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一类求解单调变分不等式的隐式方法 被引量:10

A CLASS OF IMPLICIT METHODS FOR MONOTONE VARIATIONAL INEQUALITIES
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摘要 In this paper we introduce a class of iterative methods for solution of monotone variational inequalities. The method can be viewed as an extension of the Levenberg-Marquardt method for unconstrained optimization, or the generalization of the Douglas-Rachford operator splitting methods when applied to monotone variational inequalities. Each iteration of the method consists essentially of solving a system of nonlinear equations. The convergence proof for the presented method is very In this paper we introduce a class of iterative methods for solution of monotone variational inequalities. The method can be viewed as an extension of the Levenberg-Marquardt method for unconstrained optimization, or the generalization of the Douglas-Rachford operator splitting methods when applied to monotone variational inequalities. Each iteration of the method consists essentially of solving a system of nonlinear equations. The convergence proof for the presented method is very simple
作者 何炳生
机构地区 南京大学数学系
出处 《计算数学》 CSCD 北大核心 1998年第4期337-344,共8页 Mathematica Numerica Sinica
基金 国家自然科学基金!19671041 江苏省自然科学基金 国家教委博士点专项基金
关键词 变分不等式 隐式方法 单调变分不等式 收敛性 variational inequality, implicit method
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参考文献11

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同被引文献23

  • 1P. T. HARKER,J. S. PANG. Finite-dimensional variational inequality and nonlinear complementarity problems: A survery of theory, algorithms and applications[J]. Math.Progr. ,1990, 48(2): 161-220.
  • 2B. C. EAVES. On the basic theorem of complementarity[J].Math. Progr. ,1983, 26:40-47.
  • 3S. L. WANG, H. YANG,B. S. HE. Solving a class of asymmetric variational inequalities by a New alternating direction method[J]. Comp. and Math. with Appl. 2000,40:927-937.
  • 4B. S. HE. Inexact implicit methods for monotone general variational inequalities[J]. Math. Progr. 1999,86:199-217.
  • 5B. S. HE,L. Z. LIAO. Improvements of some projection methods for monotone nonlinear variational inequalities[J].Opt. Theory and appl. 2002, 112(1) :111-128.
  • 6HARKER P T,PANG J S.Finite-dimensional variational inequality and nonlinear complementarity problems:a survery of theory,algorithms and applications[J].Math Progr,1990,48(2):161-220.
  • 7EAVES B C.On the basic theorem of complementarity[J].Math Progr,1971,1(1):68-75.
  • 8WANG S L,YANG H,HE B S.Solving a class of asymmetric variational inequalities by a new alternating direction method[J].Comp and Math with Appl,2000,40(8):927-937.
  • 9HE B S.Inexact implicit methods for monotone general variational inequalities[J].Math Progr,1999,86(1):199-217.
  • 10P. T. HARKER, J. S. PANG. Finite-dimensional variational inequality and nonlinear complementarity problems: A survery of theory, algorithms and applications[J]. Math. Progr. , 1990, 48(2) : 161-220.

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