Optimality analysis for ϵ-quasi solutions of optimization problems via ϵ-upper convexificators: a dual approach

The theory of duality is of fundamental importance in the study of vector optimization problems and vector equilibrium problems. A Mond–Weir-type dual model for such problems is important in practice. Therefore, studying such problems with a dual approach is really useful and necessary in the litera...

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Bibliographic Details
Published in:Journal of global optimization 2024-11, Vol.90 (3), p.651-669
Main Author: Van Su, Tran
Format: Article
Language:English
Subjects:
Computer Science
Constraints
Efficiency
Equilibrium
Euclidean space
Mathematical functions
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
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Summary:The theory of duality is of fundamental importance in the study of vector optimization problems and vector equilibrium problems. A Mond–Weir-type dual model for such problems is important in practice. Therefore, studying such problems with a dual approach is really useful and necessary in the literature. The goal of this article is to formulate Mond–Weir-type dual models for the minimization problem (P), the constrained vector optimization problem ( CVOP ) and the constrained vector equilibrium problem (CVEP) in terms of ϵ -upper convexificators. By applying the concept of ϵ -pseudoconvexity, some weak, strong and converse duality theorems for the primal problem (P) and its dual problem ( DP ), the primal vector optimization problem ( CVOP ) and its Mond–Weir-type dual problem (MWCVOP), the primal vector equilibrium problem (P) and its Mond–Weir-type dual problem (MWCVEP) are explored.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-024-01415-y