On Set Containment Characterizations for Sets Described by Set-Valued Maps with Applications

In this paper, dual characterizations of the containment of two sets involving convex set-valued maps are investigated. These results are expressed in terms of the epigraph of a conjugate function of infima associated with corresponding set-valued maps. As an application, we establish characterizations of weak and proper efficient solutions of set-valued optimization problems in the sense of vector criteria.