A new nonmonotone QP-free infeasible method

We propose a nonmonotone QP-free infeasible method without using 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. We do not use a penalty function and a filter on nonmonotone line searches.The acceptance of trial step is more flexible by means of nonmonotone technique. This method is implementable and globally convergent. Without the second order correction we prove that the method has superlinear convergence rate. Preliminary numerical results show that the algorithm is robust and effective.