New Generalized Second‐Order Contingent Epiderivatives and Set‐Valued Optimization Problems

In this paper, we introduce the concept of a generalized second‐order composed contingent epiderivative for set‐valued maps and discuss its relationship to the generalized second‐order contingent epiderivative. We also investigate some of its properties. Then, by virtue of the generalized second‐order composed contingent epiderivative, we establish a unified second‐order sufficient and necessary optimality condition for set‐valued optimization problems, which is a generalization of the corresponding results in the literature.