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| 扩展的拟牛顿法 | |
| 引用本文： | 刘伟,张兰,赵陆一.扩展的拟牛顿法[J].纺织高校基础科学学报,2008,21(4):487-491. |
| 作者姓名： | 刘伟 张兰 赵陆一 |
| 作者单位： | 1. 西北大学,数学系,陕西,西安,710127 2. 西安航空职业技术学院,基础部,陕西,西安,710089 3. 陕西省生产力促进中心,陕西,西安,710054 |
| 摘 要： | 拟牛顿算法被认为是当今解无约束最优化问题的最有效方法之一，它产生了一系列对目标函数二阶导数的近似矩阵Bk＋1．校正产生的Bk＋1，其实质是在Bk的基础上加一修正矩阵Ak，即Bk＋1=Bk＋Ak．研究了Ak应满足什么样的条件，给出了满足该条件的Ak的3种公式及6种合适的选取． |
| 关 键 词： | 无约束优化 拟牛顿方程 全局收敛性 |
The extended quasi-Newton methods |
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| LIU Wei,ZHANG Lan,ZHAO Lu-yi.The extended quasi-Newton methods[J].Basic Sciences Journal of Textile Universities,2008,21(4):487-491. | |
| Authors: | LIU Wei ZHANG Lan ZHAO Lu-yi |
| Affiliation: | LIU Wei ,ZHANG Lan ,ZHAO Lu-yi (1. Department of Mathematics,Northwestern University, Xi＇an 710127,China; 2. Department of Basic course, Xi＇an Aeronautical Polytechnic Institute, Xi＇an 710089,China; 3. Shaanxi Provincial Productivity Promotion Center, Xi＇an 710054,China) |
| Abstract: | One of effective methods for solving the contemporary unconstrained optimization problems is Quasi-Newton methods which produce a series of matrix Bk＋1 for the approx-imation matrix of second order derivatives of the objective function. The nature of Bk＋1 is Bk＋1= Bk＋Ak, in which Bk is the approximation matrix at the last iteration, Ak is some matrix. What conditions Ak can satisfy is studied. Three formulaes and six reasonable choices of Ak based on the conditions are given. |
| Keywords: | unconstrained optimization quasi-Newton equation global convergence |
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