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# A Note on a Globally Convergent Newton Method for Solving Monotone Variational Inequalities

## Patrice Marcotte and Jean-Pierre Dussault

BibTeX reference

It is well-known (see Pang and Chan [7]) 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.

, 8 pages

### Publication

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Operations Research Letters, 6(1), 35–42, 1987 BibTeX reference