In recent years, there has been a growing amount of research interests on the finite-dimensional variational inequality and nonlinear complementarity problems. Among the many algorithms applicable for solving these problems, one particular algorithm stands out as the most promising. This is Newton's method. Despite the successes this method has achieved in practice, the method is intrinsically a locally convergent algorithm in the sense that unless the initial iterate is close to the solution, convergence is, in general, not guaranteed. It is the objective of our research to attempt to enlarge the domain of convergence of Newton's method. The approach is based on the classical idea of continuation for solving systems of nonlinear equations, and makes use of some recent results of sensitivity analysis for the variation inequality/complementarity problems.
