Abstract:
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.