On the Low Rank Solutions for Linear Matrix Inequalities

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 AuYeung and Poon [1] and Barvinok [3]. In Au-Yeung and Poon's approach, an earlier unpublished manuscript of Bohnenblust [6] played an essential role. Both proofs in [1] and [3] are nonconstructive in nature. The aim of this paper is to offer a constructive and polynomial-time 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.

• Type: Journal
• Year: 2008
• Where: MOR
• Authors: Wenbao Ai, Yongwei Huang, Shuzhong Zhang
• Keywords: Linear Matrix Inequalities, Low Rank Solution, MOR 2008, Polynomial-time Procedure