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.