Title :
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
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;
Conference_Titel :
Decision and Control, 1995., Proceedings of the 34th IEEE Conference on
Conference_Location :
New Orleans, LA
Print_ISBN :
0-7803-2685-7
DOI :
10.1109/CDC.1995.478622
