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Some convergence properties of a method of multipliers for linearly constrained monotone variational inequalities. (English) Zbl 0963.49006
Summary: Variational inequalities have important application 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 {\it D. Gabay} and {\it B. Mercier} [Comput. Math. Appl. 2, 17-40 (1976; Zbl 0352.65034)]. The inequalities are helpful in understanding the algorithm.

MSC:
49J40Variational methods including variational inequalities
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
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References:
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