Decomposition method for a class of monotone variational inequality problems

In the solution of the monotone variational inequality problem VI (Ω, F), with (Formula Presented) uJ*l F(u) = \f(x)-ATy\ V = VXV, Iy J IAx-b J the augmented Lagrangian method (a decomposition method) is advantageous and effective when script Y sign = ℛ^m. For some problems of interest, where both the constraint sets script X sign and script Y sign are proper subsets in ℛⁿ and ℛ^m, the original augmented Lagrangian method is no longer applicable.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.