The volumetric barrier for semidefinite programming

• 成果类型: Article
• 署名作者: Anstreicher, KM
• 署名单位: University of Iowa
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.25.3.365.12212
• 发表日期: 2000
• 页码: 365-380
• 关键词: convex-sets; algorithms

摘要

We consider the volumetric barrier for semidefinite programming, or generalized volumetric barrier, as introduced by Nesterov and Nemirovskii. We extend several fundamental properties of the Volumetric barrier for a polyhedral set to the semidefinite case. Our analysis facilitates a simplified proof of self-concordance for the semidefinite volumetric barrier, as well as for the combined volumetric-logarithmic barrier for semidefinite programming. For both of these barriers we obtain self-concordance parameters equal to those previously shown to hold in the polyhedral case.