| 共轭下降法的全局收敛性 |
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| 引用本文： | 袁亚湘.共轭下降法的全局收敛性[J].数学进展,1996,25(6):552-562. |
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| 作者姓名： | 袁亚湘 |
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| 作者单位： | 中国科学院计算数学与科学工程计算研究所 |
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| 摘 要： | 共轭下降法最早由Ｆｌｅｔｃｈｅｒ提出，本文证明了一类非精确线搜索条件能保证共轭下的降法的收敛性，并且构造了反例表明，如果线搜索条件放松，则共轭下降法可能不收敛，此外，我们还得到了与Ｆｌｅｃｈｅｒ－Ｒｅｅｖｅｓ方法有关的一类方法的结论。
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| 关 键 词： | 共轭梯度法 共轭下降法 线搜索 全局收敛性 |
Convergence Properties of the Conjugate Descent Method |
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| Dai Yuhong,Yuan Yaxiang.Convergence Properties of the Conjugate Descent Method[J].Advances in Mathematics,1996,25(6):552-562. |
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| Authors: | Dai Yuhong Yuan Yaxiang |
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| Abstract: | The conjugate descent(CD)method was introduced by Fletcher.This paper investigates its global convergence properties.We prove that a kind of inexact line search conditions can ensure the convergence of the CD method.Several examples are constructed to show that the CD method may fail if the search conditions are relaxed,which implies that our result can not be improved.In addition,we obtain a result on those methods related to the Fletcher-Reeves method. |
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| Keywords: | conjugate gradient method conjugate descent method Fletcher-Reeves method global convergence line search |
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