全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...
-  2018 

求解无约束问题的修正PRP共轭梯度算法
A Modified Polak-Ribière-Polyak Conjugate Gradient Algorithm for Smooth Convex Programs

DOI: 10.13718/j.cnki.xdzk.2018.09.011

Keywords: 共轭梯度法, 下降性, 全局收敛性
conjugate gradient algorithm
, descent property, global convergence

Full-Text   Cite this paper   Add to My Lib

Abstract:

提出了一种改进的PRP共轭梯度算法,其搜索方向自动具有充分下降性和信赖域性质,且在一定条件下,具有全局收敛性.数值结果表明该算法对求解无约束光滑问题是有效的.
In this paper, a modified PRP conjugate gradient algorithm is proposed. The search direction of this algorithm belongs to a trust region automatically, and its search direction possesses descent property. Under suitable conditions, the method owns global convergence. Some elementary numerical experiments indicate that the presented method is effective for unconstrained smooth problems

References

[1]  ZHANG L, ZHOU W J, LI D H. A Descent Modified Polak-Ribière-Polyak Conjugate Gradient Method and Its Global Convergence[J]. Ima Journal of Numerical Analysis, 2006, 26(4): 629-640. DOI:10.1093/imanum/drl016
[2]  YUAN G L, LU X W, WEI Z X. A Conjugate Gradient Method with Descent Direction for Unconstrained Optimization[J]. Journal of Computational and Applied Mathematics, 2009, 233(2): 519-530. DOI:10.1016/j.cam.2009.08.001
[3]  YUAN G L, WEI Z X, LU X W. Global Convergence of BFGS and PRP Methods Under a Modified Weak Wolfe-Powell Lline Search[J]. Applied Mathematical Modelling, 2017(47): 811-825.
[4]  HESTENES M R, STIEFEL E. Method of Conjugate Gradient for Solving Linear Equations[J]. Res Nation Bur Stand, 1952, 49(6): 409-436. DOI:10.6028/jres.049.044
[5]  CARDENAS S. Efficient Generalized Conjugate Gradient Algorithms I Theory[J]. Journal of Optimization Theory and Applications, 1991, 69(1): 129-137. DOI:10.1007/BF00940464
[6]  YUAN G, LU X. A Modified PRP Conjugate Gradient Method[J]. Annals of Operations Research, 2009, 166(1): 73-90.
[7]  POLYAK B T. The Conjugate Gradient Method in Extremal Problems[J]. Ussr Computational Mathematics and Mathematical Physics, 1969, 9(4): 94-112. DOI:10.1016/0041-5553(69)90035-4
[8]  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. DOI:10.1016/j.amc.2006.05.150
[9]  HAGER W W, ZHANG H. A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search[J]. Siam Journal on Optimization, 2005, 16(1): 170-192. DOI:10.1137/030601880
[10]  HAGER W W, ZHANG H. Algorithm 851:CG_DESCENT, A Conjugate Gradient Method with Guaranteed Descent[J]. ACM Transactions on Mathematical Software, 2006, 32(1): 113-137. DOI:10.1145/1132973
[11]  YUAN G L, MENG Z H, LI Y. A Modified Hestenes and Stiefel Conjugate Gradient Algorithm for Large-Scale Nonsmooth Minimizations and Nonlinear Equations[J]. Journal of Optimization Theory and Applications, 2016, 168(1): 129-152. DOI:10.1007/s10957-015-0781-1
[12]  POLAK E, RIBIERE G. Note Sur La Convergence de Methode de Directions Conjuguees[J]. Revue Francaise Information Recherche Operationnelle, 2009, 16(16): 35-43.
[13]  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
[14]  ANDREI N. An Unconstrained Optimization Test Functions Collection[J]. Advanced Modeling and Optimization, 2008, 10(1): 147-161.
[15]  YUAN G L, WEI Z X, LU X W. A BFGS Trust-Region Method for Nonlinear Equations[J]. Computing, 2011, 92(4): 317-333. DOI:10.1007/s00607-011-0146-z

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133