Local convergence of an augmented Lagrangian method for matrix inequality constrained programming
Optimization Methods & Software
Spectral radius minimization for optimal average consensus and output feedback stabilization
Automatica (Journal of IFAC)
A successive SDP-NSDP approach to a robust optimization problem in finance
Computational Optimization and Applications
ACMOS'05 Proceedings of the 7th WSEAS international conference on Automatic control, modeling and simulation
Robust output-feedback controller design via local BMI optimization
Automatica (Journal of IFAC)
A trust region method for solving semidefinite programs
Computational Optimization and Applications
A homotopy method for nonlinear semidefinite programming
Computational Optimization and Applications
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In this paper, an interior point trust region algorithm for the solution of a class of nonlinear semidefinite programming (SDP) problems is described and analyzed. Such nonlinear and nonconvex programs arise, e.g., in the design of optimal static or reduced order output feedback control laws and have the structure of abstract optimal control problems in a finite dimensional Hilbert space. The algorithm treats the abstract states and controls as independent variables. In particular, an algorithm for minimizing a nonlinear matrix objective functional subject to a nonlinear SDP-condition, a positive definiteness condition, and a nonlinear matrix equation is considered. The algorithm is designed to take advantage of the structure of the problem. It is an extension of an interior point trust region method to nonlinear and nonconvex SDPs, with a special structure which applies sequential quadratic programming techniques to a sequence of barrier problems and uses trust regions to ensure robustness of the iteration. Some convergence results are given, and, finally, several numerical examples demonstrate the applicability of the considered algorithm.