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Universal Barrier is n-Self-Concordant
Yin Tat Lee(yintat 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: Universal Barrier, Self-Concordance, s-Concave Distributions, Moment Inequalities Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization ) Category 2: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: Download: [PDF] Entry Submitted: 09/09/2018 Modify/Update this entry | ||
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