An application of anisotropic regularization to the existence of weak Pareto minimal points

Given a function f on Rⁿ, we introduce the concept of anisotropic regularization as a generalization of Tikhonov regularization f_ε(x)=f(x)+εx. When f is a continuous -function on Rⁿ and K is a box in Rⁿ, we study the properties of and the limiting behavior of solutions of a regularized box variational inequality problem , with emphasis on the existence of weak Pareto minimal points with respect to K. This work generalizes results of Sznajder and Gowda (1998) proved in the setting of nonlinear complementarity problems.