Global convergence of a trust region sequential quadratic programming method

In this paper we propose a trust region sequential quadratic programming (SQP) method to solve large-scale nonlinear optimization problems. The main shortcoming of the ordinary trust region SQP method is that the QP subproblem with the trust region constraint may not be feasible when a radius of the trust region is small. The trust region SQP methods which have been proposed so far are so complicated to resolve this shortcoming. It is not desirable in view of implementation and computational time. Moreover, many of the previous trust region SQP methods have another difficulty to solve the QP subproblem which is not necessarily convex. In this paper, we propose a new trust region SQP method which eliminates these two shortcomings. In our method, we solve two types of subproblem: one is a convex QP problem and the other is a system of linear equations.