The Optimality Conditions And Duality For Classes Of Generalized Convex Programming

In this paper, the definitions of some new generalized convex functions are given in terms of the symmetric gradient on the basis of some old convex functions. The optimality and duality for a class of fractional semi-infinite programming and multi-objective programming are studied under the new generalized convex functions. The main content of this paper includes several sides as below:Several generalized convex functions are defined in terms of the symmetric gra-dient, that is, generalized unified symmetric convex function, generalized unifiedρ-symmetric convex function, unified Fb,ε-symmetric convex function, unified Fb-symmetric pseudo-convex function and unified Fb-symmetric quasi-convex func-tion, and so on. The optimality,ε-optimality and duality for a class of fractional semi-infinite programming is established on the basis of the new generalized convex functions. The optimality conditions and dual theorems are obtained.Several generalized convex functions are defined in terms of the symmetric gra-dient, that is, (F,α,ρ,d)- symmetric convex, (F,α,ρ,d)-symmetric quasi-convex and (F,α,ρ,d)-symmetric pseudo-convex and so on. The optimality and duality for a class of multiobjective programming is researched on the basis of the new general-ized convex functions.In this paper, the definitions of some new generalized convex functions are pre-sented in terms of the symmetric gradient. The optimality,ε-optimality, and duality for a class of fractional semi-infinite programming and multiobjective programming are studied under the new generalized convex functions which extended the convex functions and enriched theory for mathematical programming.