{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T15:30:37Z","timestamp":1772119837552,"version":"3.50.1"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,1,2]],"date-time":"2024-01-02T00:00:00Z","timestamp":1704153600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,2]],"date-time":"2024-01-02T00:00:00Z","timestamp":1704153600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"crossref","award":["RGPIN-2018-05618"],"award-info":[{"award-number":["RGPIN-2018-05618"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"crossref","award":["RGPIN-2020-05133"],"award-info":[{"award-number":["RGPIN-2020-05133"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2024,2]]},"DOI":"10.1007\/s11222-023-10371-8","type":"journal-article","created":{"date-parts":[[2024,1,2]],"date-time":"2024-01-02T11:03:58Z","timestamp":1704193438000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Accelerated gradient methods for sparse statistical learning with nonconvex penalties"],"prefix":"10.1007","volume":"34","author":[{"given":"Kai","family":"Yang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Masoud","family":"Asgharian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sahir","family":"Bhatnagar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,1,2]]},"reference":[{"key":"10371_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-020-09983-1","author":"\u00d6D Akyildiz","year":"2021","unstructured":"Akyildiz, \u00d6.D., M\u00edguez, J.: Convergence rates for optimised adaptive importance samplers. Stat. Comput. (2021). https:\/\/doi.org\/10.1007\/s11222-020-09983-1","journal-title":"Stat. Comput."},{"key":"10371_CR2","doi-asserted-by":"publisher","unstructured":"Beck, A.: First-Order Methods in Optimization. SIAM-Society for Industrial and Applied Mathematics. Philadelphia, PA, USA (2017). https:\/\/doi.org\/10.5555\/3204879","DOI":"10.5555\/3204879"},{"key":"10371_CR3","doi-asserted-by":"publisher","unstructured":"Breheny, P., Huang, J.: Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection. Ann. Appl. Stat. 5(1), 232\u2013253 (2011). arxiv:1104.2748v1. https:\/\/doi.org\/10.1214\/10-AOAS388","DOI":"10.1214\/10-AOAS388"},{"issue":"4","key":"10371_CR4","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1137\/0609045","volume":"9","author":"A Edelman","year":"1988","unstructured":"Edelman, A.: Eigenvalues and condition numbers of random matrices. SIAM J. Matrix Anal. Appl. 9(4), 543\u2013560 (1988). https:\/\/doi.org\/10.1137\/0609045","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"456","key":"10371_CR5","doi-asserted-by":"publisher","first-page":"1348","DOI":"10.1198\/016214501753382273","volume":"96","author":"J Fan","year":"2001","unstructured":"Fan, J., Li, R.: Variable selection via nonconcave penalized likelihood and its oracle properties. J. Am. Stat. Assoc. 96(456), 1348\u20131360 (2001)","journal-title":"J. Am. Stat. Assoc."},{"key":"10371_CR6","doi-asserted-by":"publisher","unstructured":"Friedman, J., Hastie, T., H\u00f6fling, H., Tibshirani, R.: Pathwise coordinate optimization. Ann. Appl. Stat. 1(2), 302\u2013332 (2007). arxiv:0708.1485. https:\/\/doi.org\/10.1214\/07-AOAS131","DOI":"10.1214\/07-AOAS131"},{"issue":"1\u20132","key":"10371_CR7","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/s10107-015-0871-8","volume":"156","author":"S Ghadimi","year":"2015","unstructured":"Ghadimi, S., Lan, G.: Accelerated gradient methods for nonconvex nonlinear and stochastic programming. Math. Program. 156(1\u20132), 59\u201399 (2015). https:\/\/doi.org\/10.1007\/s10107-015-0871-8","journal-title":"Math. Program."},{"key":"10371_CR8","doi-asserted-by":"publisher","unstructured":"Ghosh, A., Thoresen, M.: Non-concave penalization in linear mixed-effects models and regularized selection of fixed effects. AStA Adv. Stat. Anal. 102(2), 179\u2013210 (2018). arxiv:1607.02883v1. https:\/\/doi.org\/10.1007\/s10182-017-0298-z","DOI":"10.1007\/s10182-017-0298-z"},{"key":"10371_CR9","first-page":"18","volume":"15","author":"SZ Ibrahim","year":"2012","unstructured":"Ibrahim, S.Z., Abdallah, M., N\u2019Guessan, A.: A mixture of local and quadratic approximation variable selection algorithm in nonconcave penalized regression. ARIMA 15, 18 (2012)","journal-title":"ARIMA"},{"key":"10371_CR10","unstructured":"Jin, C., Netrapalli, P., Jordan, M.I.: Accelerated gradient descent escapes saddle points faster than gradient descent (2017) arxiv:1711.10456"},{"issue":"484","key":"10371_CR11","doi-asserted-by":"publisher","first-page":"1665","DOI":"10.1198\/016214508000001066","volume":"103","author":"Y Kim","year":"2008","unstructured":"Kim, Y., Choi, H., Oh, H.