Generalized Semi-local Convex Functions And Generalized Semi-local Convex Programming

In this thesis, firstly, the local starshaped (E,F)-convex set is defined on the basisof the local starshaped-convex set and the (E,F)-convex set. Then, the definitions ofseveral new classes of generalized convex functions are given by using the concepts oflocal starshaped (E,F) convex sets, semi-local convex function, semi(E,F) convexfunction and B semi (E, F)-convex funct ion, which are semi-local semi convex func-tion, semi-local semi (E,F)-quasi convex function, semi-local semi (E,F)-pseudoconvex function, semi-local B semi (E,F)convex function, semi-localB semi(E,F)-quasi convex function, semi-local B semi (E,F)-pseudo convex function.Furthermore, the properties of these generalized convex functions are researched andthe questions of the optimality conditions and duality for convex programming andmulti-objective programming involving these generalized convex functions are alsodiscussed. The main content of this thesis includes the following contents:(1) The local starshaped (E,F)-convex set is defined by using the local starship-ed convex set and the (E,F)-convex set. In the local starshaped(E,F)-convex set,the concepts of generalized convex functions are given on the basis of semi-localconvex function, semi (E,F)-convex function and B semi (E,F)-convex function,such as semi-local semi (E,F)-convex function, semi-local B semi (E,F)-convexfunction. In addition, the properties of these functions are also discussed;(2) The optimality and duality results of generalized convex programming arestudied on the involved generalized convexities; (3) The optimality conditions and Mond-Weir type duality theory for multi-obje-ctive programming question involving the semi (E,F)-convex function are given andproven;In short, in this thesis, some broader sense of convex functions are defined, on thebasis of these generalized convexity, moreover, the optimal conditions and dual theoryof convex programming and multi-objective programming are obtained, which enrich-es the theories of convexity and optimality.