{
  "abstract": "We construct a coercive, locally Lipschitz, semialgebraic function on $\\mathbb R^2$ for which BFGS with Armijo--Wolfe line search converges to a non-Clarke-stationary point from a nonempty open set of initial points and inverse-Hessian estimates. This disproves the almost-sure stationarity assertion in the 2013 challenge of Lewis and Overton. The construction and proof combine analytical arguments with computer-assisted verification of explicit inequalities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34087",
  "author_total": 1,
  "authors": [
    {
      "name": "Lexiao Lai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dd1zah1x7ww0x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34087",
  "fulltext_url": null,
  "id": "dd1zah1x7ww0x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34087",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7223959273",
  "pdf_url": "https://arxiv.org/pdf/2610.34087",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dd1zah1x7ww0x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34087",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34087"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "BFGS can converge to non-Clarke-stationary points with positive probability",
  "title_text": "BFGS can converge to non-Clarke-stationary points with positive probability",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:28Z",
  "url": "https://research.draconitic.com/paper/dd1zah1x7ww0x",
  "venue": "arXiv",
  "versions": []
}