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下降对称的Polak-Ribiere-Polyak共轭梯度法
  • ISSN号：0493-2137
  • 期刊名称：《天津大学学报：自然科学与工程技术版》
  • 时间：0
  • 分类：O241.6[理学—计算数学;理学—数学]
  • 作者机构：[1]天津大学理学院,天津300072, [2]天津大学电气与自动化工程学院,天津300072, [3]哈尔滨理工大学应用科学学院,哈尔滨150080
  • 相关基金：国家自然科学基金资助项目（60874034）;国家自然科学基金青年科学基金资助项目（60704015）
作者： 刘东毅[1,2], 邵琛[3]
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, conjugate gradient method , global optimization , algorithm , symmetrical technique , descent property, line search, spectral analysis, global convergence
中文摘要：

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．

英文摘要：

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 verified by numerical experiments.

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期刊信息
  • 《天津大学学报：自然科学与工程技术版》
  • 北大核心期刊（2011版）
  • 主管单位:
  • 主办单位:天津大学
  • 主编：单平
  • 地址：天津市南开区
  • 邮编：300072
  • 邮箱：
  • 电话：022-27403448
  • 国际标准刊号：ISSN：0493-2137
  • 国内统一刊号：ISSN：12-1127/N
  • 邮发代号:6-27
  • 获奖情况:
  • 中国期刊方阵双效期刊
  • 国内外数据库收录:
  • 美国数学评论（网络版）,美国剑桥科学文摘,中国中国科技核心期刊,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）
  • 被引量:6410