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一类广义隐互补问题的外梯度法 被引量：3

The Extragradient Algorithm for a Form of Generalized Implicit Complementarity Problem
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摘要 隐互补问题在自然科学中的诸多领域有着广泛的应用.本文研究了一类广义隐互补问题.本文将外梯度法应用到这类广义隐互补问题中,研究了在伪单调的条件下算法的收敛性,并证明了算法具有R-线性收敛性. Implicit complementarity problem（ICP） can be applied to many fileds of natural science.In this article,we study a form of generalized implicit complementarity problem. The extragradient method is used to solve ICP.The extragradient algorithm is built about generalized implicit complementarity problem and porve its convergence with pseudomonotone function.
作者 郑邦贵 殷洪友
机构地区 南京工业大学理学院应用数学系 南京航空航天大学理学院
出处 《应用数学学报》 CSCD 北大核心 2011年第4期734-742,共9页 Acta Mathematicae Applicatae Sinica
关键词 广义隐互补问题 外梯度法 R-线性收敛性 generalized implicit complementarity problem the extragradient algorithm R-linearly convergence
分类号 O211.2 [理学—概率论与数理统计]
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参考文献10

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  • 2Levitin E S, Polyak B T. Constrained Minimization Problems. J. USSR Comput. Math. Math. Phys., 1966, 6:1-50.
  • 3Korpelevich G M. The Extragradient Method for Finding Saddle Points ad other Problems. J. Matecon, 1976, 12:747-756.
  • 4韩继业,修乃华,戚厚铎.非线性互补理论与算法.上海:科学技术出版社,2003.
  • 5Ahmad K, Kazmi K R, Rehman N. Fixed-point technique for implicit comlementarity problem in Hilberet lattice. J. Journal of Optimization Theory and Applications, 1997, 93:72-97.
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  • 8Noor M A. Change of Variable Method for Generalized Complementarity. J. Problems Journal Of Optimization Theory and Applications, 1999, 389--395.
  • 9Noor M A. Projection Iterative Methods for Extended General Variational Inequalities. J. Appl. Math. Comput., 2010, 32:83-95.
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同被引文献33

  • 1韩继业,修乃华,戚厚铎.非线性互补理论与算法[M].上海:上海科学技术出版社,2003.
  • 2Goldstein A A. Convex programming in Hilbert space[ J]. Bull Am Math Soc, 1964,70:709.
  • 3Levitin E S, Polyak B T, Constrained minimization problems[J]. USSR Comput Math Math Phys,1966,6:1.
  • 4Korpelevich G M. The extragradient method for finding saddle points and other problems[ J]. Matecon, 1976,12:747.
  • 5He B S, Yuan X M, Zhang J Z. Comparison of two kinds of prediction - correction methodsfor monotone variational inequalities[J]. Comput Optim Appl,2004,27:247 - 267.
  • 6Yan X H, Han D R, Sun W Y. A serf - adaptive projection method with improved step - size for solving variational inequalities[J]. Comput Math Appl,2008,55 (4) :819 - 832.
  • 7Xu M H, Yuan X M, Huang Q L. An improved general extra - gradient method with refined step size for nonlinear monotone vari- ational inequalities[J]. J Glob Optim ,2007 ,39 : 155 - 169.
  • 8Abroad K, Kazmi K R, Rehman N. Fixed -point technique for implicit comlementarity problem in Hilberet lattice[ J ]. J Optim Theo Appl, 1997,93:72 - 97.
  • 9Noor M A. Projection iterative methods for extended general variational inequalities [ J ]. J Appl Math Comput,2010,32:83 -95.
  • 10Farouq N El. Pseudomonotone variational inequalities : Convergence of the auxiliary problem method [ J ]. J Optim Theo Appl, 2001,111 (2) :305 -326.

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应用数学学报
2011年 第4期

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