Optimality conditions for an exhausterable function on an exhausterable set

Abstract: Exhausters are families of convex compact sets that allow one to represent directional derivative of the studied function at the considered point in the form of InfMax or SupMin of linear functions. Functions for which such a representation is valid we call exhausterable. The class of these functions is quite wide and contains many nonsmooth ones. The set which is given by exhausterable function is also called exhausterable. In the present paper we describe optimality conditions for an exhausterable function on an exhausterable set. These conditions can be used for solving of many nondifferentiable optimization problems. An example that illustrate obtained results is provided.