Sublinear scalarizations for proper and approximate proper efficient points in nonconvex vector optimization

F. García Castaño, M. A. Melguizo-Padial, G. Parzanese

In this presentation, we will demonstrate that, given a separation property, a $\mathcal{Q}$-minimal point in a normed space is the minimum of a specific sublinear function. This observation provides sufficient conditions, via scalarization, for nine distinct types of proper efficient points, thereby establishing a characterization in the specific instance of Benson proper efficient points. Furthermore, we will explore necessary and sufficient conditions for approximate Benson and Henig proper efficient points expressed in terms of scalarization. The separation property we consider is a variant of a previously introduced property that had been applied in the setting of reflexive Banach spaces. Our scalarization results do not rely on convexity or boundedness assumptions.

Keywords: scalarizations, proper efficient points, approximate proper efficient points

GT13.OPTCONT2 Invited Session
November 8, 2023  4:00 PM
HC1: Canónigos Room 1

M. A. Melguizo-Padial, F. García Castaño

M. Á. Sama Meige, A. Khan

G. Ruiz-Garzón, R. Osuna-Gómez, A. Rufián-Lizana, A. Beato-Moreno