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Branch-and-Cut Algorithms for the Bilinear Matrix Inequality Eigenvalue Problem (1999)
| Venue: | Comput. Optim. Appl |
| Citations: | 20 - 1 self |
BibTeX
@ARTICLE{Fukuda99branch-and-cutalgorithms,
author = {Mituhiro Fukuda and Masakazu Kojima},
title = {Branch-and-Cut Algorithms for the Bilinear Matrix Inequality Eigenvalue Problem},
journal = {Comput. Optim. Appl},
year = {1999},
volume = {19},
pages = {2001}
}
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Abstract
The optimization problem with the Bilinear Matrix Inequality (BMI) is one of the problems which have greatly interested researchers of the control and system theory in the last few years. This inequality permits to reduce in a elegant way various problems of robust control into its form. However, on the contrary of the Linear Matrix Inequality (LMI) which can be solved by interior-point-methods, the BMI is a computationally difficult object in theory and in practice. This article improves the branch-and-bound algorithm of Goh, Safonov and Papavassilopoulos (1995) by applying a better convex relaxation of the BMI Eigenvalue Problem (BMIEP), and proposes new Branch-and-Bound and Branch-and-Cut Algorithms. Numerical experiments were conducted in a systematic way over randomly generated problems, and they show the robustness and the efficiency of the proposed algorithms. Keywords: Bilinear Matrix Inequality, Branch-and-Cut Algorithm, Convex Relaxation, Cut Polytope. y Author supported b...
Keyphrases
branch-and-cut algorithm bilinear matrix inequality eigenvalue problem convex relaxation bilinear matrix inequality last year branch-and-bound algorithm cut polytope elegant way various problem linear matrix inequality robust control bmi eigenvalue problem systematic way optimization problem system theory interested researcher numerical experiment difficult object new branch-and-bound
