Vector equilibrium problems under improvement sets and linear scalarization with stability applications

Abstract

In this paper, for vector equilibrium problems where the ordering relations are defined via improvement sets, linear scalarization characterizations are established, which include the well-known ones for vector optimization problems in the literature as special cases. By applying the obtained results, some continuity (both lower and upper semicontinuities) conclusions of parametric problems with respect to vector equilibria through improvement sets are deduced using scalarization approaches. Several unsolved or interesting problems are also proposed.