Asymmetric variational inequality problems over product sets: Applications and iterative methods

In this paper, we (i) describe how several equilibrium problems can be uniformly modelled by a finite-dimensional asymmetric variational inequality defined over a Cartesian product of sets, and (ii) investigate the local and global convergence of various iterative methods for solving such a variational inequality problem. Because of the special Cartesian product structure, these iterative methods decompose the original variational inequality problem into a sequence of simpler variational inequality subproblems in lower dimensions. The resulting decomposition schemes often have a natural interpretation as some adjustment processes. This research was based on work supported by the National Science Foundation under grant ECS 811–4571.