Decomposition method with a variable parameter for a class of monotone variational inequality problems

In this paper, we focus on a useful modification of the decomposition metho d by He et al. (Ref. 1). Experience on applications has shown that the numb er of iterations of the original method depends significantly on the penalt y parameter. The main contribution of our method is that we allow the penal ty parameter to vary automatically according to some self-adaptive rules. A s our numerical simulations indicate, the modified method is more flexible and efficient in practice. A detailed convergence analysis of our method is also included.