The augmented Lagrangian method (also referred to as an alternating directi
on method) solves a class of variational inequalities (VI) via solving a se
ries of sub-VI problems. The method is effective whenever the subproblems c
an be solved efficiently. However, the subproblem to be solved in each iter
ation of the augmented Lagrangian method itself is still a VI problem. It i
s essentially as difficult as the original one, the only difference is that
the dimension of the subproblems is lower, In this paper, we propose a new
alternating direction method for solving a class of monotone variational i
nequalities. In each iteration, the method solves a convex quadratic progra
mming with simple constrains and a well-conditioned system of nonlinear equ
ations. For such 'easier' subproblems, existing efficient numerical softwar
es are applicable. The effectiveness of the proposed method is demonstrated
with an illustrative example. (C) 2000 Elsevier Science Ltd. All rights re
served.