Directional derivatives for set-valued mappings and applications

Set-valued optimisation is an important topic and has wide applications in engineering and game theory. An interesting topic in set-valued optimisation is the appropriate introduction of a derivative concept for set-valued mappings. In this paper, Dini directional derivatives are introduced and investigated for set-valued mappings. A derivative concept of a Jacobificator for set-valued mappings is introduced in terms of the Dini directional derivatives. Applications are given to present optimality conditions and mean value theorems.