Primal and Dual Variables for New QP-free Method without a Penalty Function and a Filter

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 Fischer-Burmeister NCP function for the KKT first-order optimality conditions. Locally, each iteration of this method can be viewed as a perturbation of a mixed Newton-quasi Newton iteration on both the primal and dual variables for the solution of the KKT optimality conditions. We do not use the a penalty function and a filter on line searches. This method is implement able and globally convergent. Without the second order correction we prove that the method has super linear convergence rate under some mild conditions.