WELL-POSEDNESS FOR VECTOR VARIATIONAL INEQUALITY AND CONSTRAINED VECTOR OPTIMIZATION

Abstract

In this paper we present some notions of parametric well-posedness for Stampacchia and Minty vector variational inequalities. We show that under suitable conditions, the parametric well-posedness of a Stampacchia vector variational inequality is equivalent to the parametric well-posedness of a vector optimization problem. Further, we introduce some concepts of well-posedness for a vector optimization problem with a Stampacchia vector variational inequality constraint. We prove that the well-posedness of this constrained vector optimization problem is closely related to the parametric well-posedness of its constrained vector variational inequality.