Optimality Conditions and Duality of Three Kinds of Nonlinear Fractional Programming Problems

Some assumptions for the objective functions and constraint functions are given under the conditions of convex and generalized convex, which are based on the F-convex, ρ-convex, and (F,ρ)-convex. The sufficiency of Kuhn-Tucker optimality conditions and appropriate duality results are proved involving (F,ρ)-convex, (F,α,ρ,d)-convex, and generalized (F,α,ρ,d)-convex functions. © 2013 Xiaomin Zhang and Zezhong Wu.