{
  "abstract": "We disprove a conjecture of Davis, Drusvyatskiy, and Jiang (2026) that subdifferential regularity can be removed from the generic guarantee of convergence to local minimizers for stochastic subgradient methods. We construct a globally Lipschitz, coercive, semialgebraic function in two dimensions for which the method converges to a nonminimizing Clarke critical point. For suitable power-law stepsizes, this convergence holds for open sets of initial points and linear tilts of the objective, uniformly over all perturbation sequences within a prescribed bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11298",
  "author_total": 1,
  "authors": [
    {
      "name": "Jiajin Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3sw937h9b8bmd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11298",
  "fulltext_url": null,
  "id": "3sw937h9b8bmd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11298",
  "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",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7221070289",
  "pdf_url": "https://arxiv.org/pdf/2610.11298",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3sw937h9b8bmd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11298",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11298"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Nonminimizing Attractors of Stochastic Subgradient Methods on Semialgebraic Functions",
  "title_text": "Nonminimizing Attractors of Stochastic Subgradient Methods on Semialgebraic Functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/3sw937h9b8bmd",
  "venue": "arXiv",
  "versions": []
}