Matrix cones, complementarity problems, and the bilinear matrix inequality

Author

Mesbahi, M. ; Papavassilopoulos, G.P. ; Safonov, M.G.

Author_Institution

Dept. of Electr. Eng.-Syst., Univ. of Southern California, Los Angeles, CA, USA

Volume

3

fYear

1995

fDate

13-15 Dec 1995

Firstpage

3102

Abstract

Discusses an approach for solving the bilinear matrix inequality (BMI) based on its connections with certain problems defined over matrix cones. These problems are, among others, the cone generalization of the linear programming (LP) and the linear complementarity problem (LCP) (referred to as the Cone-LP and the Cone-LCP, respectively). Specifically, the authors show that solving a given BMI is equivalent to examining the solution set of a suitably constructed Cone-LP or Cone-LCP. This approach facilitates understanding of the geometry of the BMI and opens up new avenues for the development of the computational procedures for its solution

Keywords

linear programming; matrix algebra; bilinear matrix inequality; complementarity problems; cone generalization; linear complementarity; linear programming; matrix cones; Centralized control; Computational geometry; Linear matrix inequalities; Linear programming; NP-hard problem; Optimization methods; Robust control; Robustness; Symmetric matrices;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1995., Proceedings of the 34th IEEE Conference on

Conference_Location

New Orleans, LA

ISSN

0191-2216

Print_ISBN

0-7803-2685-7

Type

conf

DOI

10.1109/CDC.1995.478622

Filename

478622