Primal Central Paths and Riemannian Distances for Convex Sets

被引：0
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作者：
Y. Nesterov
A. Nemirovski
机构：
[1] Catholic University of Louvain,CORE
[2] Technion-Israel Institute of Technology,undefined
来源：
Foundations of Computational Mathematics | 2008年 / 8卷
关键词：
Riemannian geometry; Convex optimization; Structural optimization; Interior-point methods; Path-following methods; Self-concordant functions; Polynomial-time methods; 52A41; 53C22; 68Q25; 90C22; 90C25; 90C51; 90C60;
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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 ν-self-concordant barrier, the length of the central path is within a factor O(ν1/4) of the length of the shortest geodesic curve.
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页码：533 / 560
页数：27
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