Decomposition method for a class of monotone variational inequality problems

In the solution of the monotone variational inequality problem VI(Omega, F), with [GRAPHICS] the augmented Lagrangian method (a decomposition method) is advantageous and effective when Y = R-m. For some problems of interest, where both the constraint sets X and Y are proper subsets in R-n and R-m, the original augmented Lagrangian method is no longer applicable. For this class of variational inequality problems, we introduce a decomposition method and prove its convergence. Promising numerical results are presented, indicating the effectiveness of the proposed method.