Continuation-type Newton method for solving the monotone variational inequality problem

We first present a continuation-type Newton method for solving the monotone variational inequality problems. The method uses the technique of the inexact linear search for assuring its global convergence, and improves essentially the method of Taji K et al (1993), which can only solve the strongly monotone variational inequality problems, and has locally quadratic convergent rate under some conditions. In the last section, numerical results indicate the stability and efficiency of the proposed method.