{
  "abstract": "We give an example of a function satisfying a two-sided Polyak-Łojasiewicz condition but for which a gradient descent-ascent flow line fails to converge to the saddle point, circling around it instead. We can even impose the function to be strongly convex in one variable and to satisfy a PL condition in the other variable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2602.16517",
  "author_total": 1,
  "authors": [
    {
      "name": "Jean-Christophe Mourrat"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0sa0dv095m5kf.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "0sa0dv095m5kf",
  "issns": [],
  "landing_url": "https://hal.science/hal-05777135v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-oc"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05777135/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0sa0dv095m5kf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:47Z",
      "native_id": "hal-05777135",
      "source": "hal",
      "url": "https://hal.science/hal-05777135v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-oc",
      "subfield": "optimisation-control"
    }
  ],
  "title": "PL conditions do not guarantee convergence of gradient descent-ascent dynamics",
  "title_text": "PL conditions do not guarantee convergence of gradient descent-ascent dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:47Z",
  "url": "https://research.draconitic.com/paper/0sa0dv095m5kf",
  "venue": "HAL",
  "versions": []
}