Back to Search Start Over

On the Low Rank Solutions for Linear Matrix Inequalities.

Authors :
Wenbao Ai
Yongwei Huang
Shuzhong Zhang
Source :
Mathematics of Operations Research; Nov2008, Vol. 33 Issue 4, p965-975, 11p
Publication Year :
2008

Abstract

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 In the approach of Au-Yeung and Poon an earlier unpublished manuscript of Bohnenblust played an essential role.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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
0364765X
Volume :
33
Issue :
4
Database :
Complementary Index
Journal :
Mathematics of Operations Research
Publication Type :
Academic Journal
Accession number :
35829178
Full Text :
https://doi.org/10.1287/moor.1080.0331