The entropic barrier is n-self-concordant

12/21/2021

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by   Sinho Chewi, et al.

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For any convex body K ⊆ℝ^n, S. Bubeck and R. Eldan introduced the entropic barrier on K and showed that it is a (1+o(1)) n-self-concordant barrier. In this note, we observe that the optimal bound of n on the self-concordance parameter holds as a consequence of the dimensional Brascamp-Lieb inequality.