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- Title
CHARACTERIZATION OF E-BENSON PROPER EFFICIENT SOLUTIONS OF VECTOR OPTIMIZATION PROBLEMS WITH VARIABLE ORDERING STRUCTURES IN LINEAR SPACES.
- Authors
JIAN-WEN PENG; WEN-BIN WEI; GHOSH, DEBDAS; JEN-CHIH YAO
- 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.
- Subjects
VECTOR spaces; MATHEMATICAL optimization; MATHEMATICAL variables; VECTOR-valued measures; MATHEMATICAL analysis
- Publication
Journal of Nonlinear & Variational Analysis, 2024, Vol 8, Issue 4, p659
- ISSN
2560-6921
- Publication type
Article
- DOI
10.23952/jnva.8.2024.4.11