New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization

doi:10.1007/s11075-020-01017-1

	New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization
	Zhao, Ting 3; Liu, Hongwei 3; Liu, Zexian 1,2
刊名	NUMERICAL ALGORITHMS
	2020-10-28
页码	34
关键词	Conjugate gradient method p-regularization model Subspace technique Nonmonotone line search Unconstrained optimization
ISSN号	1017-1398
DOI	10.1007/s11075-020-01017-1
英文摘要	In this paper, two new subspace minimization conjugate gradient methods based on p-regularization models are proposed, where a special scaled norm in p-regularization model is analyzed. Different choices of special scaled norm lead to different solutions to the p-regularized subproblem. Based on the analyses of the solutions in a two-dimensional subspace, we derive new directions satisfying the sufficient descent condition. With a modified nonmonotone line search, we establish the global convergence of the proposed methods under mild assumptions. R-linear convergence of the proposed methods is also analyzed. Numerical results show that, for the CUTEr library, the proposed methods are superior to four conjugate gradient methods, which were proposed by Hager and Zhang (SIAM J. Optim. 16(1):170-192, 2005), Dai and Kou (SIAM J. Optim. 23(1):296-320, 2013), Liu and Liu (J. Optim. Theory. Appl. 180(3):879-906, 2019) and Li et al. (Comput. Appl. Math. 38(1):2019), respectively.
资助项目	National Science Foundation of China[11901561] ; Guangxi Natural Science Foundation[2018GXNSFBA281180] ; China Postdoctoral Science Foundation[2019M660833]
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000582812700002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/52394]
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, Hongwei
作者单位	1.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math & Sci Engn Comp, AMSS, Beijing 100190, Peoples R China 2.Guizhou Univ, Sch Math & Stat, Guiyang 550025, Peoples R China 3.Xidian Univ, Sch Math & Stat, Xian 710126, Peoples R China
推荐引用方式 GB/T 7714	Zhao, Ting,Liu, Hongwei,Liu, Zexian. New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization[J]. NUMERICAL ALGORITHMS,2020:34.
APA	Zhao, Ting,Liu, Hongwei,&Liu, Zexian.(2020).New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization.NUMERICAL ALGORITHMS,34.
MLA	Zhao, Ting,et al."New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization".NUMERICAL ALGORITHMS (2020):34.