A Note on Globally Convergent Newton Method for Strongly Monotone Variational Inequalities

Newton's method for solving variational inequalities is known to be locally quadratically convergent. By incorporating a line search strategy for the regularized gap function, Taji et al. (1993) have proposed a modification of a Newton's method which is globally convergent and whose rate of convergence is quadratic. But the quadratic convergence has been shown only under the assumptions that the constraint set is polyhedral convex and the strict complementarity condition holds at the solution. In this paper, we show that the quadratic rate of convergence is also achieved without both the polyhedral convex assumption and the strict complementarity condition. Moreover, the line search procedure is simplified.