{
  "abstract": "This paper considers a class of structured cardinality penalized optimization problems with nonsmooth convex loss functions, for which the proximal mapping associated with the structured $\\ell_0$ penalty is generally unavailable. To overcome this difficulty, we develop a chain of exact reformulations based on variable splitting, exact penalization, and continuous relaxation, and establish rigorous equivalence relationships among these resulting models. In particular, we define a class of strong local minimizers for the original problem and show that these minimizers are equivalent to weak $d$-stationary points of the relaxation problem. Further, we propose a safeguarded accelerated proximal alternating direction method of multipliers (SAP-ADMM). We prove that the sequence generated by SAP-ADMM converges to a weak $d$-stationary point of the relaxation problem. Depending on the parameter settings and algorithmic regime, we establish $O(1/k)$ or $o(1/k)$ convergence rates for both the objective function value gap and the KKT residual. Numerical experiments on signal and image denoising demonstrate the effectiveness of both the proposed models and SAP-ADMM in terms of reconstruction quality and computational efficiency.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14559",
  "author_total": 3,
  "authors": [
    {
      "name": "Wei Bian"
    },
    {
      "name": "Hongyuan Tao"
    },
    {
      "name": "Fan Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aaf3tv01rvj5z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14559",
  "fulltext_url": null,
  "id": "aaf3tv01rvj5z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14559",
  "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",
      "2206|Sparse and Compressive Sensing Techniques"
    ]
  ],
  "openalex": "W7221820415",
  "pdf_url": "https://arxiv.org/pdf/2610.14559",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aaf3tv01rvj5z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14559",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14559"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Safeguarded Accelerated Proximal ADMM Algorithm for Solving Structured Cardinality Penalized Optimization Problems",
  "title_text": "A Safeguarded Accelerated Proximal ADMM Algorithm for Solving Structured Cardinality Penalized Optimization Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/aaf3tv01rvj5z",
  "venue": "arXiv",
  "versions": []
}