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Universal Barrier Is n -Self-Concordant

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yin Tat Lee & Man–Chung Yue, 2021. "Universal Barrier Is n -Self-Concordant," Mathematics of Operations Research, INFORMS, vol. 46(3), pages 1129-1148, August.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:3:p:1129-1148
    DOI: 10.1287/moor.2020.1113
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