摘要 : In the paper, we introduce two new concepts on differentiability for set-valued maps, named by the higher-order generalized tangent epiderivative and the higher-order weak tangent epiderivative. Then, we study some basic propertie... 展开 In the paper, we introduce two new concepts on differentiability for set-valued maps, named by the higher-order generalized tangent epiderivative and the higher-order weak tangent epiderivative. Then, we study some basic properties and calculus rules for these notions. Finally, we mention their applications to two topics in set-valued optimization: optimality conditions and sensitivity analysis. More precisely, optimality conditions for some particular optimization problems are established and sensitivity analysis for the solution map of the parametric inclusion is given using higher-order generalized (weak) tangent epiderivatives. Several examples are proposed to illustrate the obtained results. 收起