The Optimality Conditions And Duality Of The Multi-Objective Programming Problems Under Generalized Invex Functions

Generalized convex functions and the optimality conditions and duality involving generalized convex functions play a central role in the programming.In this thesis,firstly,the present situation of multi-objective programming problems under generalized invex functions is introduced.Secondly,the condition and basic definitions of multi-objective programming problems under generalized invex functions are introduce,for example,the math model of multi-Objective programming Problems,several optimal solutions of multi-objective programming Problems and duality theorem.Thirdly,the concept of generalized (Fb,a,ρ,d,φ)-convex functions, (Fb,a,ρ,d,φ)-quasi-convex functions and (Fb,a,ρ,d,φ)-pseudo-convex functions are defined.The linear nature and closeness are obtained under generalized (Fb,a,ρ,d,φ)-convex functions,the sufficient optimality conditions and duality theorem are established under the (Fb,a,ρ,d,φ)-pseudo-convex functions and (Fb,a,ρ,d,φ)-quasi-convex functions,specially for the wolfe dual problems, the weak,strong and strictly duality results are proofed.