Major Efficiency Of Multiobjective Programming With Generalized Convexity

This thesis discusses a type of generalized convexity and the optimal conditions, dualtheories of major efficient solutions in multiobjective programming.The first problem we study is about the major efficient solutions of multiobjective pro-gramming with type I functions. In chapter 2, some sufficient conditions, Fritz John typenecessary conditions and Kuhn-Tucker type necessary conditions of major efficient solu-tions for type I multiobjective programming are developed. Also included in this part is thedual theories for type I multiobjective programming.The second problem we study is about the major efficient solutions of semi-preinvexmultiobjective programming. Chapter 3 deals with the semi-preinvex multiobjective pro-gramming. In this part, the sufficient conditions for semi-preinvex functions are investi-gated, which provide fundamental theories for studying optimal conditions in semi-preinvexmultiobjective programming. Furthermore, sufficient conditions, necessary conditions anddual theories of major efficient solutions for semi-preinvex multiobjective programming aredeveloped.