A line search filter secant method for nonlinear equality constrained optimization

This paper formulates and analyzes a line search method for general nonlinear equality constrained optimization based on filter methods for step acceptance and secant methods for search direction. The feature of the new algorithm is that the secant algorithm is used to produce a search direction, a backtracking line search procedure is used to generate step size, some filtered rules are used to determine step acceptance, second order correction technique is used to reduce infeasibility and overcome the Maratos effect. Global convergence properties of this method are analyzed: under mild assumptions it is showed that every limit point of the sequence of iterates generated by the algorithm is feasible, and that there exists at least one limit point that is a stationary point for the problem. Moreover, it is also established that the Maratos effect can be overcome in our new approach by adding second order correction steps so that fast local superlinear convergence to a second order sufficient local solution is achieved. Finally, the results of numerical experiments are reported to show the effectiveness of the line search filter secant method.