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山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (6): 16-23.doi: 10.6040/j.issn.1671-9352.0.2015.267

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建立在DY法上的两类混合共轭梯度法

王开荣1,高佩婷2   

  1. 重庆大学数学与统计学院, 重庆 401331
  • 收稿日期:2015-06-01 出版日期:2016-06-20 发布日期:2016-06-15
  • 作者简介:王开荣(1965— ),男,教授,博士,研究方向为最优化理论及算法. E-mail: kairong@cqu.edu.cn
  • 基金资助:
    重庆市研究生教育教学改革研究项目(yjg143046)

Two mixed conjugate gradient methods based on DY

WANG Kai-rong1, GAO Pei-ting2   

  1. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
  • Received:2015-06-01 Online:2016-06-20 Published:2016-06-15

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摘要： 在经典的DY共轭梯度法的基础上,提出了两种混合共轭梯度,并证明了在特定的条件下,这两种算法所产生的方向均为充分下降方向,同时在广义Wolfe线搜索条件下,这两种方法又具有全局收敛性。数值试验结果表明新方法对于给定的测试函数在数值效果上明显优于DY共轭梯度法。

关键词: Wolfe线搜索, 无约束最优化问题, 充分下降性, 全局收敛性, 共轭梯度法

Abstract: Based on DY method, two mixed conjugate gradient methods(GDY1 and GDY2)were proposed. The search directions generated by GDY1 and GDY2 are sufficiently decent directions under some specific conditions, and are global convergence with general wolf line search. Numerical experiments show that the new methods outperform DY conjugate gradient method.

Key words: unconstrained optimization, conjugate gradient methods, sufficiently descent property, Wolfe line searching, global convergence

中图分类号: 

  • O221.2
[1] HESTENES M R. Iterative method for sovling linear equation[J]. JOTA, 1973, 1:322-334.
[2] ANDREI N. Open problem in conjugate gradient algorithms for unconstrained optimization[J].Bulletin of the Malaysian Mathematical Sciences Society, 2011, 34(2):319-330.
[3] FLETCHER R, REEVES C.Function minimization by conjugate gradients[J].Computer Journal, 1964(7):149-154.
[4] POLAK E, RIBIERE G. Note sur la convergence de directions conjugaees[J]. Francaise Informat Recherche Opertionelle, 1969(16):35-43.
[5] POLYA B T. The conjugate gradient method in extreme problems[J].USSR Comp Math And Math Phys, 1969(9):94-112.
[6] HESTENES M R, STIEFEL E L. Methods of conjugate gradients for solving linear systems[J].Journal of Research of the National Bureau of Standards, 1952, 5(49):409-432.
[7] FLETCHER R. Practical methods of optimization vol 1: unconstrained optimization[M].New York: Wiley & Sons, 1987.
[8] LIU Y, STOREY C. Efficient generalized conjugate gradient algorithms [J].Journal of Optimization Theory and Applications, 1991(69):129-137.
[9] DAI Y H, YUAN Y X.A nonlinear conjugate gradient method with a strong global convergence property[J].SIAM Journal of Optimization, 2000(10):177-182.
[10] AL-BAALI M. Descent property and global convergence of the Fletcher-Reeves method with inexact line search[J].IMA Journal of Numerical Analysis, 1985, 5(1):121-124.
[11] GILBERT J C, NOCEDAL J. Global convergence property of conjugate gradient methods for optimization[J]. SIAM J Opti, 1992, 2(1):21-42.
[12] POWELL M J D. Non-convex minimization calculations and the conjugate gradient method[M].Berlin, Springer, 1984.
[13] 戴志锋,陈兰平. 一种混合的HS-DY共轭梯度法[J].计算数学,2005,27(4):429-436. DAI Zhifeng, CHEN Lanping. A mixed HS-DY conjugate gradient metnod[J].Computional Mathematics, 2005, 27(4):429-436.
[14] 焦宝聪,陈兰平,潘翠英. Goldstein线搜索下混合共轭梯度法的全局收敛性[J].计算数学,2007,29(2):137-146. JIA Baocong, CHEN Lanping, PAN Cuiying.Convergence properties of a hybrid conjugate gradient methods with Goldentein line search[J].Computional Mathematics, 2007, 29(2):137-146.
[15] 郑希锋,田志远,宋立温. Wolfe线搜索下一类混合共轭梯度法的全局收敛性[J].运筹学学报,2009,13(2):18-24. DENG Xifeng, TIAN Zhiyuan, SONG Liwen. The global convergence of a mixed conjugate gradient method with Wolfe line search[J]. OR Transactions, 2009, 13(2):18-24.
[16] 江羡珍马国栋简金宝Wolfe线搜索下一个新的全局收敛共轭梯度法[J].工程数学学报,2011,28(6):779-786. JIANG Xianzhen, MA Guodong, JIAN Jinbao. A new globally convergent conjugate gradient method with wolfe line search[J].Chinese Journal of Engineering Mathematics, 2011, 28(6):779-786.
[17] 李敏,陈宇,屈爱平.一种充分下降的DY共轭梯度法及其收敛性[J].山东大学学报(理学版),2011,46(7):101-105. LI Min, CHEN Yu, QU Aiping. A sufficient decent DY conjugate gradient method and its global convergence[J].Journal of Shandong University(Natural Science), 2011, 46(7):101-105.
[18] 戴彧虹,袁亚湘.非线性共轭梯度法[M].上海:上海科学技术出版社,2001. DAI Y H, YUAN Y X. Nonlinear conjugate gradient method[M].Shanghai: Shanghai Science and Technology Publisher, 2001.
[19] MORE J J, GARBOW B S, HILSTROME K E. Testing uncontrained optimization software[J]. ACM Trans Math Software, 1981(7):17-41.
[20] 莫降涛,顾能柱,韦增欣.修正PRP共轭梯度法的全局收敛性及其数值实验[J]. 数值计算与计算机应用, 2007, 3(1):56-62. MO Jiangtao, GU Nengzhu, WEI Zengxin. Global convergence of a modified PRP conjugate gradient method and its numerical results[J]. Journal on Numerical Methods and Computer Applications, 2007, 3(1):56-62.
[21] LI Donghui, Fukushima Masao. A modified BFGS method and its global convergence in nonconvex minimization[J].Journal of Computational and Applied Mathematics, 2001, 129(12):15-35.
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