RESTART PROCEDURES FOR CONJUGATE GRADIENT METHOD
RESTART PROCEDURES FOR CONJUGATE GRADIENT METHOD
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DOI：
10.1007/bf01593790
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发表时间：
1977-01-01
影响因子：
2.7
通讯作者：
POWELL, MJD
中科院分区：
文献类型：
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作者：
POWELL, MJD
共轭梯度法对于极小化非常多变量的函数特别有用，因为它不需要存储任何矩阵。然而，该算法的收敛速度只是线性的，除非迭代过程是“重新启动”偶尔。目前，通常每n+ 1次迭代都要重新开始，其中n是变量的个数，但已知重新开始的频率应取决于目标函数。因此，本文的主要目的是提供一个算法的重新启动过程，考虑到目标函数自动。另一个目的是研究在每次迭代的搜索方向的定义中出现的乘法因子。已经提出了该因子的各种表达式，并且通常使用哪一个并不重要。然而，现在有一些理由支持其中一种表达方式。几个数值例子报告支持本文的结论。
The conjugate gradient method is particularly useful for minimizing functions of very many variables because it does not require the storage of any matrices. However the rate of convergence of the algorithm is only linear unless the iterative procedure is “restarted” occasionally. At present it is usual to restart everynor (n+ 1) iterations, wherenis the number of variables, but it is known that the frequency of restarts should depend on the objective function. Therefore the main purpose of this paper is to provide an algorithm with a restart procedure that takes account of the objective function automatically. Another purpose is to study a multiplying factor that occurs in the definition of the search direction of each iteration. Various expressions for this factor have been proposed and often it does not matter which one is used. However now some reasons are given in favour of one of these expressions. Several numerical examples are reported in support of the conclusions of this paper.