Tikhonov regularization methods for variational inequality problems

Motivated by the work of Facchinei and Kanzow (Ref. 1) on regularization me thods for the nonlinear complementarity problem and the work of Ravindran a nd Gowda (Ref. 2) for the box variational inequality problem, we study regu larization methods for the general variational inequality problem. A suffic ient condition is given which guarantees that the union of the solution set s of the regularized problems is nonempty and bounded. It is shown that sol utions of the regularized problems form a minimizing sequence of the D-gap function under a mild condition.