Optimality And Duality Of Several Types Of Multi-objective Programming

Based on the existing generalized convexity,this thesis generalizes several kinds of convex functions by using Clarke generalized gradient and Minch symmetric gradient Several generalized convex functions,such as generalized(C,?)-I type,generalized uniform(C,?)-I?-convex and generalized uniformly symmetric(G,F)-convex are given.Under the constraints of these new generalized convexities,the optimality and duality of several kinds of Multiobjective Programming are discussed,some sufficient optimality conditions,?-optimality conditions and duality theorems are obtained(1)Based on the concept of Clarke's generalized gradient and the properties of convex functional,generalized(C,?)-I type convex,generalized strict quasi(C,?)-I type convex and generalized strict pseudo-quasi(C,?)-I type convex and many other generalized convex functions are defined.The optimality sufficient conditions for multiobjective programming problems involving these generalized(C,?)-I type convex functions are studied,and the Mond-Weir type dual model is established.Some weak duality theorems,weak duality theorems and weak duality theorems are obtained Strong duality theorem and strict inverse duality theorem(2)Defines generalized uniform(C,?)-I?-(strict)convex,generalized uniform(C,?)-I?-quasi-convex and generalized uniform(C,?)-I?-pseudo-convex and other generalized convex functions.Based on these generalized convexities,the ?-optimality conditions and dual problems of this type of multi-objective fractional programming problem are studied and discussed,and some optimality conditions and duality theorems are obtained(3)Using the concept of Minch symmetric gradient and the properties of sublinear functionals,the concepts of generalized convex functions such as generalized uniform symmetric(G,F)-convex,generalized uniform symmetric(G,F)-quasi-convex and generalized uniform symmetric(G,F)-pseudo-convex are given.And under these new generalized convexity conditions,several sufficient optimality conditions are given for this type of multi-objective programming problem,and the Mond-Weir type dual model is established,some weak duality theorems,strong duality theorem and strict inverse duality theorem are obtained.