The Optimality And Duality For Multi-objective Fractional Programming Involving Unified (c,a,p,d)_s Convexity

In this paper, by using generalized unified (C,α,ρ,d) convex function,generalized unified (C,α,ρ,d) quasiconvex function and generalizedunified (C,α,ρ,d)(strictly) pseudoconvex function, the definitions of several classesof convex functions are presented in the symmetric differentiable case, that is, unified(C,α,ρ,d)_s convex function, unified (C,α,ρ,d)_s quasiconvex function, andunified (C,α,ρ,d)_s (strictly) pseudoconvex function, etc. The optimality andduality for multi-objective fractional programming are discussed involving theseconvexities. It is mainly contained two classes of in duality models, that is, parametricduality program and nonparametric duality program. The main achievements containedin this dissertation are as follow:(1) In the symmetric differentiable case, unified (C,α,ρ,d)_s convex function,unified (C,α,ρ,d)_s quasiconvex function and unified (C,α,ρ,d)_s (strictly)pseudo-convex function are defined based on generalized unified(C,α,ρ,d) convex function. The optimality conditions of multi-objective fractionalprogramming are researched under these convexities.(2) The Monde-Weir type and Lagrange type dual problems of multi-objectivefractional programming are studied with this kind of unified (C,α,ρ,d)_s convexfunction. Weak duality and strong duality theorems are obtained.(3) In case of these unified (C,α,ρ,d)_s convex functions, the parametricduality problems are discussed of multi-objective fractional programming whichincludes the parametric duality and semi-parametric duality. Their weak duality andstrong duality theorems are researched.In a word, in the symmetric differentiable case, several classes of new unified (C,α,ρ,d)_s convex functions in this paper, and then, the optimality and duality formulti-objective fractional programming are studied involving these convexities. Theseresults enriched the corresponding theory for convexities and multi-objective fractionalprogramming problems.