The optimality conditions of nonconvex set-valued vector optimization

摘要

The concepts of α-order Clarke's derivative, α-order Adjacent derivative and α-order G. Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient.