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

Year 2024, Early Access, 1 - 17

N. Abdulaleem , Jınxia Cen , Koushik Das

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.

Keywords

$E$-differentiable function, $E$-$B$-invex function, generalized $E$-$B$-invexity, $E$-optimality condition, Mond-Weir $E$-duality

References

• [1] N. Abdulaleem, E-invexity and generalized E-invexity in E-differentiable multiobjective programming, ITM Web of Conferences, EDP Sciences 24, 01002, 2019.