您的位置:山东大学 -> 科技期刊社 -> 《山东大学学报(理学版)》

山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (1): 98-101.doi: 10.6040/j.issn.1671-9352.0.2016.154

• • 上一篇    下一篇

Armijo型线搜索下的全局收敛共轭梯度法

郑秀云,史加荣   

  1. 西安建筑科技大学理学院, 陕西 西安 710055
  • 收稿日期:2016-04-11 出版日期:2017-01-20 发布日期:2017-01-16
  • 作者简介:郑秀云(1982— ),女,博士研究生, 讲师,研究方向为最优化理论及算法. E-mail:xyzhengzzf@sohu.com
  • 基金资助:
    国家自然科学基金资助项目(61403298,11401457);陕西省教育厅专项科研计划项目(16JK1435)

A globally convergent conjugate gradient method with Armijo line search

ZHENG Xiu-yun, SHI Jia-rong   

  1. School of Science, Xian University of Architecture and Technology, Xian 710055, Shaanxi, China
  • Received:2016-04-11 Online:2017-01-20 Published:2017-01-16

摘要: 通过修正搜索方向,提出了一个具有充分下降的共轭梯度法用于求解无约束优化问题。该算法不依赖于任何线搜索,在每次迭代都能产生一个充分下降方向。在一定条件下,证明了此算法在Armijo线性搜索下的全局收敛性。数值实验结果表明所提出的算法是有效的。

关键词: Armijo线搜索, 充分下降性, 共轭梯度法, 全局收敛性

Abstract: By modifying the search direction, a sufficient descent conjugate gradient method was proposed for solving unconstrained optimization problems. The proposed method can generate sufficient descent directions at each iteration without any line search. The global convergence of the proposed method was proved under Armijo line search. Some numerical experiments show that the proposed method is promising.

Key words: conjugate gradient method, global convergence, Armijo line search, sufficient descent property

中图分类号: 

  • O221.2
[1] FLETCHER R, REEVES C. Function minimization by conjugate gradients[J]. Computer Journal, 1964, 7(2):149-154.
[2] POLAK E, RIBIERE G. Note sur la convergence de methodesdirections conjugees[J]. Revue Francaise Informat Recherche Operationelle, 1969, 16(3):35-43.
[3] POLYAK B T. The conjugate gradient method in extreme problems[J]. USSR Computational Mathematics and Mathematical Physics, 1969, 9:94-112.
[4] HESTENES M R, STIEFEL E. Methods of conjugate gradients for solving linear systems[J]. Journal of Research of National Bureau of Standards, 1952, 49:409-436.
[5] DAI Yuhong, YUAN Yaxiang. A nonlinear conjugate gradient method with a strong global convergence property[J]. SIAM Journal on Optimization, 1999, 10(1):177-182.
[6] BIRGIN E G, MARTIMEZ J M. A spectral conjugate gradient method for unconstrained optimization[J]. Applied Mathematics and Optimization, 2001, 43(2):117-128.
[7] ZHANG Li, ZHOU Weijun, LI Donghui. Global convergence of a modified Fletcher-Reeves conjugate gradient method with Armijo type 1ine search[J]. Numerische Mathematik, 2006, 104(4):561-572.
[8] WAN Zhong, YANG Zhanlu, WANG Yalin. New spectral PRP conjugate gradient method for unconstrained optimization[J]. Applied Mathematics Letters, 2011, 24(1):16-22.
[9] ZHANG Li. Two modified Dai-Yuan nonlinear conjugate gradient methods[J]. Numerical Algorithms, 2009, 50(1):1-16.
[10] 董晓亮, 高岳林, 何郁波. 一类基于Armijo搜索的改进DY共轭梯度法及其全局收敛性[J]. 数值计算与计算机应用, 2011, 32(4): 253-258. DONG Xiaoliang, GAO Yuelin, HE Yubo. Global convergence of an improved DY conjugate gradient method with Armijo line search[J]. Journal on Numerical Methods and Computer Applications, 2011, 32(4):253-258.
[11] 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 descent DY conjugate gradient method and its global convergence[J]. Journal of Shandong University(Natural Science), 2011, 46(7):101-105.
[12] ZOUTENDIJK G. Nonlinear programming computational methods[M]. North-Holland, Amsterdam, 1970.
[13] MORE J J, GARBOW B S, HILLSTROME K E. Testing unconstrained optimization software[J]. ACM Transactions on Mathematical Software, 1981, 7:17-41.
[1] 林穗华. Wolfe线搜索下的修正FR谱共轭梯度法[J]. 山东大学学报(理学版), 2017, 52(4): 6-12.
[2] 王开荣,高佩婷. 建立在DY法上的两类混合共轭梯度法[J]. 山东大学学报(理学版), 2016, 51(6): 16-23.
[3] 王开荣,王书敏. 具有充分下降性的修正型混合共轭梯度法[J]. J4, 2013, 48(09): 78-84.
[4] 冯琳1,2,段复建1,和文龙1. 基于简单二次函数模型的滤子非单调信赖域算法[J]. J4, 2012, 47(5): 108-114.
[5] 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]. J4, 2011, 46(7): 101-105.
[6] 高宝,孙清滢. 基于Zhang H C非单调技术的修正HS共轭梯度算法[J]. J4, 2011, 46(7): 106-111.
[7] 程李晴1,2, 石巧连2. 一种新的混合共轭梯度算法[J]. J4, 2010, 45(6): 81-85.
[8] 程李晴. 一类共轭梯度法的全局收敛性[J]. J4, 2010, 45(5): 101-105.
[9] 王开荣,曹伟,王银河. Armijo型线搜索下的谱CD共轭梯度法[J]. J4, 2010, 45(11): 104-108.
[10] . 一类新的Wolfe线性搜索下的记忆梯度法[J]. J4, 2009, 44(7): 33-37.
[11] 孙敏 . 一种满足夹角性质的超记忆梯度方法[J]. J4, 2008, 43(6): 68-70 .
[12] 刘利英,李 莹, . 强Wolfe-Powell线搜索下共轭梯度法的全局收敛性[J]. J4, 2008, 43(5): 54-57 .
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!