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一类修正LS谱共轭梯度法的全局收敛性
  • ISSN号：1672-6693
  • 期刊名称：《重庆师范大学学报：自然科学版》
  • 时间：0
  • 分类：O221.2[理学—运筹学与控制论;理学—数学]
  • 作者机构：[1]重庆师范大学数学学院,重庆401331, [2]西华大学数学与计算机科学学院,成都610039, [3]泸州高级中学,四川泸州646000
  • 相关基金：国家自然科学基金（No.10971241;No.11171363）;重庆师范大学自然科学基金（No.08XLR022）
作者： 胡鹏[1,3], 杜学武[1], 郭翠峰[2]
关键词： 修正的Liu-Storey共轭梯度法, ARMIJO型线搜索, 全局收敛性, modified Liu Storey conjugate gradient, Arrmijo-type line search~ global convergence
中文摘要：

谱共轭梯度法是一类将共轭梯度法和谱梯度法相结合的方法。2001年由Birgin和Martinez首先提出,但该方法不能保证始终产生下降方向。本文用已有的修正方法,给出一个修正的Liu-Storey公式,并结合谱梯度法,提出了一个具有充分下降性的修正Liu-Storey谱共轭梯度法,证明了该方法在标准Armijo非精确线搜索下的全局收敛性,并易推知该方法在Armijo-Goldstein非精确线搜索准则下同样满足全局收敛性。给出的数值实验表明,新算法略优于LS方法。

英文摘要：

Spectral conjugate gradient method is a kind of method that combines conjugate gradient method with spectral gradient meth- od. In 2001, it was first put forward by Birgin and Martinez in [8], but this method can not always guarantee to generate descent di- rections. This paper first gives out a modified Liu-Storey formula which uses the modified method given by literature ~10~, and then combines the modified Liu-Storey formula with the spectral gradient method, putting forward a modified Liu-Storey spectral conjugate gradient method satisfying the sufficient descent condition. And the global convergence of the method with the standard Armijo inexact line search is proved; it is easy to deduce the method also satisfying the global convergence under the Armijo-Goldstein inexact line search rule. The given numerical results show that the new method is a little better than LS method.

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期刊信息
  • 《重庆师范大学学报：自然科学版》
  • 北大核心期刊（2011版）
  • 主管单位:重庆市教育委员会
  • 主办单位:重庆师范大学
  • 主编：杨新民
  • 地址：重庆市沙坪坝区
  • 邮编：400047
  • 邮箱：cqnuj@cqnu.edu.cn
  • 电话：023-65362431
  • 国际标准刊号：ISSN：1672-6693
  • 国内统一刊号：ISSN：50-1165/N
  • 邮发代号:78-34
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  • 被引量:4584