ADAPTIVE QUADRATICALLY REGULARIZED NEWTON METHOD FOR RIEMANNIAN OPTIMIZATION

doi:10.1137/17M1142478

	ADAPTIVE QUADRATICALLY REGULARIZED NEWTON METHOD FOR RIEMANNIAN OPTIMIZATION
	Hu, Jiang 1; Milzarek, Andre 1; Wen, Zaiwen 1; Yuan, Yaxiang2
	2018
发表期刊	SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
ISSN	0895-4798
卷号	39 期号:3 页码:1181-1207
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.
关键词	Riemannian optimization regularization trust-region methods inexactness
DOI	10.1137/17M1142478
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000453716400006
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31830
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.