{
  "abstract": "We develop and analyze multilevel gradient-regularized Newton methods for unconstrained convex optimization with Lipschitz-continuous Hessians. By computing Newton corrections in lower-dimensional subspaces, the proposed methods aim to reduce computational costs while preserving the global $\\mathcal{O}\\left(k^{-2}\\right)$ convergence rate in function values of the full-space method. To establish this rate for multilevel methods, we introduce a class of row-nested restriction operators that ensures monotonicity of the reduced-gradient norms across levels. Numerical experiments with row-nested operators demonstrate convergence behavior comparable to full-space gradient-regularized Newton, while offering substantial computational savings on large-scale instances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35195",
  "author_total": 2,
  "authors": [
    {
      "name": "Nick Tsipinakis"
    },
    {
      "name": "Matthias Voigt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3a1djze2y1k66.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35195",
  "fulltext_url": null,
  "id": "3a1djze2y1k66",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35195",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2612|Advanced Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7223875656",
  "pdf_url": "https://arxiv.org/pdf/2610.35195",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3a1djze2y1k66.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35195",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35195"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Global $\\mathcal{O}\\left(k^{-2}\\right)$ Convergence of Multilevel Gradient-Regularized Newton Methods",
  "title_text": "Global 𝒪(k^−2) Convergence of Multilevel Gradient-Regularized Newton Methods",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:46Z",
  "url": "https://research.draconitic.com/paper/3a1djze2y1k66",
  "venue": "arXiv",
  "versions": []
}