The general mixed variational inequality containing a nonlinear
term φ is a useful and an important generalization of variational inequalities.
The projection method cannot be applied to solve this problem due
to the presence of the nonlinear term. To overcome this disadvantage, Abedellah
Bnouhachem present a self-adaptive iterative method. In this paper,
we present a new self-adaptive method which can be viewed as a refinement
and improvement of the method of Bnouhachem. Global convergence of the
new method is proved under the same assumptions as Bnouhachem’s method.
Some preliminary computational results are given to show the efficiency of the
proposed method.