It is well-known (see Pang and Chan ) that Newton's method, applied to strongly monotone variational inequalities, is locally and quadratically convergent. In this paper we show that Newton's method yields a descent direction for a nonconvex, nondifferentiable merit function, even in the absence of strong monotonicity. This result is then used to modify Newton's method into a globally convergent algorithm by introducing a linesearch strategy. Furthermore, under strong monotonicity (i) the optimal face is attained after a finite number of iterations (ii) the stepsize is eventually fixed to the value one, resulting in the usual Newton step.
Published March 1986 , 8 pages