Universal Barrier Is n -Self-Concordant

Yin Tat Lee () and Man–Chung Yue ()
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Yin Tat Lee: Paul G. Allen School of Computer Science & Engineering at the University of Washington, Seattle, Washington 98195
Man–Chung Yue: Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Hong Kong

Mathematics of Operations Research, 2021, vol. 46, issue 3, 1129-1148

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: Primary: 90C51; secondary: 52A40; Primary: Nonlinear programming; secondary: convexity; universal barrier; self-concordance; interior-point methods; convex body; s -concave distributions; moment inequalities (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:46:y:2021:i:3:p:1129-1148

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