CHARACTERIZATION OF E -BENSON PROPER EFFICIENT SOLUTIONS OF VECTOR OPTIMIZATION PROBLEMS WITH VARIABLE ORDERING STRUCTURES IN LINEAR SPACES

Abstract

In this paper, using improvement-valued maps, we define two types of E -Benson proper efficient elements for subsets within a linear space under a variable ordering map C . Consequently, we delve into studying two types of E -Benson proper efficient solutions of vector optimization problems under variable ordering structures. We establish relationships among different types of E -Benson proper efficient elements. Furthermore, we demonstrate that the two types of E -Benson proper efficiency, in relation to the ordering map C , not only unify and extend certain notions of (weakly) nondominated elements but also extend some well-known notions of Benson proper efficiency under fixed ordering structures. Lastly, under suitable assumptions, we establish linear scalarization theorems for E -Benson proper efficient solutions of vector optimization problems under variable ordering structures. Several examples are also provided to illustrate the derived results. © 2024 Journal of Nonlinear and Variational Analysis.