Article Contents
Article Contents

# $V$-$E$-invexity in $E$-differentiable multiobjective programming

• In this paper, a new concept of generalized convexity is introduced for not necessarily differentiable vector optimization problems with $E$-differentiable functions. Namely, for an $E$-differentiable vector-valued function, the concept of $V$-$E$-invexity is defined as a generalization of the $E$-differentiable $E$-invexity notion and the concept of $V$-invexity. Further, the sufficiency of the so-called $E$-Karush-Kuhn-Tucker optimality conditions are established for the considered $E$-differentiable vector optimization problems with both inequality and equality constraints under $V$-$E$-invexity hypotheses. Furthermore, the so-called vector $E$-dual problem in the sense of Mond-Weir is defined for the considered $E$-differentiable multiobjective programming problem and several $E$-duality theorems are derived also under appropriate $V$-$E$-invexity assumptions.

Mathematics Subject Classification: Primary: 90C26, 90C30, 90C46, 26B25.

 Citation:

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