{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T16:44:57Z","timestamp":1747154697823,"version":"3.40.5"},"reference-count":42,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T00:00:00Z","timestamp":1722470400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T00:00:00Z","timestamp":1722470400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T00:00:00Z","timestamp":1722470400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T00:00:00Z","timestamp":1722470400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T00:00:00Z","timestamp":1722470400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T00:00:00Z","timestamp":1722470400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T00:00:00Z","timestamp":1722470400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Applied Mathematics and Computation"],"published-print":{"date-parts":[[2024,8]]},"DOI":"10.1016\/j.amc.2024.128708","type":"journal-article","created":{"date-parts":[[2024,4,9]],"date-time":"2024-04-09T18:45:40Z","timestamp":1712688340000},"page":"128708","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":2,"special_numbering":"C","title":["An efficient algorithm for Fantope-constrained sparse principal subspace estimation problem"],"prefix":"10.1016","volume":"475","author":[{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0002-6586-2862","authenticated-orcid":false,"given":"Yong-Jin","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuqi","family":"Wan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0009-0009-0159-1088","authenticated-orcid":false,"given":"Lanyu","family":"Lin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.amc.2024.128708_br0010","first-page":"9990","article-title":"Fast projection onto the capped simplex with applications to sparse regression in bioinformatics","volume":"34","author":"Ang","year":"2021","journal-title":"Adv. Neural Inf. Process. Syst."},{"year":"2017","series-title":"First-Order Methods in Optimization","author":"Beck","key":"10.1016\/j.amc.2024.128708_br0020"},{"year":"2013","series-title":"Matrix Analysis","author":"Bhatia","key":"10.1016\/j.amc.2024.128708_br0030"},{"issue":"1\u20132","key":"10.1016\/j.amc.2024.128708_br0040","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1007\/s10107-014-0853-2","article-title":"A semismooth Newton-CG based dual PPA for matrix spectral norm approximation problems","volume":"155","author":"Chen","year":"2016","journal-title":"Math. Program."},{"year":"1990","series-title":"Optimization and Nonsmooth Analysis","author":"Clarke","key":"10.1016\/j.amc.2024.128708_br0050"},{"issue":"3","key":"10.1016\/j.amc.2024.128708_br0060","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1137\/050645506","article-title":"A direct formulation for sparse PCA using semidefinite programming","volume":"49","author":"d'Aspremont","year":"2004","journal-title":"SIAM Rev."},{"year":"2005","series-title":"Convex Optimization & Euclidean Distance Geometry","author":"Dattorro","key":"10.1016\/j.amc.2024.128708_br0070"},{"year":"2012","series-title":"An introduction to a class of matrix optimization problems","author":"Ding","key":"10.1016\/j.amc.2024.128708_br0080"},{"key":"10.1016\/j.amc.2024.128708_br0090","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1007\/s10107-017-1162-3","article-title":"Spectral operators of matrices","volume":"168","author":"Ding","year":"2018","journal-title":"Math. Program."},{"issue":"1","key":"10.1016\/j.amc.2024.128708_br0100","doi-asserted-by":"crossref","first-page":"630","DOI":"10.1137\/18M1222235","article-title":"Spectral operators of matrices: semismoothness and characterizations of the generalized Jacobian","volume":"30","author":"Ding","year":"2020","journal-title":"SIAM J. Optim."},{"issue":"6","key":"10.1016\/j.amc.2024.128708_br0110","doi-asserted-by":"crossref","first-page":"A4147","DOI":"10.1137\/20M1364643","article-title":"Efficient sparse Hessian-based semismooth Newton algorithms for Dantzig selector","volume":"43","author":"Fang","year":"2021","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"10.1016\/j.amc.2024.128708_br0120","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/0898-1221(76)90003-1","article-title":"A dual algorithm for the solution of nonlinear variational problems via finite element approximation","volume":"2","author":"Gabay","year":"1976","journal-title":"Comput. Math. Appl."