Properties of scalarizing functions of set optimization problems with variable cones and applications

Abstract

In this paper, we study properties and applications of nonlinear scalarizing functions of set optimization problems with variable cones. First, we extend the nonlinear scalarizing functions in the case of variable cones based on set less order relations. Next, we investigate some basic properties of such scalarizing functions. Finally, we apply the above properties to establish the optimal conditions for set optimization problems with variable cones. Our results are new or improve the existing ones in the literature.