| 一个充分下降的改进HS共轭梯度法 |
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| 引用本文： | 江羡珍,黎会兰,刘美杏,班才竣,马月梅,欧勇伟. 一个充分下降的改进HS共轭梯度法[J]. 数学的实践与认识, 2020, 0(5): 155-164 |
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| 作者姓名： | 江羡珍 黎会兰 刘美杏 班才竣 马月梅 欧勇伟 |
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| 作者单位： | 广西民族大学理学院;玉林师范学院广西高校复杂系统优化与大数据处理重点实验室 |
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| 基金项目： | 广西自然科学基金(2016GXNSFAA380028);广西高校复杂系统优化与大数据处理重点实验室开放基金(2015CSOBDP0203);大学生创新训练项目(201510606048);广西中青年教师基础能力提升项目(2017ky0537)。 |
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| 摘 要： | 共轭梯度法是求解大规模无约束优化问题最有效的方法之一.对HS共轭梯度法参数公式进行改进,得到了一个新公式,并以新公式建立一个算法框架.在不依赖于任何线搜索条件下,证明了由算法框架产生的迭代方向均满足充分下降条件,且在标准Wolfe线搜索条件下证明了算法的全局收敛性.最后,对新算法进行数值测试,结果表明所改进的方法是有效的.
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| 关 键 词： | 无约束优化 共轭梯度法 Wolfe非精确线搜索 充分下降性 全局收敛 |
An Improved Hs Conjugate Gradient Method with Sufficient Descent Property |
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| JIANG Xian-zhen,LI Hui-lan,LIU Mei-xing,BAN Cai-zhun,MA Yue-mei,OU Yong-wei. An Improved Hs Conjugate Gradient Method with Sufficient Descent Property[J]. Mathematics in Practice and Theory, 2020, 0(5): 155-164 |
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| Authors: | JIANG Xian-zhen LI Hui-lan LIU Mei-xing BAN Cai-zhun MA Yue-mei OU Yong-wei |
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| Affiliation: | (College of Science,Guangxi University for Nationalities,Nanning 530006,China;Guangxi Universities Key Lab of Complex System Optimization and Big Data Processing,Yulin Normal University,Yulin 537000,China) |
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| Abstract: | The conjugate gradient method is one of the most effective iterative methods for solving large-scale unconstrained optimization.In this paper,we improved the parameter formula of the HS method,and proposed a sufficient descent conjugate gradient method for solving large-scale optimal problems.Depending on no any line search,we proved that the improved method satisfies sufficient descent condition at every iteration.Further,we also proved its global convergence under the standard Wolfe inexact line search condition.Some elementary numerical experiments are reported,which show that the proposed method is promising. |
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| Keywords: | unconstrained optimization conjugate gradient method sufficient descent property global convergence |
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