The Optimality Of Multiobjective Programming With S-Subdifferential Functions

In this thesis,We aimed at study nonsmooth Multiobjective programming systematically.first,we gave the Alternative Theorem of support function.Then we use it obtained the necessary optimality conditions of multiobjective programming involving S-subdifferential functions.Second,With the definition of local cone approximation,several problems of nonsmooth multiobjective programming are studied:sufficient Optimality conditions and Duality theory.The arrangement of the thesis is as follows:First of all,a brief introduction on the study of multiobjective programming is given in chapter 1.In chapter 2,we introduced the definition of local cone approximation,and devoted to applied it to the multiobjective programming,first we gave the alternative theorem of support function,Then use this theorem we obtained necessary optimality for weak efficient solutions of the S-subdifferential multiobjective programming.In chapter 3,we consider the Invex maps by means of the concept of directional Sepiderivative. Several definitions of general S-invex map are presented,and we discussed their relationships.Then,Under the assumption of general S-invexity,we get the sufficient optimality condition.In Chapter 4,We discussed the duality relations.2 kinds of dual problem had been presented,corresponding duality theorem are proved.