{
  "abstract": "In this paper, we study a penalty method for simple bilevel optimization in which the lower-level objective has a convex composite structure. Our approach is based on a vanishing-penalty reformulation, which gives rise to a sequence of penalized problems as the penalty parameter decreases. A key difficulty is that metric subregularity of the lower-level optimality mapping does not, in general, yield a uniform error bound for the penalized problems as the penalty parameter vanishes, preventing a direct application of standard proximal Newton theory. To address this difficulty, we first analyze a regularized proximal Newton step by exploiting the specific structure of simple bilevel problems, and establish the local estimates that underpin superlinear convergence. Building on this local analysis, we propose SiB-Newton, which incorporates the proximal Newton step into a globalization strategy. We establish convergence guarantees for SiB-Newton and show that, under suitable local conditions, Newton steps are eventually accepted and the iterates converge at a superlinear rate. Numerical experiments on synthetic examples verify the predicted local superlinear convergence rate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08297",
  "author_total": 4,
  "authors": [
    {
      "name": "Xiaoning Bai"
    },
    {
      "name": "Boris S. Mordukhovich"
    },
    {
      "name": "Shangzhi Zeng"
    },
    {
      "name": "Jin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8f53thyc8rh1w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08297",
  "fulltext_url": null,
  "id": "8f53thyc8rh1w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08297",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08297",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8f53thyc8rh1w.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08297",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08297"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Proximal Newton Framework with Local Superlinear Convergence for Simple Bilevel Optimization",
  "title_text": "A Proximal Newton Framework with Local Superlinear Convergence for Simple Bilevel Optimization",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:49Z",
  "url": "https://research.draconitic.com/paper/8f53thyc8rh1w",
  "venue": "arXiv",
  "versions": []
}