A proximal-point SQP trust region method for solving some special class of nonlinear semi-definite programming problems

In this paper, we consider a nonlinear semi-definite programming problem that represents the fixed order H2 and H2/H∞ synthesis problems. A proximal-point sequential quadratic programming method that makes use of trust region is developed. Furthermore, the constrained trust region method [F. Leibfritz, E.M.E. Mostafa, Trust region methods for solving the optimal output feedback design problem, Int. J. Contr. 76 (2003) 501-519], which was designed to solve a nonlinear semi-definite program representing the H2 synthesis problem, is extended to solve a more general nonlinear semi-definite program representing the fixed order H2/H∞ synthesis problem. Numerical results for the proposed methods are given.