Sufficient Conditions and Duality for a Class of Multiobjective Fractional Programming Problems with Higher-Order (F,α,ρ,d)-Convexity

Abstract

In this paper, a class of multiobjective fractional programming problems (denoted by (MFP)) is considered. First, the concept of higher-order (F,α,ρ,d)-convexity of a function f:C→R with respect to the differentiable function φ:Rn×Rn→R is introduced, where C is an open convex set in Rn and α:C×C→R+∖{0} is a positive value function. And an important property, which the ratio of higher-order (F,α,ρ,d)-convex functions is also higher-order (F,α′,ρ′,d′)-convex, is proved. Under the higher-order (F,α,ρ,d)-convexity assumptions, an alternative theorem is also given. Then, some sufficient conditions characterizing properly (or weakly) efficient solutions of (MFP) are obtained from the above property and alternative theorem. Finally, a class of dual problems is formulated and appropriate duality theorems are proved.