},{"key":"10.1016\/j.amc.2024.128708_br0130","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.jprocont.2017.03.005","article-title":"Real-time fault detection and diagnosis using sparse principal component analysis","volume":"67","author":"Gajjar","year":"2018","journal-title":"J. Process Control"},{"key":"10.1016\/j.amc.2024.128708_br0140","first-page":"41","article-title":"Sur l'approximation, par \u00e9l\u00e9ments finis d'ordre un, et la r\u00e9solution, par p\u00e9nalisation-dualit\u00e9 d'une classe de probl\u00e8mes de Dirichlet non lin\u00e9aires","volume":"2","author":"Glowinski","year":"1975","journal-title":"J. Equine Vet. Sci."},{"issue":"3","key":"10.1016\/j.amc.2024.128708_br0150","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1198\/1061860032148","article-title":"A modified principal component technique based on the LASSO","volume":"12","author":"Jolliffe","year":"2003","journal-title":"J. Comput. Graph. Stat."},{"key":"10.1016\/j.amc.2024.128708_br0160","first-page":"517","article-title":"Generalized power method for sparse principal component analysis","volume":"11","author":"Journ\u00e9e","year":"2010","journal-title":"J. Mach. Learn. Res."},{"key":"10.1016\/j.amc.2024.128708_br0170","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1515\/9783112479926-011","article-title":"Newton's method for non-differentiable functions","volume":"45","author":"Kummer","year":"1988","journal-title":"Adv. Math. Optim."},{"key":"10.1016\/j.amc.2024.128708_br0180","series-title":"Proceedings 6th French-German Colloquium on Optimization","first-page":"171","article-title":"Newton's method based on generalized derivatives for nonsmooth functions: convergence analysis","author":"Kummer","year":"1992"},{"issue":"4","key":"10.1016\/j.amc.2024.128708_br0190","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1002\/gepi.21621","article-title":"Sparse principal component analysis for identifying ancestry-informative markers in genome-wide association studies","volume":"36","author":"Lee","year":"2012","journal-title":"Genet. Epidemiol."},{"key":"10.1016\/j.amc.2024.128708_br0200","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1137\/S1052623494267127","article-title":"Practical aspects of the Moreau envelope regularization: theoretical preliminaries","volume":"7","author":"Lemar\u00e9chal","year":"1997","journal-title":"SIAM J. Optim."},{"issue":"1","key":"10.1016\/j.amc.2024.128708_br0210","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/s10107-017-1182-z","article-title":"Near-optimal stochastic approximation for online principal component estimation","volume":"167","author":"Li","year":"2018","journal-title":"Math. Program."},{"key":"10.1016\/j.amc.2024.128708_br0220","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10915-021-01541-9","article-title":"An efficient Hessian based algorithm for singly linearly and box constrained least squares regression","volume":"88","author":"Lin","year":"2021","journal-title":"J. Sci. Comput."},{"issue":"3","key":"10.1016\/j.amc.2024.128708_br0230","doi-asserted-by":"crossref","first-page":"2026","DOI":"10.1137\/18M1207752","article-title":"Efficient sparse semismooth Newton methods for the clustered Lasso problem","volume":"29","author":"Lin","year":"2019","journal-title":"SIAM J. Optim."},{"key":"10.1016\/j.amc.2024.128708_br0240","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1007\/s10957-022-02120-0","article-title":"A semismooth Newton-based augmented Lagrangian algorithm for density matrix least squares problems","volume":"195","author":"Liu","year":"2022","journal-title":"J. Optim. Theory Appl."},{"key":"10.1016\/j.amc.2024.128708_br0250","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1007\/s10589-023-00467-2","article-title":"A semismooth Newton based dual proximal point algorithm for maximum eigenvalue problem","volume":"85","author":"Liu","year":"2023","journal-title":"Comput. Optim. Appl."},{"key":"10.1016\/j.amc.2024.128708_br0260","doi-asserted-by":"crossref","first-page":"772","DOI":"10.1214\/13-AOS1097","article-title":"Sparse principal component analysis and iterative thresholding","volume":"41","author":"Ma","year":"2013","journal-title":"Ann. Stat."},{"key":"10.1016\/j.amc.2024.128708_br0270","doi-asserted-by":"crossref","first-page":"273","DOI":"10.24033\/bsmf.1625","article-title":"Proximit\u00e9 et dualit\u00e9 dans un espace hilbertien","volume":"93","author":"Moreau","year":"1965","journal-title":"Bull. Soc. Math. Fr."},{"key":"10.1016\/j.amc.2024.128708_br0280","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/BF01581275","article-title":"A nonsmooth version of Newton's method","volume":"58","author":"Qi","year":"1993","journal-title":"Math. Program."