SOME ITERATIVE METHODS FOR SOLVING GENERAL BIFUNCTION VARIATIONAL INEQUALITIES

In this paper, we introduce and analyze a new class of bifunction variational inequalities known as general bifunction variational inequality. It is shown that this new class includes bifunction variational inequalities and related optimization problems as special cases. We use the auxiliary principle techniques to suggest some iterative methods for solving general bifunction variational inequalities. We also analyze the convergence analysis of these new iterative methods under some mild conditions. As special cases, we obtain several new and known methods for solving variational inequalities and related optimization problems.