WANG Zheng-yu, SHEN Zu-he. Kantorovich Theorem for Variational Inequalities[J]. Applied Mathematics and Mechanics, 2004, 25(11): 1182-1188.
Citation: WANG Zheng-yu, SHEN Zu-he. Kantorovich Theorem for Variational Inequalities[J]. Applied Mathematics and Mechanics, 2004, 25(11): 1182-1188.

Kantorovich Theorem for Variational Inequalities

  • Received Date: 2002-10-01
  • Rev Recd Date: 2004-05-06
  • Publish Date: 2004-11-15
  • Kantorovich theorem was extended to variational inequalities by which the convergence of Newton iteration, the existence and uniqueness of the solution of the problem can be tested via computational conditions at the initial point.
  • loading
  • [1]
    Eaves B C.A locally quadratically convergent algorithm for computing stationary point[R]. Department of Operations Research,Stanford University,1978.
    [2]
    Josephy N H.Newton's method for generalized equations[R]. Mathematics Research Center,University of Wisconsin,1979.
    [3]
    Harker P T,Pang J S.Finite-dimensional variational inequalities and non-linear complementarity problems:a survey of theory,algorithms and applications[J].Mathematical Programming,1990,48(2):161—220. doi: 10.1007/BF01582255
    [4]
    Robinson S M.Generalized equations and their solutions[J].Mathematical Programming Study,1979,10(1):128—141. doi: 10.1007/BFb0120850
    [5]
    Robinson S M.Strongly regular generalized equations[J].Mathematics of Operations Research,1980,5(1):43—62. doi: 10.1287/moor.5.1.43
    [6]
    Kantorovich L V.Functional analysis and applied mathematics[J].Uspehi Mat Nauk,1948,3(6):89—185.
    [7]
    Ortega J M,Rheinboldt W C.Iterative Solutions of Nonlinear Equations in Several Variables[M].New York:Academic Press,1970.
    [8]
    Stampacchia G.Variational inequalities[A].In:Stampacchia G Ed.Theory and Applications of Monotone Operators,Proceedings of the NATO Advanced Study Institute[C].Venice:Edizioni Oderisi,Gubbio,1968,102—192.
    [9]
    Rall L B.Computational Solution of Nonlinear Operator Equations[M].New York:Wiely,1969.
    [10]
    Alefeld G E,Herzberger J.Introduction to Interval Computations[M].New York and London:Academic Press,1983.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2764) PDF downloads(732) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return