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The optimal barrier parameter of the three-dimensional power cone — arXiv:2611.06404

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.06404
License (as archived): CC0-1.0
Archived: 2026-11-05T18:27:27.905Z
SHA-256 of the archived text: 4e1e0fcc5926173508333231400fb909dfd8955af409cef37b5144406ff179e3
Stable URL of this page: https://metraipolis.com/documento/dc_65b50a159cee

How to cite

The optimal barrier parameter of the three-dimensional power cone — arXiv:2611.06404 — arXiv (en), https://arxiv.org/abs/2611.06404 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_65b50a159cee (Metraipolis archive dc_65b50a159cee, sha256 4e1e0fcc5926173508333231400fb909dfd8955af409cef37b5144406ff179e3)

BibTeX

@misc{dc65b50a159cee,
  title = {The optimal barrier parameter of the three-dimensional power cone — arXiv:2611.06404},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.06404},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_65b50a159cee; sha256 4e1e0fcc5926173508333231400fb909dfd8955af409cef37b5144406ff179e3},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.06404. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.OC, nuovi lavori del giorno).
Categorie arXiv: Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2611.06404 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-05T18:17:34.245Z dalla pagina https://arxiv.org/list/math.OC/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).