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 fε,g as a generalization of Tikhonov regularization fε(x) = f (x) + εx. When f is a continuous P0-function on Rn and K is a box in Rn, we study the properties of fε,g and the limiting behavior of solutions of a regularized box variational inequality problem BVI(fε,g,K), 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.  2003 Elsevier Science (USA). All rights reserved.