On proper minimality in set optimization

Abstract The aim of this paper is to extend some notions proper minimality from vector optimization set optimization. In particular, we focus our attention on the concepts Henig and Geoffrion minimality, which are well-known in We introduce a generalization both them with finite dimensional spaces, by considering also special class polyhedral ordering cone. framework, prove that these two equivalent, as it happens context, where property well-known. Then, study characterization minimal points through nonlinear scalarization, without convexity hypotheses.