A filter QP-free infeasible method is proposed for minimizing a smooth function subject to smooth inequality constraints.This method is introduced by solving nonsmooth equations which are equivalent to the KKT first-order optimality conditions that are constructed by the multiplier and some NCP functions.Locally,each iteration of this method can be viewed as a perturbation of a Newton or quasi-Newton iteration on both the primal and dual variables for the solution of the KKT optimality conditions.The filter method is also used in linear search.This method is implementable and globally convergent.The method proves to have superlinear convergence rate under some mild conditions.The computational results show that this algorithm is efficient and reliable.
