华东师范大学学报(自然科学版) ›› 2010, Vol. 2010 ›› Issue (1): 34-38.

• 应用数学与基础数学 • 上一篇    下一篇

一种新的修正有限内存拟牛顿法

卢慧芳1,杨月婷2   

  1. 1. 上海财经大学应用数学系, 上海 200433; 2.北华大学数学学院,吉林 吉林市 132013
  • 收稿日期:2009-02-17 修回日期:2009-05-09 出版日期:2010-01-25 发布日期:2010-01-25
  • 通讯作者: 卢慧芳

New modified limited memory quasi-Newton method (Chinese)

LU Hui-fang1,YANG Yue-ting2   

  1. 1. Department of Applied Mathematics, Shanghai University of Finance and Economics,Shanghai 200433, China; 2. Faculty of Malthematics, Beihua University, Jilin Jilin 132013, China
  • Received:2009-02-17 Revised:2009-05-09 Online:2010-01-25 Published:2010-01-25
  • Contact: LU Hui-fang

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摘要： 依据修正拟牛顿方程, 提出一种新的双循环有限内存拟牛顿法.与经典的有限内存 BFGS 方法相比, 新算法同时利用函数值和梯度信息构造拟牛顿校正矩阵,且不会增加计算量, 理论分析和数值检验说明了新算法的有效性.

关键词: 修正拟牛顿方程, 有限内存方法, 大规模优化, 修正拟牛顿方程, 有限内存方法, 大规模优化

Abstract: Based on modified quasi-Newton equation, a new limited memory quasi-Newton method with two-loop recursion was proposed. Comparing to the classical limited memory BFGS method, the new method uses more function value and gradient informations to construct the quasi-Newton update mectrix, and does not need more computational efforts. The theory analysis and numerical results show the efficiency of the proposed method.

Key words: limited memory method, large scale optimization, modified quasi-Newton equation, limited memory method, large scale optimization

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