In this paper the theory of local convergence for a class of line search filter type methods for nonlinear programming is presented. The algorithm presented here is globally convergent (see Chin ) and the rate of convergence is two-step superlinear. The proposed algorithm solves a sequence of quadratic progrmming subproblems to obtain search directions and instead of using penalty functions to determine the required step size, a filter technique is used to induce convergence. In addition to avoid the Maratos effect, the algorithm also employs second order correction (SOC) steps so that fast local convergence to the solution can be achieved. The proof technique is presented in a fairly general context which allows a range of algorithmic choices associated with choosing the Hessian matrix representation, controlling the step size and feasibility restoration.
Numerical Optimization Report, Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, January 2003.