Optimality and duality for $ E $-differentiable multiobjective programming problems involving $ E $-type Ⅰ functions

Abstract

<p style='text-indent:20px;'>In this paper, a new concept of generalized convexity is introduced for not necessarily differentiable multiobjective programming problems with <inline-formula><tex-math id="M3">\begin{document}$ E $\end{document}</tex-math></inline-formula>-differentiable functions. Namely, the concept of <inline-formula><tex-math id="M4">\begin{document}$ E $\end{document}</tex-math></inline-formula>-type Ⅰ functions is defined for <inline-formula><tex-math id="M5">\begin{document}$ E $\end{document}</tex-math></inline-formula>-differentiable multiobjective programming problem. Based on the introduced concept of generalized convexity, the sufficiency of the so-called <inline-formula><tex-math id="M6">\begin{document}$ E $\end{document}</tex-math></inline-formula>-Karush–Kuhn–Tucker optimality conditions are established for a feasible point to be an <inline-formula><tex-math id="M7">\begin{document}$ E $\end{document}</tex-math></inline-formula>-efficient or a weakly <inline-formula><tex-math id="M8">\begin{document}$ E $\end{document}</tex-math></inline-formula>-efficient solution. Further, the so-called vector Mond-Weir <inline-formula><tex-math id="M9">\begin{document}$ E $\end{document}</tex-math></inline-formula>-dual problem is defined for the considered <inline-formula><tex-math id="M10">\begin{document}$ E $\end{document}</tex-math></inline-formula>-differentiable multiobjective programming problem and several <inline-formula><tex-math id="M11">\begin{document}$ E $\end{document}</tex-math></inline-formula>-duality theorems in the sense of Mond-Weir are derived under appropriate generalized <inline-formula><tex-math id="M12">\begin{document}$ E $\end{document}</tex-math></inline-formula>-type Ⅰ functions.</p>