Higher-order optimality conditions of robust Benson proper efficient solutions in uncertain vector optimization problems

In this article, we study higher-order optimality conditions of robust Benson proper efficient solutions in uncertain vector optimization problems. One first introduces a new epiderivative of set-valued maps, the higher-order weak radial epiderivative. Then we investigate some of its properties. The concept of robust Benson proper effective solutions is proposed for uncertain vector optimization problems. In addition, applying the higher-order weak radial epiderivative, we establish the higher-order sufficient and necessary optimality conditions for the robust Benson proper effective solution in uncertain vector optimization problems without any convexity assumption.