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

Abstract

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