| 无记忆非拟 Newton 算法的导出和全局收敛性 |
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| 引用本文： | 焦宝聪,于静静,陈兰平. 无记忆非拟 Newton 算法的导出和全局收敛性[J]. 数学研究及应用, 2009, 29(3): 423-433. DOI: 10.3770/j.issn:1000-341X.2009.03.006 |
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| 作者姓名： | 焦宝聪 于静静 陈兰平 |
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| 作者单位： | 首都师范大学数学科学学院, 北京 100037;首都师范大学数学科学学院, 北京 100037; 青岛港湾职业技术学院电气工程系, 山东 青岛 266404;首都师范大学数学科学学院, 北京 100037 |
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| 基金项目： | 国家自然科学基金(No.60472071);北京市教委科研基金(No.KM200710028001). |
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| 摘 要： | In this paper, a new class of memoryless non-quasi-Newton method for solving unconstrained optimization problems is proposed, and the global convergence of this method with inexact line search is proved. Furthermore, we propose a hybrid method that mixes both the memoryless non-quasi-Newton method and the memoryless Perry-Shanno quasi-Newton method. The global convergence of this hybrid memoryless method is proved under mild assumptions. The initial results show that these new methods are efficient for the given test problems. Especially the memoryless non-quasi-Newton method requires little storage and computation, so it is able to efficiently solve large scale optimization problems.
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| 关 键 词： | 非拟牛顿法 记忆方法 全局收敛 无约束最优化问题 混合方式 线搜索 求解 |
| 收稿时间： | 2007-05-26 |
| 修稿时间： | 2008-07-06 |
Derivation and Global Convergence for Memoryless Non-quasi-Newton Method |
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| JIAO Bao Cong,YU Jing Jing and CHEN Lan Ping. Derivation and Global Convergence for Memoryless Non-quasi-Newton Method[J]. Journal of Mathematical Research with Applications, 2009, 29(3): 423-433. DOI: 10.3770/j.issn:1000-341X.2009.03.006 |
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| Authors: | JIAO Bao Cong YU Jing Jing CHEN Lan Ping |
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| Affiliation: | School of Mathematical Sciences, Capital Normal University, Beijing 100037, China;School of Mathematical Sciences, Capital Normal University, Beijing 100037, China; Department of Electrical Engineering, Qingdao Harbor Vocational Technology College, Shandong 266404, China;School of Mathematical Sciences, Capital Normal University, Beijing 100037, China |
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| Abstract: | In this paper, a new class of memoryless non-quasi-Newton method for solving unconstrained optimization problems is proposed, and the global convergence of this method with inexact line search is proved. Furthermore, we propose a hybrid method that mixes both the memoryless non-quasi-Newton method and the memoryless Perry-Shanno quasi-Newton method. The global convergence of this hybrid memoryless method is proved under mild assumptions. The initial results show that these new methods are efficient for the given test problems. Especially the memoryless non-quasi-Newton method requires little storage and computation, so it is able to efficiently solve large scale optimization problems. |
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| Keywords: | memoryless non-quasi-Newton method Wolfe line search global convergence. |
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