-S.: Smoothly clipped absolute deviation on high dimensions. J. Am. Stat. Assoc. 103(484), 1665\u20131673 (2008)","journal-title":"J. Am. Stat. Assoc."},{"issue":"1\u20132","key":"10371_CR12","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/s10107-010-0434-y","volume":"133","author":"G Lan","year":"2011","unstructured":"Lan, G.: An optimal method for stochastic composite optimization. Math. Program. 133(1\u20132), 365\u2013397 (2011). https:\/\/doi.org\/10.1007\/s10107-010-0434-y","journal-title":"Math. Program."},{"issue":"4","key":"10371_CR13","doi-asserted-by":"publisher","first-page":"1074","DOI":"10.1080\/10618600.2014.975231","volume":"24","author":"S Lee","year":"2015","unstructured":"Lee, S., Breheny, P.: Strong rules for nonconvex penalties and their implications for efficient algorithms in high-dimensional regression. J. Comput. Graph. Stat. 24(4), 1074\u20131091 (2015). https:\/\/doi.org\/10.1080\/10618600.2014.975231","journal-title":"J. Comput. Graph. Stat."},{"issue":"C","key":"10371_CR14","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/j.csda.2015.08.019","volume":"94","author":"S Lee","year":"2016","unstructured":"Lee, S., Kwon, S., Kim, Y.: A modified local quadratic approximation algorithm for penalized optimization problems. Comput. Stat. Data Anal. 94(C), 275\u2013286 (2016). https:\/\/doi.org\/10.1016\/j.csda.2015.08.019","journal-title":"Comput. Stat. Data Anal."},{"issue":"495","key":"10371_CR15","doi-asserted-by":"publisher","first-page":"1125","DOI":"10.1198\/jasa.2011.tm09738","volume":"106","author":"R Mazumder","year":"2011","unstructured":"Mazumder, R., Friedman, J.H., Hastie, T.: Sparsenet: coordinate descent with nonconvex penalties. J. Am. Stat. Assoc. 106(495), 1125\u20131138 (2011)","journal-title":"J. Am. Stat. Assoc."},{"key":"10371_CR16","unstructured":"Meckes, E.: The eigenvalues of random matrices, IMAGE, the Bulletin of the International Linear Algebra Society, no. 65, pp. 9\u201322 (2020). arxiv:2101.02928"},{"key":"10371_CR17","first-page":"543","volume":"269","author":"YE Nesterov","year":"1983","unstructured":"Nesterov, Y.E.: A method for solving the convex programming problem with convergence rate $$o(1\/k^2)$$. Dokl. Akad. Nauk SSSR 269, 543\u2013547 (1983)","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"10371_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8853-9","volume-title":"Introductory Lectures on Convex Optimization","author":"Y Nesterov","year":"2004","unstructured":"Nesterov, Y.: Introductory Lectures on Convex Optimization. Springer, New York (2004). https:\/\/doi.org\/10.1007\/978-1-4419-8853-9"},{"issue":"1","key":"10371_CR19","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/s10107-012-0629-5","volume":"140","author":"Y Nesterov","year":"2012","unstructured":"Nesterov, Y.: Gradient methods for minimizing composite functions. Math. Program. 140(1), 125\u2013161 (2012). https:\/\/doi.org\/10.1007\/s10107-012-0629-5","journal-title":"Math. Program."},{"key":"10371_CR20","unstructured":"Paquette, C., van Merri\u00ebnboer, B., Paquette, E., Pedregosa, F.: Halting time is predictable for large models: a universality property and average-case analysis (2020). arxiv:2006.04299"},{"key":"10371_CR21","doi-asserted-by":"publisher","first-page":"1173","DOI":"10.1016\/j.future.2018.04.072","volume":"108","author":"T Parnell","year":"2020","unstructured":"Parnell, T., D\u00fcnner, C., Atasu, K., Sifalakis, M., Pozidis, H.: Tera-scale coordinate descent on GPUs. Futur. Gener. Comput. Syst. 108, 1173\u20131191 (2020). https:\/\/doi.org\/10.1016\/j.future.2018.04.072","journal-title":"Futur. Gener. Comput. Syst."