Alternating direction method with self-adaptive penalty parameters for monotone variational inequalities
In this paper the alternating direction method for solving linearly constrained separate monotone variational inequalities is studied. Experience on applications has shown that the number of the iterations depends significantly on the penalty parameter for the system of linear constraint equations. The main result of the paper is a convergence theorem for this method without any monotonicity assumption on the sequence of penalty parameters. This theorem applies to a modified alternating direction method that adjusts the penalty parameter per iteration based on the iterate message. Preliminary numerical tests are given to demonstrate the advantages of this self-adaptive adjustment technique.
scientific article; zbMATH DE number 1558308