{
  "abstract": "In a real Hilbert space, we study a bilevel optimization problem that consists in minimizing an outer convex function over the zero set of a maximally monotone operator. In the smooth setting, where the outer objective is convex and Fréchet differentiable and the inner operator is single-valued, continuous and monotone, we associate with the problem a first-order dynamical system that can be viewed as a monotone flow applied to a dynamically regularized operator. Under a suitable Attouch-Czarnecki-type condition for the inner level, we establish last-iterate convergence rates for both the outer and inner residuals, together with weak convergence of the trajectories to optimal solutions of the bilevel problem. In the smooth+nonsmooth setting, we enrich the outer objective with a proper, convex, and lower semicontinuous function, while the inner operator is augmented by the subdifferential of a function with the same properties. We propose a regularized proximal-extragradient algorithm in which both the forward and backward steps are performed with respect to dynamically regularized operators and functions, respectively. Under an analogous Attouch-Czarnecki-type condition formulated for the smooth+nonsmooth case, we establish last-iterate convergence rates for both the outer and inner residuals, together with weak convergence of the iterates to optimal solutions of the bilevel problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29181",
  "author_total": 3,
  "authors": [
    {
      "name": "Radu Ioan Bot"
    },
    {
      "name": "Enis Chenchene"
    },
    {
      "name": "David Alexander Hulett"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/96430kdvrdnag.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29181",
  "fulltext_url": null,
  "id": "96430kdvrdnag",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29181",
  "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": "W7204874106",
  "pdf_url": "https://arxiv.org/pdf/2608.29181",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/96430kdvrdnag.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2608.29181",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29181"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Regularized extragradient method for structured bilevel optimization in continuous and discrete time",
  "title_text": "Regularized extragradient method for structured bilevel optimization in continuous and discrete time",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/96430kdvrdnag",
  "venue": "arXiv",
  "versions": []
}