Exhausters were proposed by V.F.Demyanov. These are families of convex compact sets that allow one to represent the directional derivative of the studied function at a point in the form of minmax or maxmin of linear functions. Functions for which such a representation is valid we call exhausterable. The set which is defined via exhausterable function is also called exhausterable. In the present work we describe optimality conditions for an exhausterable function on an exhausterable set.