| 一种充分下降的DY共轭梯度法及其收敛性 |
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| 引用本文： | 李敏,陈宇,屈爱平.一种充分下降的DY共轭梯度法及其收敛性[J].山东大学学报(理学版),2011,46(7):101-105,111. |
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| 作者姓名： | 李敏 陈宇 屈爱平 |
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| 作者单位： | 怀化学院数学系,湖南怀化,418008 |
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| 基金项目： | 怀化学院资金资助项目(HHUQ2009-01) |
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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。
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| 关 键 词： | 充分下降 DY方法 Armijo线搜索 Wolfe线搜索 全局收敛 |
A sufficient descent DY conjugate gradient method and its global convergence |
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| LI Min,CHEN Yu,QU Ai-ping.A sufficient descent DY conjugate gradient method and its global convergence[J].Journal of Shandong University,2011,46(7):101-105,111. |
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| Authors: | LI Min CHEN Yu QU Ai-ping |
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| Institution: | LI Min,CHEN Yu,QU Ai-ping(Department of Mathematics and Applied mathematics,Huaihua University,Huaihua 418008,Hunan,China) |
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| Abstract: | 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. |
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| Keywords: | sufficient descent DY method Armijo line search Wolfe line search global convergence |
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