Image space analysis for uncertain multiobjective optimization problems: Robust optimality conditions

Abstract

<p style='text-indent:20px;'>We introduce the <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{C} $\end{document}</tex-math></inline-formula>-robust efficient solution and optimistic <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{C} $\end{document}</tex-math></inline-formula>-robust efficient solution of uncertain multiobjective optimization problems (UMOP). By using image space analysis, robust optimality conditions as well as saddle point sufficient optimality conditions for uncertain multiobjective optimization problems are established based on real-valued linear (regular) weak separation function and real-valued (vector-valued) nonlinear (regular) weak separation functions. We also introduce two inclusion problems by using the image sets of robust counterpart of (UMOP) and establish the relations between the solution of the inclusion problems and the <inline-formula><tex-math id="M3">\begin{document}$ \mathcal{C} $\end{document}</tex-math></inline-formula>-robust efficient solution (respectively, optimistic <inline-formula><tex-math id="M4">\begin{document}$ \mathcal{C} $\end{document}</tex-math></inline-formula>-robust efficient solution) of (UMOP).</p>