Well-posedness and scalarization in set optimization involving ordering cones with possibly empty interior

Abstract

In this paper, we introduce three types of well-posedness for a set optimization problem (u-SOP). Some necessary and sufficient conditions for these well-posedness have been established. Two different scalar optimization problems involving a generalized oriented distance function have been considered. Characterization of u-minimal solutions of (u-SOP) in terms of solutions of these scalar optimization problems have been obtained. Finally, equivalence of well-posedness of (u-SOP) with well-posedness of these scalar optimization problems have been established.