| 矩阵乘积形式的有限存贮拟牛顿法 |
| |
| 引用本文： | 何炼坚.矩阵乘积形式的有限存贮拟牛顿法[J].高等学校计算数学学报,1998,20(2):112-120. |
| |
| 作者姓名： | 何炼坚 |
| |
| 作者单位： | 南京大学数学系 南京 |
| |
| 摘 要： | 1 引言 考虑无约束优化问题 minf(x),(1.1) x∈R~n其中f为非线性町微函数。 对于中小规模的无约束优化问题,拟牛顿法(如BFGS方法)是十分有效的。但对于大规模问题,即n相当大时,算法所需存贮相当重要,并且在每次迭代中线代数计算量也影响算法的效率。 有限存贮((1imited memory)拟牛顿法可看成是共轭梯度法的推广。这一类方法最早由Perry和Shanno提出,此后有不少人进行研究,如Gill和Murray,Buckley,Buckley和LeNir及Nocedal。 有限存贮BFGS方法由Nocedal提出,是目前一种十分有效的有限存贮拟牛顿方法,其基本出法点是减少存贮。由于BFGS修正公式可写成
|
| 关 键 词： | 矩阵 乘积 有限存贮 拟牛顿法 无约束优化 |
QUASI-NEWTON MATRICES REPRESENTED IN PRODUCT FORMS AND THEIR USE IN LIMITED MEMORY METHODS |
| |
| He Lianjian.QUASI-NEWTON MATRICES REPRESENTED IN PRODUCT FORMS AND THEIR USE IN LIMITED MEMORY METHODS[J].Numerical Mathematics A Journal of Chinese Universities,1998,20(2):112-120. |
| |
| Authors: | He Lianjian |
| |
| Institution: | Nanjing University |
| |
| Abstract: | A class of limited memory quasi-Newton methods based on a class of up-date formulas in product forms are presented. Numerical tests are performed for these methods and they show that our limited memory methods are effective for large scale unconstrained optimization problems. |
| |
| Keywords: | unconstrained optimization problems large scale limited memory quasi-Newton |
| 本文献已被 CNKI 维普 等数据库收录！ |
|
