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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 54 Issue: 1

Sufficiency and duality for E-differentiable vector optimization problems under generalized convexity

N. Abdulaleem(University of Łódz)0000-0003-1897-9977
Jınxia Cen(Zhejiang Normal University)0000-0001-9360-8821
Koushik Das(Taki Government College)
Pages
—
Publication Date
2025-02-28
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

For the $E$-differentiable vector optimization problem, the so-called vector Mond-Weir $E$-dual problem is defined, and several $E$-dual theorems are established under (generalized) $E$-$B$-invexity hypotheses.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, a new class of nonconvex vector optimization problems is considered.
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Key Findings & Data:To illustrate the aforesaid results, a nonsmooth vector programming problem with $E$-differentiable functions is studied.
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Conclusion & Impact:For the $E$-differentiable vector optimization problem, the so-called vector Mond-Weir $E$-dual problem is defined, and several $E$-dual theorems are established under (generalized) $E$-$B$-invexity hypotheses.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:$E$-differentiable function · $E$-$B$-invex function · generalized $E$-$B$-invexity

Abstract

In this paper, a new class of nonconvex vector optimization problems is considered. The concepts of $E$-$B$-pseudoinvexity and $E$-$B$-quasiinvexity are introduced for $E$-differentiable functions. Then, the sufficiency of the so-called $E$-Karush-Kuhn-Tucker optimality conditions is established for the considered $E$-differentiable vector optimization problems under (generalized) $E$-$B$-invexity. To illustrate the aforesaid results, a nonsmooth vector programming problem with $E$-differentiable functions is studied. For the $E$-differentiable vector optimization problem, the so-called vector Mond-Weir $E$-dual problem is defined, and several $E$-dual theorems are established under (generalized) $E$-$B$-invexity hypotheses.

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Cite This Article

Abdulaleem, N., Cen, J., Das, K. (2025). Sufficiency and duality for E-differentiable vector optimization problems under generalized convexity. Hacettepe Journal of Mathematics and Statistics, Volume: 54 Issue: 1. https://doi.org/10.15672/hujms.1385475

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