| 一个修正HS共轭梯度法及其收敛性 |
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| 引用本文： | 韦增欣,黄海东,陶艳蓉. 一个修正HS共轭梯度法及其收敛性[J]. 数学研究及应用, 2010, 30(2): 297-308. DOI: 10.3770/j.issn:1000-341X.2010.02.013 |
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| 作者姓名： | 韦增欣 黄海东 陶艳蓉 |
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| 作者单位： | 广西大学数学与信息科学学院, 广西 南宁 530004;广西大学数学与信息科学学院, 广西 南宁 530004;广西大学数学与信息科学学院, 广西 南宁 530004 |
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| 基金项目： | 国家自然科学基金 (Grant No.,10761001). |
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| 摘 要： | It is well-known that the direction generated by Hestenes-Stiefel (HS) conjugate gradient method may not be a descent direction for the objective function. In this paper, we take a little modification to the HS method, then the generated direction always satisfies the sufficient descent condition. An advantage of the modified Hestenes-Stiefel (MHS) method is that the scalar βkH Sffikeeps nonnegative under the weak Wolfe-Powell line search. The global convergence result of the MHS method is established under some mild conditions. Preliminary numerical results show that the MHS method is a little more efficient than PRP and HS methods.
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| 关 键 词： | 共轭梯度法 全局收敛性 Powell MHS 下降方向 目标函数 计算结果 HS方法 |
| 收稿时间： | 2007-12-22 |
| 修稿时间： | 2008-05-21 |
A Modified Hestenes-Stiefel Conjugate Gradient Method and Its Convergence |
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| Zeng Xin WEI,Hai Dong HUANG and Yan Rong TAO. A Modified Hestenes-Stiefel Conjugate Gradient Method and Its Convergence[J]. Journal of Mathematical Research with Applications, 2010, 30(2): 297-308. DOI: 10.3770/j.issn:1000-341X.2010.02.013 |
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| Authors: | Zeng Xin WEI Hai Dong HUANG Yan Rong TAO |
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| Affiliation: | College of Mathematics and Information Science,Guangxi University,Guangxi 530004,P.R.China |
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| Abstract: | It is well-known that the direction generated by Hestenes-Stiefel (HS) conjugate gradient method may not be a descent direction for the objective function. In this paper, we take a little modification to the HS method, then the generated direction always satisfies the sufficient descent condition. An advantage of the modified Hestenes-Stiefel (MHS) method is that the scalar $beta_{k}^{HS*}$ keeps nonnegative under the weak Wolfe-Powell line search. The global convergence result of the MHS method is established under some mild conditions. Preliminary numerical results show that the MHS method is a little more efficient than PRP and HS methods. |
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| Keywords: | conjugate gradient method sufficient descent condition line search global convergence. |
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