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ADAPTIVE QUADRATICALLY REGULARIZED NEWTON METHOD FOR RIEMANNIAN OPTIMIZATION
Hu, Jiang1; Milzarek, Andre1; Wen, Zaiwen1; Yuan, Yaxiang2
2018
Source PublicationSIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
ISSN0895-4798
Volume39Issue:3Pages:1181-1207
AbstractOptimization 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.
KeywordRiemannian optimization regularization trust-region methods inexactness
DOI10.1137/17M1142478
Language英语
Funding ProjectElite 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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000453716400006
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31830
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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