KMS Of Academy of mathematics and systems sciences, CAS
| An improved Dai-Kou conjugate gradient algorithm for unconstrained optimization | |
| Liu, Zexian1,2; Liu, Hongwei1; Dai, Yu-Hong2 | |
| 2019-11-02 | |
| Source Publication | COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
 |
| ISSN | 0926-6003 |
| Pages | 23 |
| Abstract | It is gradually accepted that the loss of orthogonality of the gradients in a conjugate gradient algorithm may decelerate the convergence rate to some extent. The Dai-Kou conjugate gradient algorithm (SIAM J Optim 23(1):296-320, 2013), called CGOPT, has attracted many researchers' attentions due to its numerical efficiency. In this paper, we present an improved Dai-Kou conjugate gradient algorithm for unconstrained optimization, which only consists of two kinds of iterations. In the improved Dai-Kou conjugate gradient algorithm, we develop a new quasi-Newton method to improve the orthogonality by solving the subproblem in the subspace and design a modified strategy for the choice of the initial stepsize for improving the numerical performance. The global convergence of the improved Dai-Kou conjugate gradient algorithm is established without the strict assumptions in the convergence analysis of other limited memory conjugate gradient methods. Some numerical results suggest that the improved Dai-Kou conjugate gradient algorithm (CGOPT (2.0)) yields a tremendous improvement over the original Dai-Kou CG algorithm (CGOPT (1.0)) and is slightly superior to the latest limited memory conjugate gradient software package CG_DESCENT (6.8) developed by Hager and Zhang (SIAM J Optim 23(4):2150-2168, 2013) for the CUTEr library. |
| Keyword | Conjugate gradient algorithm Limited memory Quasi-Newton method Preconditioned conjugate gradient algorithm Global convergence |
| DOI | 10.1007/s10589-019-00143-4 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | Chinese NSF[11631013] ; Chinese NSF[11971372] ; Key Project of Chinese National Programs for Fundamental Research and Development[2015CB856002] ; National Natural Science Foundation of China[11901561] ; Natural Science Foundation of Guangxi[2018GXNSFBA281180] |
| WOS Research Area | Operations Research & Management Science ; Mathematics |
| WOS Subject | Operations Research & Management Science ; Mathematics, Applied |
| WOS ID | WOS:000493670900001 |
| Publisher | SPRINGER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/50625 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Dai, Yu-Hong |
| Affiliation | 1.Xidian Univ, Sch Math & Stat, Xian 710126, Shaanxi, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Liu, Zexian,Liu, Hongwei,Dai, Yu-Hong. An improved Dai-Kou conjugate gradient algorithm for unconstrained optimization[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,2019:23. |
| APA | Liu, Zexian,Liu, Hongwei,&Dai, Yu-Hong.(2019).An improved Dai-Kou conjugate gradient algorithm for unconstrained optimization.COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,23. |
| MLA | Liu, Zexian,et al."An improved Dai-Kou conjugate gradient algorithm for unconstrained optimization".COMPUTATIONAL OPTIMIZATION AND APPLICATIONS (2019):23. |
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