| 引用本文： |
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黄海,林穗华,姚胜伟.一个基于LS公式修正的新共轭梯度算法[J].广西科学,2007,14(3):244-246,249. [点击复制]
- HUANG Hai,LIN Sui-hua,YAO Sheng-wei.A New Conjugate Gradient Method for Modified LS Formula[J].Guangxi Sciences,2007,14(3):244-246,249. [点击复制]
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| 摘要: |
| 基于LS公式βkLS提出一个求解大规模非线性优化问题的新共轭梯度法公式:βk*=gkT(gk-(‖gk‖)/(‖gk-1‖)gk-1)/(-gk-1Tdk-1),并证明新公式在σ∈(0,1/2)的SWP线搜索下具有充分下降性和全局收敛性.新方法的数值试验结果良好. |
| 关键词: 无约束优化 共轭梯度法 SWP线搜索 全局收敛 |
| DOI： |
| 投稿时间：2006-12-28 |
| 基金项目:广西自然科学基金项目(0542043);南宁师范高等专科学校科研项目(2007012)资助 |
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| A New Conjugate Gradient Method for Modified LS Formula |
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HUANG Hai1, LIN Sui-hua1, YAO Sheng-wei2
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| (1.Department of Mathematics and Computer Science, Nanning Teachers College, Longzhou, Guangxi, 532400, China;2.College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, China) |
| Abstract: |
| A conjugate gradient formula βk* based on modified formula βkLS is proposed.That is βk*=gkT (gk-‖gk‖‖gk-1‖gk-1)/ (-gk-1Tdk-1).It is proved that under the strong Wolfe-Powell line search and the parameter σ∈ (0, 1/2), the corresponding method has sufficient descent and global convergence properties.Preliminary numerical results show that the proposed method is very promising. |
| Key words: unconstrained optimination conjugate gradient method SWP line search global convergence |
