Optimality Conditions for Set-Valued Optimisation Problems Using a Modified Demyanov Difference

The aim of this paper was to provide optimality conditions for set‐valued optimisation problems with respect to the set less order relation. For this purpose, we use a slightly modified Demyanov difference in order to introduce a sort of directional derivative for set‐valued maps, which allows us to derive optimality conditions. Some results on existence and boundedness of the directional derivative are also given.