An improved Dai-Kou conjugate gradient algorithm for unconstrained optimization

doi:10.1007/s10589-019-00143-4

CSpace

	An improved Dai-Kou conjugate gradient algorithm for unconstrained optimization
	Liu, Zexian 1,2; Liu, Hongwei 1; Dai, Yu-Hong 2
	2019-11-02
发表期刊	COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
ISSN	0926-6003
页码	23
摘要	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.
关键词	Conjugate gradient algorithm Limited memory Quasi-Newton method Preconditioned conjugate gradient algorithm Global convergence
DOI	10.1007/s10589-019-00143-4
收录类别	SCI
语种	英语
资助项目	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研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000493670900001
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50625
专题	中国科学院数学与系统科学研究院
通讯作者	Dai, Yu-Hong
作者单位	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
推荐引用方式 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.