{
  "abstract": "Let $Q \\subseteq \\mathbb{R}^n$ be a open, convex, and symmetric set and let $f:Q \\rightarrow \\mathbb{R}$ be a $\\vartheta$-self-concordant barrier function, that is also symmetric. We show the associated spectral function $F(X)= \\mathcal{O}^2 (f \\circ λ)(X)$ is a $\\mathcal{O}^2\\vartheta$-self-concordant function, where $\\mathcal{O} = 8\\max\\{1+3\\vartheta, 12\\}$, on the domain of all $n \\times n$ symmetric matrices $X$, with eigenvalues $λ(X) \\in Q$. This generalizes the relationship between the standard logarithmic barriers $-\\sum_{i=1}^n\\log x_i$ and $-\\log \\det X$ and gives a solution to a conjecture by L.~Tunçel, 1995.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17442",
  "author_total": 2,
  "authors": [
    {
      "name": "Javier Peña"
    },
    {
      "name": "Hristo Sendov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4mdzy906kwm3q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17442",
  "fulltext_url": null,
  "id": "4mdzy906kwm3q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17442",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "2612|Advanced Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7221766333",
  "pdf_url": "https://arxiv.org/pdf/2610.17442",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4mdzy906kwm3q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17442",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17442"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Spectral Self-Concordant Barriers: A Proof of a Conjecture by Tunçel",
  "title_text": "Spectral Self-Concordant Barriers: A Proof of a Conjecture by Tunçel",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/4mdzy906kwm3q",
  "venue": "arXiv",
  "versions": []
}