Solving box constrained variational inequalities by using the natural residual with D-gap function globalization

We present a new method for the solution of the box constrained variational inequality problem (BVIP). Basically, this method is a nonsmooth Newton method applied to a reformulation of BVIP as a system of nonsmooth equations involving the natural residual. The method is globalized by using the D-gap function. We show that the proposed algorithm is globally and fast locally convergent. Moreover, if the problem is described by an affine function, the algorithm has a finite termination property. Numerical results for some large-scale variational inequality problems are reported.