Optimality conditions for robust weakly efficient solutions in uncertain optimization

Abstract

In this paper, we find the flimsily robust weakly efficient solution to the uncertain vector optimization problem by means of the weighted sum scalarization method and strictly robust counterpart. In addition, we introduce a higher-order weak upper inner Studniarski epiderivative of set-valued maps, and obtain two properties of the new notion under the assumption of the star-shaped set. Finally, by applying the higher-order weak upper inner Studniarski epiderivative, we obtain a sufficient and necessary optimality condition of the vector-based robust weakly efficient solution to an uncertain vector optimization problem under the condition of the higher-order strictly generalized cone convexity. As applications, the corresponding optimality conditions of the robust (weakly) Pareto solutions are obtained by the current methods.