APPROXIMATE BENSON PROPER EFFICIENT SOLUTIONS OF SET-VALUED OPTIMIZATION PROBLEMS UNDER VARIABLE ORDERING STRUCTURES
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, vol.27, no.6, pp.1369-1386, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 27 Issue: 6
- Publication Date: 2026
- Journal Name: JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Page Numbers: pp.1369-1386
- Azerbaijan State University of Economics (UNEC) Affiliated: Yes
Abstract
This paper introduces two types of approximate Benson proper efficient solutions for set-valued optimization problems (in short, SVOP) under variable ordering structures in real linear space. We establish relationships between these two types of epsilon-Benson proper efficient solution of SVOP under variable ordering structure epsilon with other types of solutions of SVOP such as nondominated solution, epsilon-nondominated solution, and weakly epsilon-nondominated solution. Finally, some linear scalarization theorems of these two types of epsilon-Benson proper efficient solutions of SVOP under a variable ordering structure are established. We also improve and generalize several known results on Benson proper efficiency.