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中文摘要：
向量优化问题的ξ-有效解是向量优化问题中重要的解的概念，它对研究有效解、弱有效解和各种真有效解的拓扑结构与稳定性以及标量化起着重要作用。在赋范线笥空间中用一致拓扑定义向量值映射间的距离，利用著名的Fort定理，在此拓扑下研究了向量优化问题中ξ-有效解集关于单调连续线性泛函和目标映射的稳定性，证明了向量优化问题的ξ-有效解集关于单调连续线性泛函是通有稳定的，关于目标映射是通有稳定的，且当单调连续线性泛函和目标映射同时扰动时是通用稳定的。
英文摘要：
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 st - 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.
同期刊论文项目
同项目期刊论文
Stampacchia Vector Equilibrium Problems and Vector Complementarity Problems, Advances in Mathematics
Connectedness and Compactness of Weak Efficient Solutions for Set-Valued Vector Equilibrium Problems
Note on Convergence Theorem of Iterative Sequences for Asymptotically Non-Expansive Mapping in a Uni
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