{
  "abstract": "We propose a mixed-order primal--dual dynamical system with implicit Hessian damping and Tikhonov regularization for linearly constrained convex optimization, and derive a corresponding fast primal--dual algorithm. The proposed dynamical system couples a second-order primal equation with a first-order dual equation without requiring twice differentiability of the objective function. An energy analysis establishes $\\mathcal{O}(t^{-2})$ convergence rates for the augmented Lagrangian gap, feasibility violation, and objective residual along an extrapolated primal trajectory. For the proposed algorithm, we construct discrete energy estimates and establish the corresponding $\\mathcal{O}(k^{-2})$ rates at the extrapolated primal iterates. In particular, in the critical regularization regimes $ε(t)=a/t^2$ and $ε_k=a/k^2$, these accelerated rates hold simultaneously with strong convergence of the primal trajectory and primal iterates to the minimum-norm solution, respectively, under suitable parameter and trajectory conditions. Numerical experiments illustrate the convergence behavior of the proposed dynamical system and the corresponding algorithm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39144",
  "author_total": 4,
  "authors": [
    {
      "name": "Hong-lu Li"
    },
    {
      "name": "Yi-bin Xiao"
    },
    {
      "name": "Xin He"
    },
    {
      "name": "Kequan Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4bfn7hjdqyx91.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39144",
  "fulltext_url": null,
  "id": "4bfn7hjdqyx91",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39144",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39144",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4bfn7hjdqyx91.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39144",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39144"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Convergence rates of mixed primal-dual dynamical systems with implicit Hessian damping and Tikhonov regularization",
  "title_text": "Convergence rates of mixed primal-dual dynamical systems with implicit Hessian damping and Tikhonov regularization",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/4bfn7hjdqyx91",
  "venue": "arXiv",
  "versions": []
}