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广义线性互补问题的共轭梯度算法

CONJUGATE GRADIENT ALGORITHM FOR GENERAL LINEAR COMPLEMENTARITY PROBLEM
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摘要 本文构造了广义线性互补问题的一个光滑价值函数,该函数具有良好的微分性质.基此价值函数提出了求解广义线性互补问题的一类不精确线搜索共轭梯度算法,证明了算法的全局收敛性,并通过数值试验检验了算法的实用性. In this paper,a smooth merit function is constructed for general linear complementarity problem （GLCP）,which possesses fine coercive property. A kind of conjugate gradient algorithm with an inexact line search is proposed for GLCP and global convergence of the method is proved. Numerical results show that this method promises
作者 王华 乌力吉
机构地区 内蒙古工业大学理学院数学系
出处 《内蒙古工业大学学报（自然科学版）》 2008年第1期6-12,共7页 Journal of Inner Mongolia University of Technology：Natural Science Edition
基金 内蒙古工业大学科研基金项目(X200614)资助
关键词 广义线性互补问题 共轭梯度算法 全局收敛 general linear complementarity problem conjugate gradient algorithm globalconvergence
分类号 O224 [理学—运筹学与控制论]
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参考文献6

  • 1Fernandes L,Friedlander A,et al.Solution of a General Liner Complementarity Problem Using Smooth Optimization and Its Application to Biliner Programming LCP[J].Appl Math Optim,2001,43:1-19.
  • 2Birgin E G,Martinez J M.A Spectral Conjugate Gradient Method for Unconstrained Optimization[J].Appl.Math,Optim,2001,43:117-128.
  • 3Dai Y H,Liao L Z.New Conjugacy Conditions and Related Nonliner Conjugate Gradient Methods[J].Appl,Math,Optim,2001,43:87-101.
  • 4乌力吉,陈国庆.非线性互补问题的一种新的光滑价值函数及牛顿类算法[J].计算数学,2004,26(3):315-328. 被引量：9
  • 5袁亚湘 孙文瑜.最优化理论与方法[M].北京:科学出版社,1995..
  • 6Jiang H Y,Qi Q.A New Nonsmooth Equations Approach to Nonlinear Complementarity Problems[J].J.Control Optim,1997,35:178-193.

二级参考文献18

  • 1G. Isac, Complementarity problems, Springer-Verlag, Berlin, 1992.
  • 2F. Facchinei and J.-S. Pang, Finite-dimensional variational inequalities and complementarity problems, Springer-Verlag, New York, 2003.
  • 3M. C. Ferris and J. S. Pang, Engineering and ecnomic applications of complementarity problems, SIAM J. Review, 39 (1997), 669-713.
  • 4R. W.Cottle, J. S Pang and R. E. Stone, The linear complementarity problem, ComputerScience and Scientific Computing, Academic Press, San Diego, CA, 1990
  • 5D. Sun and L.Qi, On NCP-functions, Computational Optimization and Applications, 13(1999), 201-220.
  • 6A. Fischer and H. Jiang, Merit functions for complementarity and related problems: A survey, Computational Optimization and Applications, 17 (2000), 159-182.
  • 7B. Chen and N. Xiu, A global and local quadratic noninterior continuation smoothing method for nonlinear complementarity problems based on Chen-Mangasarian smoothing functions, SIAM J. Optim., 9 (1999), 605-623.
  • 8C. Kanzow and H. Pieper Jacobian smoothing methods for general nonlinear complementarity problems, SIAM J. Optim., 9 (1999), 342-373.
  • 9B. Chen and P. T. Harker, A non-interior-point continuation method for linear complementarity problems, SIAM J. Matrix Anal. Appl., 14 (1993), 1168-1190.
  • 10C. Kanzow Some noninterior continuation methods for linear complementarity problems,SIAM J. Matrix Anal. Appl., 17 (1996), 851-868.

共引文献13

内蒙古工业大学学报（自然科学版）
2008年 第1期

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