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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.

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