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...

凸约束优化问题的杂交三阶投影HS-PRP方法
A Hybrid Three-Term Projected HS-PRP Method for Optimization with Convex Constraint

DOI: 10.12677/AAM.2022.118607, PP. 5750-5759

Keywords: 投影,共轭梯度法,线搜索,全局收敛
Projected
, Conjugate Gradient Method, Line Search, Global Convergence

Full-Text   Cite this paper   Add to My Lib

Abstract:

本文提出了一种杂交三阶投影HS-PRP共轭梯度法求解凸约束优化问题并证明了该算法的全局收敛性,该方法是求解无约束优化问题的三阶HS共轭梯度法的推广。数值实验结果表明,该算法是有效的。
In this paper, we propose a hybrid third-term projected HS-PRP conjugate gradient method for solving convex constrained optimization problems and establish its global convergence, which is a generalization of the third-term HS conjugate gradient method for unconstrained optimization. Numerical experimental results show that the algorithm is effective.

References

[1]  Fletcher. R. and Reeves, C.M. (1964) Function Minimization by Conjugate Gradients. The Computer Journal, 7, 149-154.
https://doi.org/10.1093/comjnl/7.2.149
[2]  Polyak, B.T. (1969) The Conjugate Gradient Method in Ex-treme problems. USSR Computational Mathematics and Mathematical Physics, 9, 94-112.
https://doi.org/10.1016/0041-5553(69)90035-4
[3]  Hestenes, M.R. and Stiefel, E. (1952) Method of Conjugate Gradient for Solving Linear System. Journal of Research of the National Bureau of Standards, 49, 409-436.
https://doi.org/10.6028/jres.049.044
[4]  Dai, Y.H. and Yuan, Y. (1999) A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property. SIAM Journal on Optimization, 10, 177-182.
https://doi.org/10.1137/S1052623497318992
[5]  Fletcher, R. (1987) Practical Methods of Optimization, Vol. 1: Unconstrained Optimization. Wiley & Sons, New York.
[6]  Liu, Y. and Storey, C. (1991) Efficient Generalized Con-jugate Gradient Algorithms, Part 1: Theory. Journal of Optimization Theory and Applications, 69, 129-137.
https://doi.org/10.1007/BF00940464
[7]  Zhou, W. and Li, D. (2014) On the Convergence Properties of the Un-modified PRP Method with a Non-Descent Line Search. Optimization Methods Software, 29, 484-496.
https://doi.org/10.1080/10556788.2013.811241
[8]  Hager, W.W. and Zhang, H. (2005) A New Conjugate Gra-dient Method with Guaranteed Descent and an Efficient Line Search. SIAM Journal on Optimization, 16, 170-192.
https://doi.org/10.1137/030601880
[9]  Gilbert, J.C. (1994) Convergence Properties of Conjugate Descent Method for Optimization. SIAM Journal on Optimization, 2, 24-32.
[10]  杨萌, 王祥玲. 修正HS共轭梯度法的全局收敛性[J]. 桂林电子科技大学学报, 2009, 29(4): 300-302.
[11]  Zhang, L., Zhou, W. and Li, D. (2006) A Descent Modified Polak-Ribière-Polyak Conjugate Gradient Method and Its Global Convergence. IMA J Numerical Analysis, 26, 629-640.
https://doi.org/10.1093/imanum/drl016
[12]  Zhang, L., Zhou, W. and Li, D. (2006) Global Convergence of a Modi-fied Fletcher Reeves Conjugate Gradient Method with Armijo-Type Line Search. Numerische Mathematik, 104, 561-572.
https://doi.org/10.1007/s00211-006-0028-z
[13]  Li, D.H. and Fukushima, M. (2001) A Modified BFGS Method and Its Global Convergence in Nonconvex Minimization. Journal of Computational and Applied Mathematics, 129, 15-35.
https://doi.org/10.1016/S0377-0427(00)00540-9
[14]  Zhang, L., Zhou, W. and Li, D. (2007) Some Descent Three-Term Conjugate Gradient Methods and Their Global Convergence. Optimization Methods and Software, 22, 697-711.
https://doi.org/10.1080/10556780701223293
[15]  Touati-Ahmed, D. and Story, C. (1990) Global Con-vergent Hybrid Conjugate Gradient Method. Journal of Optimization Theory and Applications, 64, 379-397.
https://doi.org/10.1007/BF00939455
[16]  Dai, Y.H. and Yuan, Y. (2001) An Efficient Hybrid Conjugate Method for Unconstrained Optimization. Annals of Operations Research, 103, 33-47.
https://doi.org/10.1023/A:1012930416777
[17]  Dai, Z.F. and Wen, F.H. (2015) Comments on Another Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization by Andrei. Numerical Algorithms, 69, 337-341.
https://doi.org/10.1007/s11075-014-9899-8
[18]  Zhou, W. (2021) A Projected PRP Method for Optimization with Convex Constraint. Pacilici Journal of Optimization, 17, 47-55.
[19]  Zhou W. (2013) A Short Note on the Global Con-vergence of the Unmodified PRP Method. Optimization Letters, 7, 1367-1372.
https://doi.org/10.1007/s11590-012-0511-7
[20]  Calamai, P.H. and Moré, J.J. (1987) Projected Gradient Methods for Linearly Constrained Problems. Mathematical Programming, 39, 93-116.
https://doi.org/10.1007/BF02592073

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133