ADAPTIVE QUADRATICALLY REGULARIZED NEWTON METHOD FOR RIEMANNIAN OPTIMIZATION

doi:10.1137/17M1142478

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	ADAPTIVE QUADRATICALLY REGULARIZED NEWTON METHOD FOR RIEMANNIAN OPTIMIZATION
	Hu, Jiang 1; Milzarek, Andre 1; Wen, Zaiwen 1; Yuan, Yaxiang2
刊名	SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
	2018
卷号	39 期号:3 页码:1181-1207
关键词	Riemannian optimization regularization trust-region methods inexactness
ISSN号	0895-4798
DOI	10.1137/17M1142478
英文摘要	Optimization on Riemannian manifolds widely arises in eigenvalue computation, density functional theory, Bose-Einstein condensates, low rank nearest correlation, image registration, signal processing, and so on. We propose an adaptive quadratically regularized Newton method which approximates the original objective function by the second-order Taylor expansion in Euclidean space but keeps the Riemannian manifold constraints. The regularization term in the objective function of the subproblem enables us to utilize a Cauchy-point-like condition as the standard trust-region method for proving global convergence. The subproblem can be solved inexactly either by first-order methods or by performing corresponding Riemannian Newton-type steps. In the latter case, we can further take advantage of negative curvature directions. Both global convergence and superlinear local convergence are guaranteed under mild conditions. Extensive computational experiments and comparisons with other state-of-the-art methods indicate that the proposed algorithm is very promising.
资助项目	Elite Program of Computational and Applied Mathematics for Ph.D. Candidates at Peking University ; Boya Postdoctoral Fellowship ; NSFC[11331012] ; NSFC[11461161005] ; NSFC[11421101] ; NSFC[91730302] ; National Basic Research Project[2015CB856002]
WOS研究方向	Mathematics
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000453716400006
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/31829]
专题	计算数学与科学工程计算研究所
通讯作者	Hu, Jiang
作者单位	1.Peking Univ, Beijing Int Ctr Math Res, Beijing, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Hu, Jiang,Milzarek, Andre,Wen, Zaiwen,et al. ADAPTIVE QUADRATICALLY REGULARIZED NEWTON METHOD FOR RIEMANNIAN OPTIMIZATION[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,2018,39(3):1181-1207.
APA	Hu, Jiang,Milzarek, Andre,Wen, Zaiwen,&Yuan, Yaxiang.(2018).ADAPTIVE QUADRATICALLY REGULARIZED NEWTON METHOD FOR RIEMANNIAN OPTIMIZATION.SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,39(3),1181-1207.
MLA	Hu, Jiang,et al."ADAPTIVE QUADRATICALLY REGULARIZED NEWTON METHOD FOR RIEMANNIAN OPTIMIZATION".SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 39.3(2018):1181-1207.