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.
参考文献/References:
[1] Hestenes M R.Iterative methods for solving linear equations[J].Journal of Optimization Theory & Applications,1973,11(4):323-334.
[2] Fletcher R,Reeves C M.Function minimization by conjugate gradients[J].Computer Journal,1964,7(2):149-154.
[3] 陈宝林.最优化理论与算法[M].2版.北京:清华大学出版社,2005.
[4] Dai Y H.Conjugate Gradient Methods with Armijo-type Line Searches[J].Acta Mathematicae ApplicataeSinica,2002,18(1):123-131.
[5] Polyak B T.The conjugate gradient method in extremal problems[J].Ussr Computational Mathematics & Mathematical Physics,1969,9(4):94-112.
[6] Hestenes M R,Stiefel E.Methods of Conjugate Gradients for Solving Linear Systems[J].J.res.nat.bur.stand,1952,49(6):409-436.
[7] Fletcher R.Practical Methods of Optimization,Vol Ⅰ:Unconstrained Optimization[M].New York: John Wiley & Sons Press,1987,10-30.
[8] Liu Y,Storey C.Efficient generalized conjugate gradient algorithms,Part 1:Theory[J]. Journal of Optimization Theory and Applications,1991,69(1):129-137.
[9] Dai Y H,Yuan Y.A nonlinear conjugate gradient method with a strong global convergence property[J].SIAM Journal on Optimization,2000,10(1):177-182.
[10] Powell M J D.Restart procedures for the conjugate gradient method[J].Mathematical Programming,1977,12(1):241-254.
[11] 黄元元.求解无约束优化问题及非线性方程组的共轭梯度法[D].西安:西安电子科技大学,2014.
[12] 连淑君,徐衍聪.Armijo搜索下共轭梯度算法的全局收敛性[J].曲阜师范大学学报(自然科学版),2000,26(2):26-29.
[13] Li Y H,Riofrio C A,Cevher V.A General Convergence Result for Mirror Descent with Armijo Line Search[J].2018.
[14] Zhu M,Gao T,Zhang B,et al.An Efficient Elman Neural Networks Based on Improved Conjugate Gradient Method with Generalized Armijo Search[C].International Conference on Intelligent Computing.Springer,Cham,2018:1-7.
[15] Zhang B,Wang J,Wu S,et al.Fully Complex-Valued Wirtinger Conjugate Neural Networks with Generalized Armijo Search[C].International Conference on Intelligent Computing.Springer,Cham,2018:123-133.
相似文献/References:
[1]胡春华.基于分数阶导数和变分迭代法的人口预测算法[J].成都信息工程大学学报,2017,(01):78.[doi:10.16836/j.cnki.jcuit.2017.01.013]
HU Chun-hua.An Algorithm of Population Forecast with Fractional
Derivative and Variational Iteration Method[J].Journal of Chengdu University of Information Technology,2017,(02):78.[doi:10.16836/j.cnki.jcuit.2017.01.013]
[2]卞广钱,周 磊.基于模糊贴近度的属性约简[J].成都信息工程大学学报,2017,(01):86.[doi:10.16836/j.cnki.jcuit.2017.01.015]
BIAN Guang-qian,ZHOU Lei.Attribute Reduction based on Fuzzy Closeness Degree[J].Journal of Chengdu University of Information Technology,2017,(02):86.[doi:10.16836/j.cnki.jcuit.2017.01.015]
[3]王 容,罗文力,廖群英.方程φ3(n)=n/d 的可解性[J].成都信息工程大学学报,2017,(01):95.[doi:10.16836/j.cnki.jcuit.2017.01.017]
WANG Rong,LUO Wen-li,LIAO Qun-ying.On the Solvability of the Equation φ3(n)=n/d[J].Journal of Chengdu University of Information Technology,2017,(02):95.[doi:10.16836/j.cnki.jcuit.2017.01.017]
[4]马 斌,吴泽忠.基于人工蜂群算法的供应链网络均衡问题研究[J].成都信息工程大学学报,2017,(03):336.[doi:10.16836/j.cnki.jcuit.2017.03.016]
MA Bin,WU Ze-zhong.Research on Supply Chain Network Equilibrium Model
based on Artificial Bee Colony Algorithm[J].Journal of Chengdu University of Information Technology,2017,(02):336.[doi:10.16836/j.cnki.jcuit.2017.03.016]
[5]丁云红,陈勇明.基于改进灰靶决策的女子七项全能排名模型[J].成都信息工程大学学报,2017,(06):678.[doi:10.16836/j.cnki.jcuit.2017.06.018]
DING Yun-hong,CHEN Yong-ming.Women's Heptathlon Ranking Model based
on Improved Gray Target Decision[J].Journal of Chengdu University of Information Technology,2017,(02):678.[doi:10.16836/j.cnki.jcuit.2017.06.018]
[6]黄 艳,吴泽忠.基于Lévy飞行的一种改进鲸鱼算法[J].成都信息工程大学学报,2021,36(01):24.[doi:10.16836/j.cnki.jcuit.2021.01.005]
HUANG Yan,WU Zezhong.An Improved Whale Algorithm based on Lévy Flight[J].Journal of Chengdu University of Information Technology,2021,36(02):24.[doi:10.16836/j.cnki.jcuit.2021.01.005]
[7]熊 茜,吴泽忠.基于BFGS算法的广义Lagrange乘子法研究[J].成都信息工程大学学报,2020,35(02):221.[doi:10.16836/j.cnki.jcuit.2020.02.014]
XIONG Qian,WU Zezhong.Research on Generalized Lagrange Multiplier Method based on BFGS Algorithm[J].Journal of Chengdu University of Information Technology,2020,35(02):221.[doi:10.16836/j.cnki.jcuit.2020.02.014]
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)