The Optimality And Duality For A Class Of Multiobjective Semi-infinite Fractional Programming

In this thesis,the author presents new generalized convexities of the same class by means of local cone approximation K,K-directional derivative and K-subdifferential,that is generalized(C,?,?,d)K,?-convexity,generalized(C,?,?,d)K,?-pseudo-convex-ity,generalized(C,?,?,d)K,?-quasi-convexity,and so on.The optimality and duality for a class of multi objective semi-infinite fractional programming are studied relating to these generalized convexities.The main results contained in this thesis are as follows:(1)Several concepts of generalized convexities are given which based on(C,?,?,d)-convexity;(2)On the basis of generalized(C,?,?,d)K,?-convexity,the optimality conditions for a class of multi objective semi-infinite fractional programming are discussed;(3)The Mond-Weir duality and Wolfe duality for a class of multi objective semi-infinite fractional programming involving these generalized convexities are studied;In conclusion,new generalized convexities of the same class are presented in this thesis.And optimality and duality for a class of multi objective semi-infinite fractional programming are studied involving these generalized convexities.The results are theoretical extending to some general convexity.At the same time,the generalized convexity and the corresponding theories for multi objective semi-infinite programming are enriched.