The Optimality Conditions And Mixed Type Duality For Generalized Convex Multi-Objective Programming Problems

In this paper,we mainly make further ressearch about the generalized (F,α,ρ, d)-convex functions. This type functions can be seen as the generalization of (F,ρ)-convex functions and p-invex functions. First, the model of the Mixed type duality is given, the Wolfe and Mond-Weir type duals can be seen its special cases. Un-der the (F,α,ρ, d)-onvex functions, the weak,strong and strictly converse duality theories were established. Liang only considered differentiable situation when he defined (F,α,ρ, d)-convex functions. Second, In the paper we considered their non-differentiable situation. The K-(F,α,ρ,d)-B convex functions are defined for Lipschitz functions by using the cone-subdifferential and multi-objective fractional programs are studied. The generalized K-K-T optimality condition,weak,strong and strictly converse duality theorems are obtained in this paper. third, the second order mixed type duality in multi-objective programming problems with (F,α,ρ,d)-convex functions are discussed. The results about weak duality, strong duality and strictly converse duality are established under second order (F,α,ρ,d)-B convex functions.