JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (1): 98-101.doi: 10.6040/j.issn.1671-9352.0.2016.154

Previous Articles     Next Articles

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

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

CLC Number: 

  • 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] LIN Sui-hua. A modified FR spectral conjugate gradient method with Wolfe line search [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 6-12.
[2] WANG Kai-rong, GAO Pei-ting. Two mixed conjugate gradient methods based on DY [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 16-23.
[3] WANG Kai-rong, WANG Shu-min. The modified hybrid conjugates gradient methods with sufficient descent property [J]. J4, 2013, 48(09): 78-84.
[4] FENG Lin1,2, DUAN Fu-jian1, HE Wen-long1. A filter non-monotone trust region algorithm with a simple quadratic model [J]. J4, 2012, 47(5): 108-114.
[5] LI Min, CHEN Yu, QU Ai-ping. A sufficient descent DY conjugate gradient method and its global convergence [J]. J4, 2011, 46(7): 101-105.
[6] GAO Bao, SUN Qing-ying. Modified HS conjugate gradient method based on Zhang H C nonmonotone technique [J]. J4, 2011, 46(7): 106-111.
[7] CHENG Li-qing1,2, SHI Qiao-lian2. A new hybrid conjugate gradient method [J]. J4, 2010, 45(6): 81-85.
[8] CHENG Li-qing. The global convergence of a class of conjugate gradient methods [J]. J4, 2010, 45(5): 101-105.
[9] WANG Kai-rong, CAO Wei, WANG Yin-he. A spectral CD conjugate gradient method with Armijo-type line search [J]. J4, 2010, 45(11): 104-108.
[10] SUN Min . A modified super-memory gradient method with angle property [J]. J4, 2008, 43(6): 68-70 .
[11] LIU Li-ying,LI Ying , . Global convergence of a conjugate gradient method with strong Wolfe-Powell line search [J]. J4, 2008, 43(5): 54-57 .
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!