Exponentially Semi E-preinvexity: Properties and Applications

Abstract

 Generalized exponential convexity has been one of the most important concept in generalized convex analysis, not only because of its structural properties used to relax convexity assumptions, but also because of its various applications in applied fields, especially in mathematics and optimization theory. In this paper, a class of two types of generalized convex functions is introduced, namely exponential semi -preinvex functions and exponentially quasi semi -preinvex functions. Several insights are presented, starting with providing a necessary and a sufficient condition for a function to be semi -preinvex function. Also, several general algebraic properties of these functions are estalished. Moreover, various characterizations and conditions are provided to relate these functions to their levels and graph sets. Finally, some optimality properties for nonlinear optimization problems with exponentially -preinvex functions, exponentially semi -preinvex functions and exponentially quasi semi -preinvex functions are shown. Two examples are presented to illustrate the new functions developed in this work.