|
|
- 2018
一类修正的FR型谱共轭梯度法
|
Abstract:
提出了一类WFR型谱共轭梯度法，并且该算法在任何线搜索下都具有充分下降性.在标准Wolfe线搜索下，证明了新算法具有全局收敛性.数值实验结果表明新算法优于VFR法.
In this paper, a spectral conjugate gradient WFR method is put forward, which always possesses the sufficient descent property with any line search. It is proved under the standard Wolfe line search that the new spectral conjugate gradient method possesses global convergence. A series of numerical tests indicate that the new algorithm is superior to the VFR method
| [1] | HESTENES M R, STIEFEL E. Methods of Conjugate Gradients for Solving Linear Systems[J]. Journal of Research of the National Bureau of Standards, 1952, 49(6): 409-436. DOI:10.6028/jres.049.044 |
| [2] | YUAN G L, LU X W. A Modified PRP Conjugate Gradient Method[J]. Annals of Operations Research, 2009, 166(1): 73-90. DOI:10.1007/s10479-008-0420-4 |
| [3] | LU A G, LIU H W, ZHENG X Y, et al. A Variant Spectral-Type FR Conjugate Gradient Method and Its Global Convergence[J]. Applied Mathematics and Computation, 2011, 217(12): 5547-5552. DOI:10.1016/j.amc.2010.12.028 |
| [4] | DOLAN E D, MORé J J. Benchmarking Optimization Software with Performance Profiles[J]. Mathematical Programming, 2002, 91(2): 201-213. DOI:10.1007/s101070100263 |
| [5] | POLAK E, RIBIèRE G. Note Sur La Convergence De Méthodes De Directions Conjuguées[J]. Rev. franaise Informat. recherche Opérationnelle, 1968, 16(16): 35-43. |
| [6] | YAO S W, WEI Z X, HUANG H. A Note about WYL's Conjugate Gradient Method and Its Applications[J]. Applied Mathematics and Computation, 2007, 191(2): 381-388. DOI:10.1016/j.amc.2007.02.094 |
| [7] | HUANG H, LIN S H. A Modified Wei-Yao-Liu Conjugate Gradient Method for Unconstrained Optimization[J]. Applied Mathematics and Computation, 2014, 231(1): 179-186. |
| [8] | FLETCHER R, REEVES C M. Function Minimization by Conjugate Gradients[J]. Computer Journal, 1964, 7(2): 149-154. DOI:10.1093/comjnl/7.2.149 |
| [9] | POLYAK B T. The Conjugate Gradient Method in Extremal Problems[J]. Ussr Computational Mathematics and Mathematical Physics, 1969, 9(69): 94-112. |
| [10] | DAI Z, WEN F. Another Improved Wei-Yao-Liu Nonlinear Conjugate Gradient Method with Sufficient Descent Property[J]. Applied Mathematics and Computation, 2012, 218(14): 7421-7430. DOI:10.1016/j.amc.2011.12.091 |
| [11] | ANDREI N. An Unconstrained Optimization Test Functions Collection[J]. Environmental Science and Technology, 2008, 10(1): 6552-6558. |
| [12] | BIRGIN E G, MARTíNEZ J M. A Spectral Conjugate Gradient Method for Unconstrained Optimization[J]. Applied Mathematics and Optimization, 2001, 43(2): 117-128. DOI:10.1007/s00245-001-0003-0 |
| [13] | 戴彧虹, 袁亚湘. 非线性共轭梯度法[M]. 上海: 上海科学出版社, 2000: 10-13. |
| [14] | 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. DOI:10.1137/S1052623497318992 |
