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 an d effective when Y = R-m. For some problems of interest, where both the con straint sets X and Y are proper subsets in R-n and R-m, the original augmen ted Lagrangian method is no longer applicable. For this class of variationa l inequality problems, we introduce a decomposition method and prove its co nvergence. Promising numerical results are presented, indicating the effect iveness of the proposed method.