A regularized smoothing Newton method for box constrained variational inequality problems with P-0-functions

Based on Qi, Sun, and Zhou's smoothing Newton method, we propose a regulari zed smoothing Newton method for the box constrained variational inequality problem with P-0-function (P-0 BVI). The proposed algorithm generates an in finite sequence such that the value of the merit function converges to zero . If P-0 BVI has a nonempty bounded solution set, the iteration sequence mu st be bounded. This result implies that there exists at least one accumulat ion point. Under CD-regularity, we prove that the proposed algorithm has a superlinear (quadratic) convergence rate without requiring strict complemen tarity conditions. The main feature of our global convergence results is th at we do not assume a priori the existence of an accumulation point. This a ssumption is used widely in the literature due to the possible unboundednes s of level sets of various adopted merit functions. Preliminary numerical r esults are also reported.