Solving a variational inequality problem is equivalent to finding a solutio
n of a system of nonsmooth equations. Recently, we proposed an implicit met
hod, which solves monotone:variational inequality problem via solving a ser
ies of systems of nonlinear smooth (whenever the operator is smooth) equati
ons. It can exploit the facilities of the classical Newton-like methods for
smooth equations. In this paper, we extend the method to solve a class of
general variational inequality problems
Q(u*) is an element of Omega, (upsilon - Q(u*))(T) F(u*) greater than or eq
ual to 0, For All upsilon is an element of Omega.
Moreover, we improve the implicit method to allow inexact solutions of the
systems of nonlinear equations at each iteration. The method is shown to pr
eserve the same convergence properties as the original implicit method.