Universal Barrier Is n-Self-Concordant
成果类型：
Article
署名作者：
Lee, Yin Tat; Yue, Man-Chung
署名单位：
University of Washington; University of Washington Seattle; Hong Kong Polytechnic University
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.2020.1113
发表日期：
2021
页码：
1129-1148
关键词：
摘要：
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.