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凸二次规划梯度类算法中步长对收敛速度的影响

发表时间:2009-01-15  浏览量:1924  下载量:668
全部作者: 何炳生,崔睿峗,李敏,申远,徐明华,袁晓明
作者单位: 南京大学数学系;东南大学经济管理学院;江苏工业学院数理学院;香港浸会大学数学系
摘 要: 将一类求解约束凸二次规划的自调比投影收缩算法用来求解无约束凸二次规划,相当于梯度算法中将最速下降法步长动态地乘上一个小于1的因子。本文对无约束凸二次规划的数值试验表明:对维数不小于5的问题,梯度算法中将最速下降法的步长乘上[0.3,0.99]中的一个因子,一般会使迭代次数得到数量级的减少。进一步的试验表明:为了加快收敛速度,步长可以在最速下降法的步长左右一定范围内变动,但使用短步长的频率应该有不低的比例。使用最速下降法时,高精度的一维寻查会导致总体迭代次数的大量增加,不仅徒劳而且是有害的。
关 键 词: 运筹学;无约束凸二次规划;负梯度方法;线搜索精度
Title: A note on the step-sizes of gradient-like methods for solving convex quadratic programming
Author: HE Bingsheng, CUI Ruiyun, LI Min, SHEN Yuan, XU Minghua, YUAN Xiaoming
Organization: Department of Mathematics, Nanjing University; School of Economics and Management, Southeast University; School of Mathematics and Physics, Jiangsu Polytechnic University; Department of Mathematics, Hong Kong Baptist University
Abstract: When a class of gradient-projection methods for constrained convex quadratic programming is applied to the unconstrained one, it can be viewed as the steepest descent method with a reduced step-size. It is observed that the numerical performance is improved considerably via scaling the step-sizes simply by a multiplier in [0.3, 0.99]. The further experiments indicate that the step size can vary in a range around the step size of the steepest descent method. To speed up the convergence, a certain ratio of short step size should be adopted during the iterations. While the steepest descent method is being applied, line search with high accuracy will lead to an extremely slow convergence. Thus it is unnecessary and harmful.
Key words: operations research; unconstrained convex quadratic programming; negative gradient methods; line search accuracy
发表期数: 2009年1月第1期
引用格式: 何炳生,崔睿峗,李敏,等. 凸二次规划梯度类算法中步长对收敛速度的影响[J]. 中国科技论文在线精品论文,2009,2(1):1-9.
 
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