A Class Of Generalized E-Convex Functions And Their Applications

Convexity is a very important mathematical concepts, it is the theoretical basis and useful tool to study mathematical programming, optimization theory and other disciplines. However, a large number of functions in practical problems are non-convex functions, there are the limitations of their own research, in order to further discuss the problem of mathematical programming, etc. The paper on the basis of previous work, weakening and promoting the concept of convexity, increasing the application of practical problems, therefore, the study of generalized convex optimization theory and its application is necessary. This thesis study on E-convex function for further analysis, proposed a new semi E-preinvex function and quasi E-preinvex, discussed the linkages between the E-convex functions, proved some nature of generalized convex functions and the characteristics of the solution set, obtained the appropriate optimality conditions and its application. The thesis is divided into four chapters:The first chapter is an overview of generalized convexity, indicated the convexity and generalized convexity role in optimization theory, briefly descripted the convexity and generalized convexity of process and its application in optimization theory, the thesis described the semi strongly E-convex function's saddle point and the E-convex function's further promotion of rational.The second chapter established Fritz John saddle point and Kuhn Tucker saddle point about semi strongly E-convex function, it demonstrates the existence of two saddle poin -ts,and applied it in semi strongly E-convex programming, obtained the corresponding sufficient conditions for optimality, enrching the general E-convex function's optimum conditions.The third chapter is a further promotion of E-convex function, Introduced a new concept of semi E- preinvex function and quasi E- preinvex function, illustrated the relations between semi E- preinvex function, semi E- convex function and E- preinvex function, demonstrated the interrelation between semi E- preinvex function and quasi E- preinvex function theoretically, and got some simple properties of such functions and features of the optimal solution set, proposed optimality conditions of differentiable semi E- preinvex function optimization.Finally, a summary of this thesis, and made further efforts.