Tight bounds on Lyapunov rank

被引：2
|
作者：
Orlitzky, Michael [1 ]
机构：
[1] Towson Univ, Dept Math, 7800 York Rd, Towson, MD 21252 USA
来源：
OPTIMIZATION LETTERS | 2022年 / 16卷 / 02期
关键词：
Lyapunov rank; Bilinearity rank; Lorentz cone; Proper cone;
D O I：
10.1007/s11590-021-01750-z
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
The Lyapunov rank of a cone is the number of independent equations obtainable from an analogue of the complementary slackness condition in cone programming problems, and more equations are generally thought to be better. Bounding the Lyapunov rank of a proper cone in R-n from above has been an open problem. Gowda and Tao gave an upper bound of n(2) - n that was later improved by Orlitzky and Gowda to (n - 1)(2). We settle the matter and show that the Lyapunov rank of (n(2) - n)/2 + 1 corresponding to the Lorentz cone is maximal.
引用
收藏
页码：723 / 728
页数：6
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