},{"key":"10371_CR22","volume-title":"Numerical Mathematics","author":"A Quarteroni","year":"2000","unstructured":"Quarteroni, A.: Numerical Mathematics. Springer, New York (2000)"},{"issue":"2","key":"10371_CR23","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1080\/10618600.2012.681250","volume":"22","author":"N Simon","year":"2013","unstructured":"Simon, N., Friedman, J., Hastie, T., Tibshirani, R.: A sparse-group lasso. J. Comput. Graph. Stat. 22(2), 231\u2013245 (2013). https:\/\/doi.org\/10.1080\/10618600.2012.681250","journal-title":"J. Comput. Graph. Stat."},{"key":"10371_CR24","doi-asserted-by":"publisher","unstructured":"Spall, J.C.: Cyclic seesaw process for optimization and identification. J. Optim. Theory Appl. 154(1), 187\u2013208 (2012). https:\/\/doi.org\/10.1007\/s10957-012-0001-1","DOI":"10.1007\/s10957-012-0001-1"},{"key":"10371_CR25","unstructured":"Su, W., Boyd, S., Cand\u00e8s, E.J.: A differential equation for modeling Nesterov\u2019s accelerated gradient method: theory and insights. In: Proceedings of the 27th International Conference on Neural Information Processing Systems\u2014Volume 2. NIPS\u201914, pp. 2510\u20132518. MIT Press, Cambridge (2014)"},{"issue":"1","key":"10371_CR26","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","volume":"58","author":"R Tibshirani","year":"1996","unstructured":"Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B (Methodol.) 58(1), 267\u2013288 (1996)","journal-title":"J. R. Stat. Soc. Ser. B (Methodol.)"},{"key":"10371_CR27","doi-asserted-by":"publisher","unstructured":"Wang, L., Kim, Y., Li, R.: Calibrating nonconvex penalized regression in ultra-high dimension. Ann. Stat. 41(5), 2505\u20132536 (2013), arxiv:1311.4981v1. https:\/\/doi.org\/10.1214\/13-AOS1159","DOI":"10.1214\/13-AOS1159"},{"issue":"6","key":"10371_CR28","doi-asserted-by":"publisher","first-page":"1129","DOI":"10.1007\/s11222-014-9498-5","volume":"25","author":"Y Yang","year":"2014","unstructured":"Yang, Y., Zou, H.: A fast unified algorithm for solving group-lasso penalize learning problems. Stat. Comput. 25(6), 1129\u20131141 (2014). https:\/\/doi.org\/10.1007\/s11222-014-9498-5","journal-title":"Stat. Comput."},{"issue":"1","key":"10371_CR29","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1080\/10618600.2013.878662","volume":"24","author":"D Yu","year":"2015","unstructured":"Yu, D., Won, J.-H., Lee, T., Lim, J., Yoon, S.: High-dimensional fused lasso regression using majorization-minimization and parallel processing. J. Comput. Graph. Stat. 24(1), 121\u2013153 (2015). https:\/\/doi.org\/10.1080\/10618600.2013.878662","journal-title":"J. Comput. Graph. Stat."},{"key":"10371_CR30","doi-asserted-by":"publisher","unstructured":"Zhang, C.-H.: Nearly unbiased variable selection under minimax concave penalty. Ann. Stat. 38(2), 894\u2013942 (2010) arxiv:1002.4734v1. https:\/\/doi.org\/10.1214\/09-AOS729","DOI":"10.1214\/09-AOS729"},{"issue":"2","key":"10371_CR31","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1111\/j.1467-9868.2005.00503.x","volume":"67","author":"H Zou","year":"2005","unstructured":"Zou, H., Hastie, T.: Regularization and variable selection via the elastic net. J. R. Stat. Soc. Ser. B (Stat. Methodol.) 67(2), 301\u2013320 (2005)","journal-title":"J. R. Stat. Soc. Ser. B (Stat. Methodol.)"},{"issue":"4","key":"10371_CR32","first-page":"1509","volume":"36","author":"H Zou","year":"2008","unstructured":"Zou, H., Li, R.: One-step sparse estimates in nonconcave penalized likelihood models. Ann. Stat. 36(4), 1509\u20131533 (2008). arxiv:0808.1012v1","journal-title":"Ann. Stat."}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-023-10371-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11222-023-10371-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-023-10371-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,7]],"date-time":"2024-11-07T02:20:44Z","timestamp":1730946044000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11222-023-10371-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,2]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,2]]}},"alternative-id":["10371"],"URL":"https:\/\/doi.org\/10.1007\/s11222-023-10371-8","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-2310550\/v1","asserted-by":"object"}]},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1,2]]},"assertion":[{"value":"24 November 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 December 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 January 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"59"}}