| 含参数Dai-Yuan共轭梯度法及其收敛性 |
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| 引用本文： | 张劲松,李红. 含参数Dai-Yuan共轭梯度法及其收敛性[J]. 华东交通大学学报, 2008, 25(1): 127-129 |
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| 作者姓名： | 张劲松 李红 |
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| 作者单位： | 九江学院 理学院 江西 九江 332005;九江学院 理学院 江西 九江 332005 |
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| 基金项目： | 江西省高校省级教改重点资助项目(JXJG-07-17-47) |
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| 摘 要： | 通过对Dai-Yuan共轭梯度法的分析，将βk^KY推广到更一般的形式．根据搜索方向的下降性要求，得出含参数Dai—Yuan共轭梯度法．在Wolfe条件下，证明了方法的收敛性；在强Wolfe条件下，证明了方法的充分下降性．含参数Dai-Yuan共轭梯度法不仅仅是Dai—Yuan共轭梯度法在形式上的推广，其参数的合理选择有望使Dai-Yuan共轭梯度法良好的数值表现得到进一步改善．
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| 关 键 词： | Dai-Yuan共轭梯度法 Wolfe条件 收敛性 充分下降性 |
| 文章编号： | 1005-0523(2008)01-0127-03 |
| 修稿时间： | 2007-12-17 |
Dai-Yuan Conjugate Gradient Method with Parameter and Its Convergence |
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| ZHANG Jin-song,LI Hong. Dai-Yuan Conjugate Gradient Method with Parameter and Its Convergence[J]. Journal of East China Jiaotong University, 2008, 25(1): 127-129 |
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| Authors: | ZHANG Jin-song LI Hong |
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| Affiliation: | ( College of Science, Jiujiang University, Jiujiang 332005, China) |
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| Abstract: | Through the analysis of Dai-Yuan conjugate gradient method,βk^KY will be generalized to a more common form. According to the request of descent property of searching direction, Dai-Yuan conjugate gradient method with parameter is obtained. In the condition of Wolfe line search, its convergence is proved ; in the condition of Strong Wolfe line search, its plenary descent property is proved. Dai-Yuan conjugate gradient method with parameter is generalizing its form, the ratio- nal election of its parameter is also expected to improve the better numerical representation of Dai-Yuan conjugate gradient method. |
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| Keywords: | Dai-Yuan conjugate gradient wolfe condition convergence plenary descent property. |
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