HUANG Fei,WU Zezhong.Analysis and Comparison of Several Conjugate Gradient Methods based on Armijo Search Step Length[J].Journal of Chengdu University of Information Technology,2019,(02):209-215.[doi:10.16836/j.cnki.jcuit.2019.02.0017]
基于Armijo搜索步长的几种共轭梯度法的分析对比
- Title:
- Analysis and Comparison of Several Conjugate Gradient Methods based on Armijo Search Step Length
- 文章编号:
- 2096-1618(2019)02-0209-07
- Keywords:
- applied mathematics; optimization theory; FR conjugate gradient method; PRP conjugate gradient method; HS conjugate gradient method; unconstrained optimizations; Armijo-type line search
- 分类号:
- O221.2
- 文献标志码:
- A
- 摘要:
- 共轭梯度法是解决无约束优化问题的一种重要方法,使用不精确的Armijo搜索步长的方法,利用MATLAB工具对FR共轭梯度法、PRP共轭梯度法、HS共轭梯度法3种方式的收敛效果进行对比。结果表明:在低次函数里使用FR共轭梯度法效果较好,在高次函数里使用PRP共轭梯度法或HS共轭梯度法的收敛效果较好,并且在函数波动较大时,初值的选择应尽量靠近收敛点,才能有不错的收敛效果。
- Abstract:
- Conjugate gradient method is an important method to solve the problem of unconstrained optimization. In this paper, the method of inaccurate Armijo-type line search is used, the convergence effects of FR conjugate gradient method, PRP conjugate gradient method and HS conjugate gradient method were compared using MATLAB tools. The results show that the FR conjugate gradient method is better in subharmonic function better convergence using PRP conjugate gradient method or HS conjugate gradient method in higher order functionshen the function fluctuates greatly, the initial value should be chosen as close as possible to the convergence point in order to have a good convergence effect.
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备注/Memo
收稿日期:2018-09-13 基金项目:国家自然科学基金资助项目(71672013); 四川省软件科学研究计划资助项目(2014ZR0016); 四川省社科重点研究基地资助项目(Xq14B06)