In this paper, we present a new class of functions called semi (p, e)-convex functions which represent a combination of  p- convex and semi e-convex functions. We discuss some important properties and characteristics of this class. For applying this class of new functions to optimize programming, we present some optimality properties such that the cost function of the optimization programming is semi (p, e)-convex and the set of constraints is (p, e)-convex.