(Λ,C)-contingent derivatives of set-valued maps

In this paper a new notion of differentiability of set-valued maps is introduced. Based on ordered spaces techniques, (Λ,C)-lower and (Λ,C)-upper contingent derivatives are defined. Conditions for (Λ,C)-differentiability are given. Furthermore we show that these concepts are suitable for the formulation of optimality conditions for set-valued optimization problems with set-optimization criteria.