A Class Of E-Convex Function And Application In Optimization

There are a large number of non-convex functions in practical problems, and they have similar nature in the non-linear programming as convex functions. In order to enlarge their applications, this paper mainly studies a class of important generalized convex function—E-convex function, and gives some criterias of a class of E-convex functions . We not only introduce the concept of pseudo-E- monotone and quasi-E- monotone, discuss the relationships between a class of E-convex function and their gradients , we also give applications on this type of E-convex function in the E-convex programming.This paper contains five chapters. We introduced significance of the subject , research present situation and the content of the paper in the first chapter; In chapter II, we presented some basic knowledge and gived a class of E-convex function of criterias; Next the applications on a class of E-convex function in the optimization theory are discussed in chapter III; In chapter IV, the relationships between a class of E-convex function and their gradients are studied. We made a summary of the full text and presented some problems of this topic to be thought in the last chapter.