Generic Stability of the ξ-efficient Solutions In Vector Optimization Problems
Xun-Hua Gong · Journal of Nanchang University · 2007
The ξ-efficient solution in vector optimization problems in an important solution concept.It plays an import role in studying efficient solution,weak efficient solution,topological architecture and stability of various proper efficient solutions,and scalarization.In this paper,the distance between two objective mappings is defined by the uniform topology in a normed space.In this topology,using the famous Fort theorem,it studies the stability of ξ-efficient solutions in vector optimization problems about objective mappings and monotone continuous linear functions,and proves that the solution set of ξ-efficiency in vector optimization problems is generically stable about its monotone continuous liner function,generically stable about its objective mapping,and generically stable about its monotone continuous liner function and objective mapping.