Preinvex Function And Its Generalization

This article mainly consistes of two sections: In the first section, the structure of invex sets and the relation among general sets , convex sets and invex sets are respectively characterized by means of the scattering points which will be defined in this paper, and the characteristic of the optimal solution of the programming min_x∈S f(x) is analysed useing the scatting point, where f(x) is a preinvex function on the feasible field S. Preinvex functions are characterized by epigraph which is defined in the following, and the properties of preinvex functions are given by the characterization.In the second section, semistrict preinvex functions and strict preinvex functions are introduced and the relation between semistrict preinvex function and other general convex functions are also given.