We consider the nonlinear programming problem with equality and inequality constraints. In order to find a Kuhn–Tucker point, we use an equivalent formulation of the Kuhn-Tucker conditions consisting of nonlinear equations only. Then Newton's method is used to solve this system of nonlinear equations. Thus, we have to solve only one linear system at each iteration. By using a decomposition principle, we are able to reduce the dimension of this linear system. Some quasi–Newton variants and a local convergence theory are given. Finally, we present the results of some numerical experiments