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

Tran Su ()
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Tran Su: The University of Danang - University of Science and Education

Journal of Global Optimization, 2024, vol. 90, issue 3, No 4, 669 pages

Abstract: Abstract 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 $$\epsilon $$ ϵ -upper convexificators. By applying the concept of $$\epsilon $$ 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.

Keywords: Vector optimization problems; Duality; $$\epsilon $$ ϵ -Quasi optimal solutions; $$\epsilon $$ ϵ -Pseudoconvexity; $$\epsilon $$ ϵ -Upper convexificators (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-024-01415-y

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