Abstract: A new class of generalized convex functions were defined by using differential Exhausters, including upper Exhauster convex function and lower Exhauster convex function. By using the generalized convexity of functions, we proved the sufficiency of the necessary conditions of optimality under the condition of upper Exhauster convexity and lower Exhauster convexity for unconstrained nonsmooth minimum and maximum problems.

Key words:  Exhauster convex function; , generalized convex function, optimality condition