Primal-relaxed dual global optimization approach
Journal of Optimization Theory and Applications
SIAM Review
A cone programming approach to the bilinear matrix inequality problem and its geometry
Mathematical Programming: Series A and B
Cones of Matrices and Successive Convex Relaxations of Nonconvex Sets
SIAM Journal on Optimization
Geometry of Cuts and Metrics
High-Performance Parallel and Distributed Computing for the BMI Eigenvalue Problem
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
Successive Linearization Methods for Nonlinear Semidefinite Programs
Computational Optimization and Applications
Predictive LPV control of a liquid-gas separation process
Advances in Engineering Software
Output Feedback H∞ Control for Uncertain Piecewise Linear Systems
Journal of Dynamical and Control Systems
Automatica (Journal of IFAC)
Design of PDC fuzzy controllers under persistent disturbances and application in mechanical systems
Advances in Engineering Software
Engineering Applications of Artificial Intelligence
Solutions of polynomial systems derived from the steady cavity flow problem
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
H∞filtering of networked systems with time-varying sampling rates
ACC'09 Proceedings of the 2009 conference on American Control Conference
Model-Checking markov chains in the presence of uncertainties
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Robust output-feedback controller design via local BMI optimization
Automatica (Journal of IFAC)
H∞ output feedback control for uncertain stochastic systems with time-varying delays
Automatica (Journal of IFAC)
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The optimization problem with the Bilinear Matrix Inequality (BMI) is one of the problems which have greatly interested researchers of system and control theory in the last few years. This inequality permits to reduce in an elegant way various problems of robust control into its form. However, in contrast to 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 (Journal of Global Optimization, vol. 7, pp. 365–380, 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.