A set scalarization function based on the oriented distance: first properties and applications to set optimization

B. Jiménez, V. Novo, A. Vílchez Medina

In the framework of normed spaces ordered by a convex cone not necessarily solid, we consider two set scalarization functions of type sup-inf, which are extensions of the oriented distance of Hiriart-Urruty. We studdy their basic properties and, moreover, we use these functions to characterize the lower and upper set less preorders of Kuroiwa and the strict lower and strict upper set relations. Finally, we apply the obtained results to characterize several concepts of minimal solution to a set optimization problem defined by a set-valued map. Minimal and weak minimal solutions with respect to the lower and upper set less relations are between the concepts considered.

Keywords: set optimization scalarization oriented distance minimal solution

J. E. Martínez Legaz, V. Roshchina, M. Todorov

M. A. Melguizo Padial, F. García Castaño

J. Parra López, M. J. Cánovas Cánovas, M. A. López Cerdá, B. Mordukhovich