Optimality And Duality For Multi-objective Programming Involving Generalized(F,α,ρ,d)-V-Convexity

In this paper, firstly, the definitions of several classes of generalized convexfunctions are presented by means the concept of Clarke generalized subdifferential, thatis(F,α,ρ,d)-V-pseudo-convex,weak strictly (F,α,ρ,d)-V-pseudo-convex,strictly(F,α,ρ,d)-V-pseudo-convex,(F,α,ρ,d)-V-quasiconvex, andweak(F,α,ρ,d)-V-quasiconvex, generalized convex function.Secondly, the optimality,Mond-Weir duality for multiobjective fractional programming are studiedinvolving these generalized convexities. At last, the optimality,Wolfe typeduality,Mond-Weir type duality and mixed type duality for multiobjective semi-infiniteprogramming are studied involving the several classes of generalized convexfunctions.The article consists of the following sections.1. A classe of generalized convex functions are defined on the basis of(F,α,ρ,d)-V-convex, that is (F,α,ρ,d)-V-pseudoconvex and(F, α,ρ,d) V quasiconvex functions. And the optimality conditions for multiobjective fractionalprogramming are studied involving these generalized convexities.2. The Mond-Weir duality for multiobjective fractional programming are studiedinvolving these generalized(F,α,ρ,d)-V-convexities. And the weak dualitytheorems, strong duality theorems, and inverse duality theorems are obtained.3. Optimality conditions for multiobjective semi-infinite programming are studiedinvolving these generalized(F,α,ρ,d)-V-convex functions. 4. A mixed typical duality for multiobjective semi-infinite programming are studiedinvolving these generalized(F,α,ρ,d)-V-convexities,which includes Wolfe type andMond-Weir type duality. And the weak duality theorems and strong duality theorems areobtained.