{
  "abstract": "This work considers stepsize schedules for gradient descent on smooth strongly convex objectives. We develop a curvature-dependent concatenation framework for constructing stepsize schedules of arbitrary length with sharp worst-case guarantees. Within this framework, we introduce two families of schedules for the function-value gap and gradient norm of the last iterate, respectively. For each fixed condition number $κ=L/μ>1$, both families attain iteration complexity $Θ(κ^ρ\\log(1/ε))$ for sufficiently small $ε$, where $ρ=\\log_{\\sqrt2+1}2\\approx0.7864$. This complexity is optimal up to a subpolynomial factor in $κ$ among predetermined nonnegative stepsize schedules. The framework also recovers the strongly convex silver schedule at power-of-two iteration budgets and applies to smooth convex and smooth weakly convex functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05242",
  "author_total": 2,
  "authors": [
    {
      "name": "Zehao Zhang"
    },
    {
      "name": "Rujun Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1mgj1kz7kcew7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05242",
  "fulltext_url": null,
  "id": "1mgj1kz7kcew7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05242",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05242",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1mgj1kz7kcew7.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.05242",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05242"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Accelerated Concatenation of Stepsize Schedules for Smooth Strongly Convex Gradient Descent",
  "title_text": "Accelerated Concatenation of Stepsize Schedules for Smooth Strongly Convex Gradient Descent",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/1mgj1kz7kcew7",
  "venue": "arXiv",
  "versions": []
}