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凸集值映射的整体误差界 被引量：1

Global error bound for convex multifunctions
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摘要 考虑了凸集值映射的整体误差界,推广Li和Singer(1998)的主要定理到无界情形并肯定地回答了该文的猜想.作为应用,给出了线性Hoffman误差界定理一个简单的新证明. Global error bound for convex multifunctions is considered,the main theorem in Li and Singer (1998) is generalized to the unbounded case,and an affirmative answer to the conjecture is also given.As applications,a new and simple proof for linear Hoffman error bound theorem is given.
作者 黄辉
机构地区 云南大学数学系
出处 《高校应用数学学报（A辑）》 CSCD 北大核心 2003年第3期357-364,共8页 Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金 国家自然科学基金(19861004) 云南省应用基础研究基金
关键词 整体误差界 凸集值映射 线性Hoffman误差界 global error bound convex multifunction linear Hoffman error bound
分类号 O177.91 [理学—基础数学]
  • 相关文献

参考文献10

  • 1Hoffman A. On approximate solutions of systems of linear inequalities[J]. J. Res. Natl. Bur.Standards, 1952,49 : 263-265.
  • 2Luo Zhiqiang,Tseng P. Error bounds and convergence analysis of matrix splitting algorithms forthe affine variational inequality problem[J].SIAM J. Optim. , 1992,2;43-54.
  • 3Mangasarian Q L. Convergence of iterates of an inexact matrix splitting algorithm for the symmetric monotone linear complementarity problem[J]. SIAM J. Optim. , 1991,1 : 114-122.
  • 4Pang Jongshi. Error bounds in mathematical programming[J]. Math. Programming, 1997,79:299-332.
  • 5Li Wu,Singer I. Global error bounds for convex multifunctions and applications[J]. Math. Oper.Res. , 1998,23 : 443-462.
  • 6Robinson S. Regularity and stability for convex multivalued functions[J]. Math. Oper. Res. , 1976,1:130-143.
  • 7Ursecu C. Multifunctions with closed convex graph[J]. Czechoslovak Math. J. , 1975,25:438-411.
  • 8Clarke F H. Optimization and Nonsmooth Analysis[M]. New York:John Wiley & Sons, 1983,51.
  • 9Richard B H. Geometric Functional Analysis and Its Applications [M]. Berlin.. Springer-Verlag,1975,15.
  • 10Rockafellar R T. Convex Analysis[M]. Berlin:Princeton University Press, 1972,171.

同被引文献9

  • 1Richard B H.Geometric Functional Analysis and Its Applications[M].Berlin:Springer-Verlag,1975.
  • 2Hoffman A.On approximate solutions of systems linear inequalities[J].J Res Natl Bur Standards,1952,49:263-265.
  • 3Luo Zhiqiang,Tseng P.Error bounds and convergence analysis of matrix splitting algorithms for the affine variational inequality problem[J].SIAM J Optim,1992,2:43-54.
  • 4Mangasarian Q L.Convergence of iterates of an inexact matrix splitting algorithm for the symmetric monotone linear complementarity problem[J].SIAM J Optim,1991,1:114-122.
  • 5Pang Jongshi.Error bounds in mathematical programming[J].Math Programming(Set B),1997,79:299-332.
  • 6Li Wu,Singer I.Global error bounds for convex multifunction and applications[J].Math Oper Res,1998,23:443-462.
  • 7Robinson S M.Regularity and stability for convex multivalued functions[J].Math Oper Res,1976,1:130-143.
  • 8黄辉.集值映射的误差界[J].中山大学学报（自然科学版）,2003,42(4):12-14. 被引量：1
  • 9郑喜印.集包含的误差界[J].中国科学（A辑）,2003,33(6):631-643. 被引量：1

引证文献1

高校应用数学学报（A辑）
2003年 第3期

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