Higher order duality in multiobjective fractional programming with support functions

In this paper a new class of higher order (F,ρ,σ)-type I functions for a multiobjective programming problem is introduced, which subsumes several known studied classes. Higher order Mond-Weir and Schaible type dual programs are formulated for a nondifferentiable multiobjective fractional programming problem where the objective functions and the constraints contain support functions of compact convex sets in Rn. Weak and strong duality results are studied in both the cases assuming the involved functions to be higher order (F,ρ,σ)-type I. A number of previously studied problems appear as special cases.     

一类多目标广义分式规划问题的最优性条件和对偶

研究了一类不可微多目标广义分式规划问题．首先,在广义Abadie约束品性条件下,给出了其真有效解的Kuhn—Tucker型必要条件．随后,在（C,a,P,d）一凸性假设下给出其真有效解的充分条件．最后,在此基础上建立了一种对偶模型,证明了对偶定理．得到的结果改进了相关文献中的相应结论．     

Optimality conditions and duality for a class of nondifferentiable multiobjective generalized fractional programming problems

This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of （F, α, ρ, d）-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.