Title :
A simple numerical method for minimizing the maximum eigenvalues of symmetric matrices via nonlinear differential equation solvers
Author :
Imae, J. ; Furudate, Takashi ; Sugawara, Shizuka
Author_Institution :
Dept. of Mech. Eng., Iwate Univ., Morioka, Japan
Abstract :
In this paper, we present a simple numerical method for solutions of linear/bilinear matrix inequalities (LMI/BMI) problems, more exactly a method for minimizing the maximum eigenvalues of real valued symmetric matrices. Nonlinear differential equation solvers are used in our approach. First, we convert the non-differentiable minimization problem for the maximum eigenvalues into one of differentiable optimization problems by means of interior point methods. Second, making use of differential equation solvers, we present a simple method for finding the solutions of the optimization problems. Finally, we demonstrate the effectiveness of the algorithm through some simulation experiences
Keywords :
eigenvalues and eigenfunctions; matrix algebra; minimisation; nonlinear differential equations; differentiable optimization; interior point methods; linear/bilinear matrix inequalities; maximum eigenvalues; nondifferentiable minimization problem; nonlinear differential equation solvers; numerical method; symmetric matrices; Differential equations; Eigenvalues and eigenfunctions; Ellipsoids; Hydrogen; Linear matrix inequalities; Mechanical engineering; Minimization methods; Optimization methods; Robust control; Symmetric matrices;
Conference_Titel :
Decision and Control, 1996., Proceedings of the 35th IEEE Conference on
Conference_Location :
Kobe
Print_ISBN :
0-7803-3590-2
DOI :
10.1109/CDC.1996.577575
