{
  "abstract": "We propose a regularized proximal quasi-Newton method (RPQN) for minimizing the sum of a continuously differentiable, possibly nonconvex function and a proper, lower semicontinuous, prox-bounded, possibly nonconvex regularizer. The method uses adaptive quadratic regularization and limited-memory quasi-Newton models. We establish global convergence under weak assumptions, without requiring global Lipschitz continuity of the gradient, and prove convergence of the entire sequence, with rates, under the Kurdyka-Lojasiewicz property. To solve the proximal subproblems efficiently, we exploit compact limited-memory representations and derive a compact representation of the Kleinmichel rank-one update, which preserves positive definiteness under the same condition as BFGS. Numerical experiments on logistic and Student's regression demonstrate competitive performance and the effectiveness of the proposed approach.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.11627",
  "author_total": 3,
  "authors": [
    {
      "name": "Simeon vom Dahl"
    },
    {
      "name": "Alberto De Marchi"
    },
    {
      "name": "Christian Kanzow"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1rdtkf54x5wbz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.11627",
  "fulltext_url": null,
  "id": "1rdtkf54x5wbz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.11627",
  "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": "W7161041088",
  "pdf_url": "https://arxiv.org/pdf/2605.11627",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1rdtkf54x5wbz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2605.11627",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.11627"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Proximal Limited-Memory Quasi-Newton Methods for Nonsmooth Nonconvex Optimization",
  "title_text": "Proximal Limited-Memory Quasi-Newton Methods for Nonsmooth Nonconvex Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/1rdtkf54x5wbz",
  "venue": "arXiv",
  "versions": []
}