A new scalarization approach and applications in set optimization

Abstract

In this paper, we introduce a new nonlinear scalarization function and apply it to investigate optimality conditions and scalar representations for minimal sets and set optimization problems with the set less order relation. First, we propose a new scalarization function for sets belonging to the power set of a normed space and discuss its properties. Next, we apply such properties to formulate sufficient and necessary optimality conditions for strictly minimal and weakly minimal sets. Finally, under suitable adjustments, we provide nonlinear scalarization functions and investigate scalar representations of strictly efficient solution and weakly efficient solution sets of the reference problems.