Some convergence properties of a method of multipliers for linearly constrained monotone variational inequalities

Variational inequalities have important applications in mathematical programming. The alternative direction methods are suitable and often used in the literature in solving large-scale, linearly constrained variational inequalities arising in transportation research. In this paper, we present a few inequalities associated with the alternative direction method of multipliers given by Gabay and Mercier. The inequalities are helpful in understanding the algorithm.