Primal central paths and Riemannian distances for convex sets

被引：8
|
作者：
Nesterov, Y. [1 ]
Nemirovski, A. [2 ]
机构：
[1] Catholic Univ Louvain, CORE, B-1348 Louvain La Neuve, Belgium
[2] Technion Israel Inst Technol, Haifa, Israel
来源：
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS | 2008年 / 8卷 / 05期
关键词：
Riemannian geometry; convex optimization; structural optimization; interior-point methods; path-following methods; self-concordant functions; polynomial-time methods;
D O I：
10.1007/s10208-007-9019-4
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this paper, we study the Riemannian length of the primal central path in a convex set computed with respect to the local metric defined by a self-concordant function. Despite some negative examples, in many important situations, the length of this path is quite close to the length of a geodesic curve. We show that in the case of a bounded convex set endowed with a nu-self-concordant barrier, the length of the central path is within a factor O(nu(1/4)) of the length of the shortest geodesic curve.
引用
收藏
页码：533 / 560
页数：28
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