In the solution of the monotone variational inequality problem VI(Omega, F)
, with
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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ted Lagrangian method is no longer applicable.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.