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使用拟牛顿迭代公式的广义共轭梯度法

邓乃扬,陈志   

  1. 北京工业大学 ,北京工业大学
  • 出版日期:1983-04-14 发布日期:1983-04-14

邓乃扬,陈志. 使用拟牛顿迭代公式的广义共轭梯度法[J]. 计算数学, 1983, 5(4): 435-443.

CENERALIZED CONJUGATE GRADIENT METHODS WITH QUASI-NEWTON UPDATES

  1. Deng Nai-yang;Chen Zhi Beijing Polytechnique University
  • Online:1983-04-14 Published:1983-04-14
当容易计算目标函数f的梯度g(x)= f(x),但存贮不允许使用完整的拟牛顿法(QN)时,广义共轭梯度法(CG)_H是一个很有前途的方法.它的基本迭代公式是
Consider the unconstrained optimization problems. When the computer storage is notenough to execute a complete Quasi-Newton method, QN+GCG type method (the combina-tion of Quasi-Newton method and generalized conjugate gradient method) is prospective.This paper proposes a method, in Which the generalized QN updates are used as much aspossible, moreover, a more reasonable precondition matrix H can be constructed.
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[1] R.Fletcher, Practical methods of optimization, Vol. 1, 1980.
[2] M. R. Hesteness, Conjugate direction methods in optimization, 1980.
[3] A. G. Buckley, Conjugate gradient metrods. NATO Advanced Research Institute on Nonlinear Optimization, Cambridge, England. July, 13th--24th. 1981.
[4] 邓乃扬,陈志,一个采用新重新开始策略的共轭梯度法,北京工业大学学报,8(1982) ,No.3,74-80.
[5] R. Fletcher, A new approach to variable metric algorithms, Computer J.,13(1970) . 317-322.
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