Jian-Wen Peng, Wen-Bin Wei, Debdas Ghosh, Jen-Chih Yao, 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 -Benson proper efficient elements for subsets within a linear space under a variable ordering map . Consequently, we delve into studying two types of -Benson proper efficient solutions of vector optimization problems under variable ordering structures. We establish relationships among different types of -Benson proper efficient elements. Furthermore, we demonstrate that the two types of -Benson proper efficiency, in relation to the ordering map , 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 -Benson proper efficient solutions of vector optimization problems under variable ordering structures. Several examples are also provided to illustrate the derived results.
How to Cite this Article:
J.W. Peng, W.B. Wei, D. Ghosh, J.C. Yao, Characterization of E-Benson proper efficient solutions of vector optimization problems with variable ordering structures in linear spaces, J. Nonlinear Var. Anal. 8 (2024), 659-680.
