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| 一种新的非线性共轭梯度法及收敛性 | |
| 引用本文： | 刘金魁,王开荣,杜祥林,贾松芳.一种新的非线性共轭梯度法及收敛性[J].数值计算与计算机应用,2009,30(4):247-254. |
| 作者姓名： | 刘金魁 王开荣 杜祥林 贾松芳 |
| 作者单位： | 1. 重庆二峡学院,数学与计算机科学学院,重庆万州,404000 2. 重庆大学数理学院,重庆,400030 3. 重庆三峡学院,数学与计算机科学学院,重庆万州,404000 |
| 摘 要： | 在LS方法基础上,提出了一种新的求解无约束最优化问题的共轭梯度法.新方法通过一个新的公式计算参数,克服了LS方法的数值效果不稳定和收敛性弱的缺点,并且在强Wolfe线搜索下证明了该方法具有充分下降性和全局收敛性.大量的数值试验表明新方法是稳定的、有效的. |
| 关 键 词： | 无约束优化 共轭梯度法 强Wolfe线搜索 充分下降性 全局收敛性 |
GLOBAL CONVERGENCE OF A NEW NONLINEAR CONJUGATE GRADIENT METHOD |
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| Liu Jiukui,Wang Kairong,Du Xianglin,Jia Songfang.GLOBAL CONVERGENCE OF A NEW NONLINEAR CONJUGATE GRADIENT METHOD[J].Journal on Numerical Methods and Computer Applications,2009,30(4):247-254. | |
| Authors: | Liu Jiukui Wang Kairong Du Xianglin Jia Songfang |
| Affiliation: | Liu Jiukui (College of Mathematics and Computer Science, Chongqing Three Gorges University, Chongqing Wanzhou 404000, China) Wang Kairong (College of Mathematics and Physics, Chongqing University, Chongqing 400030, China) Du Xianglin Jia Songfang (College of Mathematics and Computer Science, Chongqing Three Gorges University, Chongqing Wanzhou 404000, China) |
| Abstract: | A new conjugate gradient mehod is proposed to solve unconstrained optimization prob-lems on the basis of LS method. We adopt a new formula for calculating parameter in the new mehod which can overcome the effects of the LS method in numerical instability and weak convergence of the deficiencies. And under the strong Wolfe line search, the sufficient descent property and the global convergence of the new mehod was proved. A large number of numerical experiments show that the new mehod is stable and effective. |
| Keywords: | Unconstrained optimization Conjugate gradient method Strong Wolfe line search Sufficient descent property Global convergence |
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