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向量优化问题中ξ-有效解的通有稳定性 被引量：3

Generic Stability of the ξ-efficient Solutions In Vector Optimization Problems
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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。 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.
作者 陈剑尘 龚循华
机构地区 南昌大学数学系
出处 《南昌大学学报（理科版）》 CAS 北大核心 2007年第4期307-311,共5页 Journal of Nanchang University(Natural Science)
基金 国家自然科学基金资助项目(10561007) 江西省自然科学基金资助项目(01110067)
关键词 ξ-有效解 usco映射 通有稳定性 ξ - efficient solution usco mapping generic stability
分类号 O021 [理学]
  • 相关文献

参考文献13

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二级参考文献11

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共引文献9

同被引文献48

  • 1彭定涛,曹素元.上图像拓扑与多目标优化问题加权解的通有稳定性[J].运筹学学报,2006,10(4):81-88. 被引量：10
  • 2Fu J Y. Symmetric vector quasi-equilibrium problems. Journal of Mathematical Analysis and Applications, 2003, 285:708-713.
  • 3Yu J, Xiang S W. The stability of the set of KKM points. Nonlinear Analysis, 2003, 54:839-844.
  • 4Lin Z. The study of the system of generalized vector quasi-equilibrium problems. Journal of Global Optimization, 2006, 36:627-635.
  • 5Isac G, Yuan X Z. The Existence of Essentially Connected Components of Solutions for Variational Inequalities//Giannes F, eds. Vector Variational Inequalities and Vector Equilibria. Netherlands: Kluver Acadmic Publishers. 2000:253-265.
  • 6Zhou Y H, Xiang S W, Yang H. Stability of solutions for Ky Fan's section theorem with some applications. Nonlinear Analysis, 2005, 62:1127-1136.
  • 7Xiang S W, Zhou Y H. On essential sets and essential components of efficient solutions for vector optimization problems. Journal of Mathematical Analysis and Applications, 2006, 315:317-326.
  • 8Yu J, Yang H. The essential components of the of equilibrium points for set-valued maps. Journal of Mathematics Applications, 2004, 300:334-342.
  • 9Isac G, Yuan G X Z. The essential components of coincident points for weakly inward and outward set- valued mappings. Applied Mathematics Letters, 1999, 12:121-126.
  • 10Yang H, Yu J. Essential components of the set of weakly Pareto-Nash equilibrium points. Appl Math Lett, 2002, 15:553-560.

引证文献3

二级引证文献12

南昌大学学报（理科版）
2007年 第4期

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