},{"key":"10.1016\/j.amc.2024.128708_br0290","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1093\/biomet\/asac041","article-title":"Gradient-based sparse principal component analysis with extensions to online learning","volume":"110","author":"Qiu","year":"2023","journal-title":"Biometrika"},{"year":"1970","series-title":"Convex Analysis","author":"Rockafellar","key":"10.1016\/j.amc.2024.128708_br0300"},{"key":"10.1016\/j.amc.2024.128708_br0310","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1287\/moor.1.2.97","article-title":"Augmented Lagrangians and applications of the proximal point algorithm in convex programming","volume":"1","author":"Rockafellar","year":"1976","journal-title":"Math. Oper. Res."},{"key":"10.1016\/j.amc.2024.128708_br0320","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1137\/0314056","article-title":"Monotone operators and the proximal point algorithm","volume":"14","author":"Rockafellar","year":"1976","journal-title":"SIAM J. Control Optim."},{"key":"10.1016\/j.amc.2024.128708_br0330","first-page":"97","article-title":"Selective factor extraction in high dimensions","volume":"104","author":"She","year":"2017","journal-title":"Biometrika"},{"key":"10.1016\/j.amc.2024.128708_br0340","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1016\/j.jmva.2007.06.007","article-title":"Sparse principal component analysis via regularized low rank matrix approximation","volume":"99","author":"Shen","year":"2008","journal-title":"J. Multivar. Anal."},{"key":"10.1016\/j.amc.2024.128708_br0350","article-title":"Fantope projection and selection: a near-optimal convex relaxation of sparse PCA","volume":"26","author":"Vu","year":"2013","journal-title":"Adv. Neural Inf. Process. Syst."},{"author":"Wang","key":"10.1016\/j.amc.2024.128708_br0360"},{"author":"Wang","key":"10.1016\/j.amc.2024.128708_br0370"},{"key":"10.1016\/j.amc.2024.128708_br0380","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1137\/120864192","article-title":"A proximal point algorithm for log-determinant optimization with group Lasso regularization","volume":"23","author":"Yang","year":"2013","journal-title":"SIAM J. Optim."},{"key":"10.1016\/j.amc.2024.128708_br0390","doi-asserted-by":"crossref","first-page":"2197","DOI":"10.1137\/19M1267830","article-title":"A proximal point dual Newton algorithm for solving group graphical Lasso problems","volume":"30","author":"Zhang","year":"2020","journal-title":"SIAM J. Optim."},{"key":"10.1016\/j.amc.2024.128708_br0400","doi-asserted-by":"crossref","first-page":"1737","DOI":"10.1137\/080718206","article-title":"A Newton-CG augmented Lagrangian method for semidefinite programming","volume":"20","author":"Zhao","year":"2010","journal-title":"SIAM J. Optim."},{"key":"10.1016\/j.amc.2024.128708_br0410","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1198\/106186006X113430","article-title":"Sparse principal component analysis","volume":"15","author":"Zou","year":"2006","journal-title":"J. Comput. Graph. Stat."},{"key":"10.1016\/j.amc.2024.128708_br0420","doi-asserted-by":"crossref","first-page":"1311","DOI":"10.1109\/JPROC.2018.2846588","article-title":"A selective overview of sparse principal component analysis","author":"Zou","year":"2018","journal-title":"Proc. IEEE"}],"container-title":["Applied Mathematics and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/api.elsevier.com\/content\/article\/PII:S0096300324001802?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/api.elsevier.com\/content\/article\/PII:S0096300324001802?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T04:42:37Z","timestamp":1719031357000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/linkinghub.elsevier.com\/retrieve\/pii\/S0096300324001802"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8]]},"references-count":42,"alternative-id":["S0096300324001802"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/j.amc.2024.128708","relation":{},"ISSN":["0096-3003"],"issn-type":[{"type":"print","value":"0096-3003"}],"subject":[],"published":{"date-parts":[[2024,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"An efficient algorithm for Fantope-constrained sparse principal subspace estimation problem","name":"articletitle","label":"Article Title"},{"value":"Applied Mathematics and Computation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/j.amc.2024.128708","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2024 Elsevier Inc. All rights reserved.","name":"copyright","label":"Copyright"}],"article-number":"128708"}}