{
  "abstract": "We consider the problem (P): ${\\min}_{x\\in \\mathbb{R}^n}\\, f(x)+g(x)$ under the Euclidean geometry, where $f$ is convex and $(M,ν)$-Hölder smooth on $\\mathbb{R}^n$, and $g$ is proper, closed and convex on $\\mathbb{R}^n$, admits a generalized linear minimization oracle (GLMO), and has bounded domain with diameter $D$. An first-order active-hull (AH) method has access to both the first-order oracle (FO) of $f$ and the GLMO of $g$, and outputs a point that lies in the convex hull of all the past GLMO returns. We propose a new first-order AH method for solving (P), which is based on our newly developed ``recentered homotopy smoothing framework''. We show that in the high-dimensional regime, this method achieves the optimal FO and GLMO complexties simultaneously for all $ν\\in[0,1]$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.10916",
  "author_total": 1,
  "authors": [
    {
      "name": "Renbo Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aqy56bfcxt2k9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.10916",
  "fulltext_url": null,
  "id": "aqy56bfcxt2k9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.10916",
  "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/2611.10916",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aqy56bfcxt2k9.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:34Z",
      "native_id": "2611.10916",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.10916"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "An Optimal First-Order Active-Hull Method for Convex Composite Hölder Smooth Optimization",
  "title_text": "An Optimal First-Order Active-Hull Method for Convex Composite Hölder Smooth Optimization",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:34Z",
  "url": "https://research.draconitic.com/paper/aqy56bfcxt2k9",
  "venue": "arXiv",
  "versions": []
}