Abstract: In this paper, we propose a  QP-free infeasible method without a penalty function and a filter  for constrained nonlinear optimization  problems. This iterative method is  based on the solution of nonsmooth equations which  are obtained by the multipliers and the piecewise linear relationship NCP function for the KKT first-order optimality conditions.  Locally, each iteration of this method can be viewed as a perturbation of the mixed Newton-quasi Newton iteration on both  primal and dual variables for the solution of  KKT optimality conditions. We do not  use  a penalty function and a filter on line searches. This method is  implementable and globally convergent. Without the second order correction we  prove that the method has superlinear convergence rate under some mild conditions.

Key words: filter, QP-free , method, constraint, convergence, NCP function