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

Authors:
Bingsheng He;Hai Yang
Affiliations:
Department of Mathematics, Nanjing University, Nanjing, 210093, People's Republic of China;Department of Civil Engineering, The Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong, People's Republic of China
Venue:
Operations Research Letters
Year:
1998

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Abstract

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.