| 下降对称的Polak-Ribiere-Polyak共轭梯度法 |
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| 引用本文： | 刘东毅,邵琛.下降对称的Polak-Ribiere-Polyak共轭梯度法[J].天津大学学报(自然科学与工程技术版),2010,43(4). |
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| 作者姓名： | 刘东毅 邵琛 |
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| 作者单位： | 刘东毅,LIU Dong-yi(天津大学理学院,天津,300072;天津大学电气与自动化工程学院,天津,300072);邵琛,SHAO Chen(天津大学理学院,天津,300072) |
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| 基金项目： | 国家自然科学基金，国家自然科学基金杰出青年科学基金 |
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| 摘 要： | 应用Powell对称化技术于Polak-Ribiere-Polyak共轭梯度法,提出了一种下降对称的Polak-Ribiere-Polyak共轭梯度法.对任意线性搜索,它都满足下降性质.在强Wolfe线搜索的条件下,利用矩阵的谱分析和Zoutendijk条件,证明了此算法的全局收敛性.最后,通过数值实验并且与Polak-Ribiere+(PR+)算法作比较,验证了该算法的性能和有效性与实用性.
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| 关 键 词： | 共轭梯度法 全局最优化 算法 对称化技术 下降性质 线搜索 谱分析 全局收敛性 |
Descent Symmetrical Polak-Ribiere-Polyak Conjugate Gradient Method |
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| LIU Dong-yi,SHAO Chen.Descent Symmetrical Polak-Ribiere-Polyak Conjugate Gradient Method[J].Journal of Tianjin University(Science and Technology),2010,43(4). |
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| Authors: | LIU Dong-yi SHAO Chen |
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| Institution: | LIU Dong-yi1,2,SHAO Chen3(1.School of Sciences,Tianjin University,Tianjin 300072,China,2.School of Electrical Engineering , Automation,3.School of Applied Science,Harbin University of Science , Technology,Harbin 150080,China) |
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| Abstract: | Applying Powell symmetrical technique to the Polak-Ribiere-Polyak conjugate gradient method,a descent symmetrical Polak-Ribiere-Polyak conjugate gradient method was proposed,which satisfied the descent property for any line search.Under the strong Wolfe line search conditions,the global convergence of the new method was testified by the spectral analysis of matrix and Zoutendijk condition.Finally,compared with the Polak-Ribiere+(PR+) algorithm,the performance and the availability of the new algorithm are ve... |
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| Keywords: | conjugate gradient method global optimization algorithm symmetrical technique descent property line search spectral analysis global convergence |
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