Characterization of the barrier parameter of homogeneous convex cones

被引：32

作者：

Guler, O

Tuncel, L ^{[1
]}

机构：

[1] Univ Waterloo, Fac Math, Dept Combinator & Optimizat, Waterloo, ON N2L 3G1, Canada

[2] Univ Maryland Baltimore Cty, Dept Math & Stat, Baltimore, MD 21228 USA

来源：

MATHEMATICAL PROGRAMMING | 1998年 / 81卷 / 01期

基金：

加拿大自然科学与工程研究理事会; 美国国家科学基金会;

关键词：

barrier functions; self-concordance; Caratheodory number; homogeneous cones; Siegel domain; rank;

D O I：

10.1007/BF01584844

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We characterize the smallest (best) barrier parameter of self-concordant barriers for homogeneous convex cones. In particular, we prove that this parameter is the same as the rank of the cone which is the number of steps in a recursive construction of the cone (Siegel domain construction). We also provide lower bounds on the barrier parameter in terms of the Caratheodory number of the cone. The bounds are tight for homogeneous self-dual cones. (C) 1998 The Mathematical Programming Society. Inc, Published by Elsevier Science B.V.

引用

页码：55 / 76

页数：22

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