| Abstract: | The Newton method for variational inequality problem is locally and quadrat- ically convergent. By using a differentiable merit function, Tan, Fukushima andIbaraki1] have given a globally convergent modified Newton method for the stronglymonotone variational inequality problem and proved their method to be quadratically convergent finder some additional assumptions. In this paper we propose topresent a trust region-type modification of Newton method for the strictly monotone variational inequality problem using the same'merit function as that in 1]. Itis then shown that our method is well defined and globally convergent and that,under the same assumptions as those in 1], our algorithm reduces to the basicNewton method and hence the rate of convergence is quadratic. Computationalexperimence indicates the efficiency of the proposed method. |
