收稿日期: 2016-05-16
网络出版日期: 2017-03-23
基金资助
重庆市研究生教育教学改革研究项目(yjg143046)
A class of conjugate gradient algorithm with sufficient descent property
Received date: 2016-05-16
Online published: 2017-03-23
徐晓光 , 王开荣 . 一类具有充分下降性的共轭梯度算法[J]. 华东师范大学学报(自然科学版), 2017 , 2017(2) : 44 -51,60 . DOI: 10.3969/j.issn.1000-5641.2017.02.006
On the basis of some famous conjugate gradient algorithms, a class of new nonlinear conjugate gradient algorithm is proposed for solving unconstrained optimization problems, which can generate sufficient descent directions at each iteration regardless of any line search. Under the Wolfe line searches, the global convergence of the proposed algorithm is proved. Numerical experiment results show that the proposed method is promising.
[1] 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, 49(6):409-436.
[2] FLETCHER R, REEVES C M. Function minimization by conjugate gradients[J]. Computer Journal, 1964, 7(2):149-154.
[3] POLYAK B T. The conjugate gradient method in extremal problems[J]. USSR Computational Mathematics and Mathematical Physics, 1969, 9(4):94-112.
[4] POLAK E, RIBIÊRE G. Note sur la convergence de methodes de directions conjuguées[J]. Rev Franaise de Informat Recherche Opérationnelle, 1969, 16(1):35-43.
[5] FLETCHER R. Practical Methods of Optimization, Vol I:Unconstrained Optimization[M]. New York:Wiley and Sons, 1987.
[6] LIU Y, STOREY C. Efficient generalized conjugate gradient algorithms, part 1:Theory[J]. Journal of Optimization Theory and Applications, 1991, 69(1):129-137.
[7] DAI Y H, YUAN Y. A nonlinear conjugate gradient method with a strong global convergence property[J]. Siam Journal on Optimization, 1999, 10(1):177-182.
[8] ZOUTENDIJK G. Nonlinear programming, computational methods[M]//Integer and Nonlinear Programming. Amsterdam:North-Holland Publishing Company, 1970.
[9] AL-BAALI M. Descent property and global convergence of the Fletcher-Reeves method with inexact line search[J]. IMA Journal of Numerical Analysis. 2010, 5(1):121-124.
[10] GILBERT J C, NOCEDAL J. Global convergence properties of conjugate gradient methods for optimization[J]. SIAM Journal on Optimization, 1992, 2(1):21-42.
[11] WEI Z, YAO S, LIU L. The convergence properties of some new conjugate gradient methods[J]. Applied Mathematics and Computation, 2006, 183(2):1341-1350.
[12] HUANG H, WEI Z, YAO S. The proof of the sufficient descent condition of the Wei-Yao-Liu conjugate gradient method under the strong Wolfe-Powell line search[J]. Applied Mathematics and Computation, 2007, 189(2): 1241-1245.
[13] TOUATI-AHMED D, STOREY C. Efficient hybrid conjugate gradient techniques[J]. Journal of Optimization Theory and Applications, 1990, 64(2):379-397.
[14] 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结果[J].数值计算与计算机应用, 2007, 28(1):56-62.
[15] DAI Z, WEN F. Another improved WeiõYaoõLiu nonlinear conjugate gradient method with sufficient descent property[J]. Applied Mathematics and Computation, 2012, 218(14):7421-7430.
[16] 戴彧虹. 非线性共轭梯度法[M]. 上海:上海科学技术出版社, 2000.
[17] ANDREI N. An unconstrained optimization test functions collection[J]. Adv Model Optim, 2008, 10(1):147-161.
/
〈 |
|
〉 |