JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (6): 16-23.doi: 10.6040/j.issn.1671-9352.0.2015.267
Previous Articles Next Articles
WANG Kai-rong1, GAO Pei-ting2
CLC Number:
[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. |
|