@article{c6382ea6a696404ebf61cdb972e75324,
title = "Universal barrier is n-self-concordant",
abstract = "This paper shows that the self-concordance parameter of the universal barrier on any n-dimensional proper convex domain is upper bounded by n. This bound is tight and improves the previous O(n) bound by Nesterov and Nemirovski. The key to our main result is a pair of new, sharp moment inequalities for s-concave distributions, which could be of independent interest.",
keywords = "Convex body, Interior-point methods, Moment inequalities, S-concave distributions, Self-concordance, Universal barrier",
author = "Lee, {Yin Tat} and Yue, {Man Chung}",
note = "Funding Information: Funding: This work was supported by the National Science Foundation Division of Computing and Communication Foundations [Grants 1740551 and 1749609], Division of Mathematical Sci-ences [Grant 1839116], and the Engineering and Physical Sciences Research Council [Grant EP/ M027856/1]. Y. T. Lee is supported by the National Science Foundation [Awards CCF-1749609, DMS-1839116, and DMS-2023166], Microsoft Research Faculty Fellowship, Sloan Research Fel-lowship, and Packard Fellowships. M.-C. Yue is supported by Hong Kong Research Grants Council [Grant 25302420]. Funding Information: Funding: This work was supported by the National Science Foundation Division of Computing and Communication Foundations [Grants 1740551 and 1749609], Division of Mathematical Sciences [Grant 1839116], and the Engineering and Physical Sciences Research Council [Grant EP/ M027856/1]. Y. T. Lee is supported by the National Science Foundation [Awards CCF-1749609, DMS-1839116, and DMS-2023166], Microsoft Research Faculty Fellowship, Sloan Research Fellowship, and Packard Fellowships. M.-C. Yue is supported by Hong Kong Research Grants Council [Grant 25302420]. Publisher Copyright: {\textcopyright} 2021 INFORMS.",
year = "2021",
month = aug,
doi = "10.1287/MOOR.2020.1113",
language = "English",
volume = "46",
pages = "1129--1148",
journal = "Mathematics of Operations Research",
issn = "0364-765X",
publisher = "INFORMS Institute for Operations Research and the Management Sciences",
number = "3",
}