Inexact implicit method with variable parameter for mixed monotone variational inequalities

In this paper, we focus on a useful modification of the implicit method by Noor (Ref. 1) for mixed variational inequalities. Experience on application s has shown that the number of iterations of the original method depends si gnificantly on the penalty parameter. One of the contributions of the propo sed method is that we allow the penalty parameter to be variable. By introd ucing a self-adaptive rule, we find that our method is more flexible and ef ficient than the original one. Another contribution is that we require only an inexact solution of the nonlinear equations at each iteration. A detail ed convergence analysis of our method is also included.