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ADAPTIVE QUADRATICALLY REGULARIZED NEWTON METHOD FOR RIEMANNIAN OPTIMIZATION

文献类型：期刊论文

作者Hu, Jiang1; Milzarek, Andre1; Wen, Zaiwen1; Yuan, Yaxiang2
刊名SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
出版日期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
DOI10.1137/17M1142478
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
WOS记录号WOS:000453716400006
出版者SIAM PUBLICATIONS
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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