A nonsmooth version of Newton’s method

Newton’s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized Jacobian instead of the derivative. This extension includes the B-derivative version of Newton’s method as a special case. Convergence theorems are proved under the condition of semismoothness. It is shown that the gradient function of the augmented Lagrangean for C²-nonlinear programming is semismooth. Thus, the extended Newton’s method can be used in the augmented Lagrangean method for solving nonlinear programs.