A regularization approach for variational inequalities ☆

This paper is devoted to a regularization approach for variational inequalities. A general method based on the theory of linear continuous and linear compact operators is developed for the stable approximation of ill-posed variational inequalities. Variational inequalities are considered for noncoercive monotone and pseudo-monotone operators. The approach is shown to be successful in handling variational inequalities formulated in reflexive, as well as in nonreflexive spaces.