SOME NEW CLASSES OF NONCONVEX FUNCTIONS

Abstract

In this paper, we introduce and study a new class of convex functions, which is called the convex function. These functions are nonconvex functions and include the convex functions as special cases. We study some properties of convex functions. It is shown that the minimum of the convex functions on the convex set can be characterized by a class of variational inequalities, which is called the directional variational inequalities. Some open problems are suggested for further research.