A combined relaxation method for nonlinear variational inequalities

When applied to variational inequalities, combined relaxation (CR) methods are convergent under mild assumptions. Namely, the underlying mapping need not be strictly monotone. In this paper, we describe a class of CR methods for nonlinear variational inequality problems (NVI), which involve two, rather than one, nonlinear mappings and a nonsmooth convex function. We establish a convergence result for the CR method in the monotone case and also show that it attains a linear rate of convergence under the additional strong monotonicity assumption. Implementation issues are also discussed.