{
  "abstract": "We determine the optimal logarithmically homogeneous self-concordant barrier parameter for the three-dimensional power cone. Although several self-concordant barriers for this cone have been constructed, its optimal barrier parameter had remained unknown. For a power cone with exponent $c\\in(0,1)$, we prove that the optimal parameter is $\\frac{3}{1+\\min\\{c,1-c\\}}$. Except at $c=1/2$, this value is strictly smaller than the parameter $3-2\\min\\{c,1-c\\}$ of Chares' conjectured barrier. At $c=1/2$, the optimal parameter equals $2$, in agreement with the optimal barrier parameter of the second-order cone. The proof combines a sharp lower bound for arbitrary logarithmically homogeneous self-concordant barriers with an explicit barrier attaining the bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06404",
  "author_total": 3,
  "authors": [
    {
      "name": "Rui-Jin Zhang"
    },
    {
      "name": "Wenhao Fu"
    },
    {
      "name": "Yu-Hong Dai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1zecyhz4457fs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06404",
  "fulltext_url": null,
  "id": "1zecyhz4457fs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06404",
  "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/2611.06404",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1zecyhz4457fs.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06404",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06404"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "The optimal barrier parameter of the three-dimensional power cone",
  "title_text": "The optimal barrier parameter of the three-dimensional power cone",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/1zecyhz4457fs",
  "venue": "arXiv",
  "versions": []
}