On the Low Rank Solutions for Linear Matrix Inequalities

被引：13
|
作者：
Ai, Wenbao [1 ]
Huang, Yongwei [2 ]
Zhang, Shuzhong [2 ]
机构：
[1] Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China
[2] Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Hong Kong, Hong Kong, Peoples R China
来源：
MATHEMATICS OF OPERATIONS RESEARCH | 2008年 / 33卷 / 04期
关键词：
rank reduction; linear matrix inequality; joint numerical range;
D O I：
10.1287/moor.1080.0331
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：
In this paper we present a polynomial-time procedure to find a low-rank solution for a system of linear matrix inequalities (LMI). The existence of such a low-rank solution was shown in the work of Au-Yeung and Poon and the work of Barvinok. In the approach of Au-Yeung and Poon an earlier unpublished manuscript of Bohnenblust played an essential role. Both proofs in the work of Au-Yeung and Poon and that of Barvinok are nonconstructive in nature. The aim of this paper is to provide a polynomial-time constructive procedure to find such a low-rank solution approximatively. Extensions of our new results and their relations to some of the known results in the literature are discussed.
引用
收藏
页码：965 / 975
页数：11
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