| GLOBAL CONVERGENCE OF THE DAI-YUAN CONJUGATE GRADIENT METHOD WITH PERTURBATIONS |
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| 引用本文： | Changyu WANG Meixia LI. GLOBAL CONVERGENCE OF THE DAI-YUAN CONJUGATE GRADIENT METHOD WITH PERTURBATIONS[J]. 系统科学与复杂性, 2007, 20(3): 416-428. DOI: 10.1007/s11424-007-9037-y |
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| 作者姓名： | Changyu WANG Meixia LI |
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| 作者单位： | [1]Institute of Operations Research, Qufu Normal University, Qufu 273165, China. [2]Department of Mathematics, Weifang University, Weifang 261061, China. |
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| 基金项目： | The work is supported by the National Natural Science Foundation of China under Grant No. 10571106. |
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| 摘 要： | In this paper, the authors propose a class of Dai-Yuan （abbr. DY） conjugate gradient methods with linesearch in the presence of perturbations on general function and uniformly convex function respectively. Their iterate formula is xk＋1 = xk ＋ αk（sk ＋ ωk）, where the main direction sk is obtained by DY conjugate gradient method, ωk is perturbation term, and stepsize αk is determined by linesearch which does not tend to zero in the limit necessarily. The authors prove the global convergence of these methods under mild conditions. Preliminary computational experience is also reported.
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| 关 键 词： | 共轭梯度法 整体收敛 扰动 凸函数 |
| 修稿时间： | 2005-03-04 |
Global Convergence of the Dai-Yuan Conjugate Gradient Method with Perturbations |
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| Changyu Wang,Meixia Li. Global Convergence of the Dai-Yuan Conjugate Gradient Method with Perturbations[J]. Journal of Systems Science and Complexity, 2007, 20(3): 416-428. DOI: 10.1007/s11424-007-9037-y |
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| Authors: | Changyu Wang Meixia Li |
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| Affiliation: | (1) Institute of Operations Research, Qufu Normal University, Qufu, 273165, China;(2) Department of Mathematics, Weifang University, Weifang, 261061, China |
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| Abstract: | In this paper, the authors propose a class of Dai-Yuan (abbr. DY) conjugate gradient methods with linesearch in the presence of perturbations on general function and uniformly convex function respectively. Their iterate formula is x k+1 = x k + α k (s k + ω k ), where the main direction s k is obtained by DY conjugate gradient method, ω k is perturbation term, and stepsize α k is determined by linesearch which does not tend to zero in the limit necessarily. The authors prove the global convergence of these methods under mild conditions. Preliminary computational experience is also reported. The work is supported by the National Natural Science Foundation of China under Grant No. 10571106. |
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| Keywords: | Conjugate gradient method global convergence perturbation uniformly convex. |
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