Optimality And Higher Order Duality In Nonlinear Programming

The optimality conditions and duality are the most important components of nonlinear programming theory, they are also hot spots of nonlinear programming problem. These years, many authors have been studying the optimality conditions and duality of fractional programming under the assumptions of varied kinds of generalized convexity.This thesis studies the optimality conditions and higher order duality of the fractional programming under higher order generalized convexity assumptions. It is composed of the following three aspects:1. The type of minmax fractional programming problem (P) min x∈Rn supy∈Yf(x,y)h(x,y) is discussed, and the sufficient optimality conditions of problem (P) are given under a generalized convexity assumption.2. A generalized convex functions-higher order generalized ( F ,ρ,d)?convex functions are introduced, and the higher order Schaible and higher order Mond-weir dual problems of problem (P) are formulated, the corresponding weak duality, strong duality, and strict converse duality theorems are established under the assumptions of higher order generalized ( F ,ρ,d)?convexity; and the higher order mixed dual problem of problem (P) is given, the corresponding weak duality, strong duality and strict converse duality theorems are proved under the higher order ( F ,ρ,d)?convexity assumptions.3 . The higher order symmetric dual problem of the type of fractional programming problem (MP) min f (x,y)h(x,y) is formulated, the corresponding weak duality, strong duality and converse duality theorems are established under the higher orderη?pseudo-invex and higher orderη?pseudo-incavex assumptions.