一种新的广义凸多目标分式规划的对偶定理

Duality theorems for multi-objective fractional programming with a new formulation of generalized convexity

本文给出了一类新的广义凸函数-(F,α,ρ,θ)-b-凸函数,讨论了多目标分式规划(MFP)的三种对偶模型:Mond-Weir型对偶、Lagrange型对偶、Schaible型对偶,并基于(F,α,ρ,θ)-b-凸性证明了各自相应的弱、强对偶定理。

In this paper,we present a new formulation of generalized convex function（F,α,ρ,θ）-b-convex function.Then three duality types of（MFP） which are Mond-Weir type,Lagrange type and Schaible type are discussed.At the same time,the weak duality theorems and strong duality theorems are proved for the three types of duality respectively based on the（F,α,ρ,θ）-b-convexity.