A kind of unified proper efficiency in vector optimization (Q1724630)

Summary: Based on the ideas of the classical Benson proper efficiency, a new kind of unified proper efficiency named \(S\)-Benson proper efficiency is introduced by using Assumption (B) proposed by Flores-Bazán and Hernández, which unifies some known exact and approximate proper efficiency including \((C, \varepsilon)\)-proper efficiency and \(E\)-Benson proper efficiency in vector optimization. Furthermore, a characterization of \(S\)-Benson proper efficiency is established via a kind of nonlinear scalarization functions introduced by Göpfert et al.