Barrier functions in interior point methods
成果类型：
Article
署名作者：
Guler, O
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.21.4.860
发表日期：
1996
页码：
860-885
关键词：
摘要：
We show that the universal barrier function of a convex cone introduced by Nesterov and Nemirovskii is the logarithm of the characteristic function of the cone. This interpretation demonstrates the invariance of the universal barrier under the automorphism group of the underlying cone. This provides a simple method for calculating the universal barrier for homogeneous cones. We identify some known barriers as the universal barrier scaled by an appropriate constant. We also calculate some new universal barrier functions. Our results connect the field of interior point methods to several branches of mathematics such as Lie groups, Jordan algebras, Siegel domains, differential geometry, complex analysis of several variables, etc.
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