The Optimality Conditions And Lagrange Duality Of Vector Extremum Problems In Abstract Space

In this thesis,some topics on the infinite dimensional vector extremum problems are discussed. The concept of ( v ,OY ;U+) generalized subconvexlike map is defined by relative interior, and some important proper ties of the new concept are discussed in local convex linear topological space, and the alternative theorem of the map is established. By applying the previous alternative theoremand other some conclusions, the optimality conditions for the vector extremum problems with generalized inequality constraint are obstained.Under the assumption of generalized convex in paper[62], the optimality conditions for the vector extremum problems with generalized inequality constraint in order linear space are obstained by alternative theorem in paper[62]. Scalarization results of vector extremum optimization are obstained, and the theorem of existence of lagrangian multipliers is proved in order linear space. Finally, in linear space, the conscepts of F-J saddle point and K-T saddle point are defined, the relations between them and weak efficient solution of vector extremum problems with generalized inequality constraint are discussed. Based on these, Vector-valued lagrange duality of vector extremum problems are established, including weak duality,strong duality and convex duality theorem in linear space.