Abstract
A sequential quadratic programming method with line search is analyzed and studied for finding the local solution of a nonlinear semidefinite programming problem resulting from the discrete-time output feedback problem. The method requires an initial feasible point with respect to two positive definite constraints. By parameterizing the optimization problem we ease that requirement. The method is tested numerically on several test problems chosen from the benchmark collection (Leibfritz, 2004).
Highlights
In this paper, the following nonlinear semidefinite programming (NSDP) problem is considered: min J (X) s.t
Leibfritz and Mostafa [2] proposed an interior-point trust region method for a special class of NSDP problems resulting from the continuous-time static output feedback (SOF) problem
An SQP method with line search is introduced for finding the local solution of some NSDP problem resulting from the discrete-time static output feedback design problem
Summary
The following nonlinear semidefinite programming (NSDP) problem is considered: min J (X) s.t. Where J : Rn×n × Rp×r → R, H : Rn×n × Rp×r → Rn×n, G : Rn×n × Rp×r → Rn×n are sufficiently smooth matrix functions, where G ≻ 0 means that G is positive definite. This problem is assumed to be nonlinear and generally nonconvex. Jarre [1] introduced an interior-point method for nonconvex semi-definite programs. Leibfritz and Mostafa [2] proposed an interior-point trust region method for a special class of NSDP problems resulting from the continuous-time SOF problem. Freund et al [7] proposed a sequential semidefinite programming approach for a nonlinear program with nonlinear semidefinite constraints
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