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一种充分下降的DY共轭梯度法及其收敛性 被引量：6

A sufficient descent DY conjugate gradient method and its global convergence
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摘要 基于已有的DY方法和HZ方法,提出了一种修正的DY共轭梯度法(MDY算法)。该算法产生的搜索方向为充分下降方向,且这一性质与所采用的线搜索方法无关。在一定的条件下证明了保守MDY算法(CMDY算法)基于Armijo线搜索和Wolfe线搜索求解非凸优化问题的全局收敛性。相关的数值试验结果验证了该方法的有效性。 A modified DY conjugate gradient method（MDY） is proposed based on the DY method and HZ method. This method can generate sufficient descent directions for the objective functions, and this property is independent of the line search method used. Under mild conditions, it is proved that the conservative MDY method with Armijo line search or Wolfe line search converges globally even if the minimization function is nonconvex. Numerical results show that the proposed method is efficient.
作者 李敏 陈宇 屈爱平
机构地区 怀化学院数学系
出处 《山东大学学报（理学版）》 CAS CSCD 北大核心 2011年第7期101-105,111,共6页 Journal of Shandong University(Natural Science)
基金 怀化学院资金资助项目(HHUQ2009-01)
关键词 充分下降 DY方法 ARMIJO线搜索 WOLFE线搜索 全局收敛 sufficient descent DY method Armijo line search Wolfe line search global convergence
分类号 O224 [理学—运筹学与控制论]
  • 相关文献

参考文献8

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二级参考文献12

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共引文献10

同被引文献29

  • 1李梅霞,王长钰.线搜索下带误差项的Dai-Yuan共轭梯度算法(英文)[J].工程数学学报,2006,23(5):891-900. 被引量：6
  • 2潘翠英,陈兰平.求解无约束优化问题的一类新的下降算法[J].应用数学学报,2007,30(1):88-98. 被引量：19
  • 3戴或虹,袁亚湘.非线性共轭梯度法[M].上海:上海科学技术出版社,2001.
  • 4Fletcher R, Reeves C. Function minimization by conjugate gradients[J]. Computer Journal, 1964, 7: 149-154.
  • 5Polak E, Ribiere G. Note sur la eonvergenee de diretions eonjugees [J]. Rev fran-eaise informat recherche opertionelle, 1969, 16 35-43.
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  • 8Liu Y, Storey C. Effcient generalized conjugate gradient algorithms [J] . Journal of optimiztion theory and applicatons, 1991, 69: 129-137.
  • 9Dai Y H, Yuan Y. A nonlinear conjugate gradient with a strong global conver-gence property [J] . Siam Journal on optimizton, 2000, 10: 177-182.
  • 10DAI YUHONG, LIAO LIZHI. New conjugate condi- tions and related nonlinear conjugategradient methods [ J]. Applied Mathematics and Optimization, 2001, 43: 87-101.

引证文献6

二级引证文献13

山东大学学报（理学版）
2011年 第7期

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