Application in Set Optimization

\(-C\) or \(-\mathcal {K}\) representing functionals are an important tool in set optimization. In this area of optimization, one investigates optimization problems with a set-valued objective map. But here we study these problems in a more general framework, that is, we ask about minimal sets within a family of sets. As in the previous chapter, we investigate problems with a fixed order structure given by a convex one C, and those with a variable order structure introduced by a suitable set-valued map \(\mathcal {K}\) . In both cases, the main topic is the characterization of minimal sets.