[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. |