Alternating direction method with self-adaptive penalty parameters for monotone variational inequalities

The alternating direction method is one of the attractive approaches for so lving linearly constrained separate monotone variational inequalities. Expe rience on applications has shown that the number of iterations depends sign ificantly on the penalty parameter for the system of linear constraint equa tions. While the penalty parameter is a constant in the original method, in this paper we present a modified alternating direction method that adjusts the penalty parameter per iteration based on the iterate message. Prelimin ary numerical tests show that the self-adaptive adjustment technique is eff ective in practice.