Limit vector variational inequality problems via scalarization

Abstract

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. We solve a general vector variational inequality problem in a finite—dimensional setting, where only approximation sequences are known instead of exact values of the cost mapping and feasible set. We establish a new equivalence property, which enables us to replace each vector variational inequality with a scalar set-valued variational inequality. Then, we approximate the scalar set-valued variational inequality with a sequence of penalized problems, and we study the convergence of their solutions to solutions of the original one.