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

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  • Tran Su

    (The University of Danang - University of Science and Education)

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.

Suggested Citation

  • Tran Su, 2024. "Optimality analysis for $$\epsilon $$ ϵ -quasi solutions of optimization problems via $$\epsilon $$ ϵ -upper convexificators: a dual approach," Journal of Global Optimization, Springer, vol. 90(3), pages 651-669, November.
    • Handle: RePEc:spr:jglopt:v:90:y:2024:i:3:d:10.1007_s10898-024-01415-y
    DOI: 10.1007/s10898-024-01415-y
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    References listed on IDEAS

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