Family of perturbation methods for variational inequalities

In recent years, the so-called auxiliary problem principle has been used to derive many iterative type algorithms for solving optimal control, mathematical programming, and variational inequality problems. In the present paper, we use this principle in conjunction with the epiconvergence theory to introduce and study a general family of perturbation methods for solving nonlinear variational inequalities over a product space of reflexive Banach spaces. We do not assume that the monotone operator involved in our general variational inequality problem is of potential type. Several known iterative algorithms, which can be obtained from our theory, are also discussed.This work was completed while the second author was visiting the Department of Mathematics of the University of Washington, Seattle, Washington under financial support from the Belgian Fonds National de la Recherche Scientifique, Grant FNRS: B8/5-JS-9. 549.