{
  "abstract": "We study the optimization of convex objectives with $(L,κ-1)$-Hölder-continuous gradients in $\\ell_q$ over $R B_p^d$, $1<κ\\le 2$. (MG26) provides selectors with a movement bound for the problem of chasing high-dimensional convex nested sets for every $p<q$ and generally reduces Lipschitz convex optimization to bounds on the movement of selectors. We couple that movement with Hölder descent yielding a polynomial-runtime first-order method whose feasible output, in the high-dimensional regime $T\\le d$ and for $p<\\min\\{q,2\\}$, has error $$ \\widetilde O_{κ,p,q}\\!\\left( \\frac{LR^κ}{T^{κ(1+1/p-(1/q-1/2)_+)-1}} \\right), $$ after $T$ queries to a first-order oracle, solving the COLT 2015 open problem of (Guz15), up to logarithmic factors. At $(p,q)=(1,2)$, the rate is $\\widetilde{O}(LR^κ/T^{2κ-1})$, including $\\widetilde{O}(LR^2/T^{3})$ cubic decay in the smooth case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21880",
  "author_total": 4,
  "authors": [
    {
      "name": "David Martínez-Rubio"
    },
    {
      "name": "Brian Bullins"
    },
    {
      "name": "Cristóbal Guzmán"
    },
    {
      "name": "Mathieu Molina"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0fyvmhjatdea8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21880",
  "fulltext_url": null,
  "id": "0fyvmhjatdea8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21880",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7213865625",
  "pdf_url": "https://arxiv.org/pdf/2609.21880",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0fyvmhjatdea8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21880",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21880"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Near-Optimal Acceleration for Smooth $\\ell_p$ / $\\ell_q$ Nondual Convex First-Order Oracle Optimization",
  "title_text": "Near-Optimal Acceleration for Smooth ℓ_p / ℓ_q Nondual Convex First-Order Oracle Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/0fyvmhjatdea8",
  "venue": "arXiv",
  "versions": []
}