Linear and conic scalarizations for obtaining properly efficient solutions in multiobjective optimization

The existence of equivalent scalar problems for properly efficient point of a given multiobjective optimization problem over arbitrary cones is studied by so many authors. This paper emphasizes two scalarizations, i.e., linear scalarization and conic scalarization, and studies geometrical viewpoint on the relationship between proper efficiency and these scalarizations. We also show that conic scalarization is a generalization of linear scalarization based on augmented dual cone which provides a new type of trade-off for properly efficient solutions.