ASYMMETRIC VARIATIONAL INEQUALITY PROBLEMS OVER PRODUCT SETS - APPLICATIONS AND ITERATIVE METHODS

The author describes how several equilibrium problems can be uniformly modeled by a finite-dimensional asymmetric variational inequality defined over a Cartesian product of sets, and investigates 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.