BriefGPT.xyz
Dec, 2014
熵障碍：一种简单且最优的通用自协调障碍
The entropic barrier: a simple and optimal universal self-concordant barrier
HTML
PDF
Sébastien Bubeck, Ronen Eldan
TL;DR
本文通过对数凹分布的基本几何和指数族内元素的基础对偶性证明了一致测度空间中凸体均匀测度的Cramér变换是一种$(1+o(1))n$-自共轭障碍，改进了Nesterov和Nemirovski的开创性成果，这为具有最佳自共轭参数的凸体提供了第一个显式的通用障碍物构造。
Abstract
We prove that the Fenchel dual of the log-Laplace transform of the uniform measure on a
convex body
in $\mathbb{R}^n$ is a $(1+o(1)) n$-
self-concordant barrier
. This gives the first construction of a universal ba
→