial Halpern forward-backward splitting algorithms that encompasses the classical forward-backward splitting method and its inertial variants as special cases. Numerical experiments on split feasibility, sparse signal recovery, and image deblurring illustrate the effectiveness of the proposed algorithm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02479",
  "author_total": 2,
  "authors": [
    {
      "name": "Yan Tang"
    },
    {
      "name": "Jun Dong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5kate0mmzc6wv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02479",
  "fulltext_url": null,
  "id": "5kate0mmzc6wv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02479",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7207717770",
  "pdf_url": "https://arxiv.org/pdf/2609.02479",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5kate0mmzc6wv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02479",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02479"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Accelerated Convergence of a Second-Order Dynamical System and its Application to Splitting Algorithms for Comonotone Inclusions",
  "title_text": "Accelerated Convergence of a Second-Order Dynamical System and its Application to Splitting Algorithms for Comonotone Inclusions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/5kate0mmzc6wv",
  "venue": "arXiv",
  "versions": []
}