I. Introduction
SET-valued optimization (also called set optimization) is a rapidly developing branch of applied mathematics (see [6], [8] and the references therein). It deals with optimization problems where the objectives and/or the constraints are defined by set-valued maps. Set-valued optimization has important applications both in mathematics and in other fields of knowledge. As the authors of [8] write (p. 1), “For instance, duality principles in vector optimization, gap functions for vector variational inequalities, inverse problems for partial differential equations and variational inequalities, fuzzy optimization, image processing, viability theory, and mathematical economics all lead to optimization problems that can be conveniently cast as set-valued optimization problems”.