{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T13:38:55Z","timestamp":1740145135346,"version":"3.37.3"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,7,26]],"date-time":"2022-07-26T00:00:00Z","timestamp":1658793600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,7,26]],"date-time":"2022-07-26T00:00:00Z","timestamp":1658793600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100020771","name":"Young Scientists Fund of the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12001367"],"award-info":[{"award-number":["12001367"]}],"id":[{"id":"10.13039\/501100020771","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100007219","name":"Natural Science Foundation of Shanghai","doi-asserted-by":"publisher","award":["21ZR1442800"],"award-info":[{"award-number":["21ZR1442800"]}],"id":[{"id":"10.13039\/100007219","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2023,3]]},"DOI":"10.1007\/s11590-022-01907-4","type":"journal-article","created":{"date-parts":[[2022,7,26]],"date-time":"2022-07-26T04:02:47Z","timestamp":1658808167000},"page":"413-435","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Convergence rate analysis of proximal iteratively reweighted $$\\ell _1$$ methods for $$\\ell _p$$ regularization problems"],"prefix":"10.1007","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8821-7260","authenticated-orcid":false,"given":"Hao","family":"Wang","sequence":"first","affiliation":[]},{"given":"Hao","family":"Zeng","sequence":"additional","affiliation":[]},{"given":"Jiashan","family":"Wang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,7,26]]},"reference":[{"issue":"1","key":"1907_CR1","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/s10107-007-0133-5","volume":"116","author":"H Attouch","year":"2009","unstructured":"Attouch, H., Bolte, J.: On the convergence of the proximal algorithm for nonsmooth functions involving analytic features. Math. Program. 116(1), 5\u201316 (2009). https:\/\/doi.org\/10.1007\/s10107-007-0133-5","journal-title":"Math. Program."},{"issue":"2","key":"1907_CR2","doi-asserted-by":"publisher","first-page":"438","DOI":"10.1287\/moor.1100.0449","volume":"35","author":"H Attouch","year":"2010","unstructured":"Attouch, H., Bolte, J., Redont, P., Soubeyran, A.: Proximal alternating minimization and projection methods for nonconvex problems: An approach based on the kurdyka-\u0142ojasiewicz inequality. Math. Oper. Res. 35(2), 438\u2013457 (2010)","journal-title":"Math. Oper. Res."},{"issue":"1\u20132","key":"1907_CR3","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/s10107-011-0484-9","volume":"137","author":"H Attouch","year":"2013","unstructured":"Attouch, H., Bolte, J., Svaiter, B.F.: Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized gauss-seidel methods. Math. Program. 137(1\u20132), 91\u2013129 (2013)","journal-title":"Math. Program."},{"issue":"1","key":"1907_CR4","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1007\/s10107-013-0701-9","volume":"146","author":"J Bolte","year":"2014","unstructured":"Bolte, J., Sabach, S., Teboulle, M.: Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Math. Program. 146(1), 459\u2013494 (2014). https:\/\/doi.org\/10.1007\/s10107-013-0701-9","journal-title":"Math. Program."},{"issue":"1","key":"1907_CR5","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1007\/s10107-013-0701-9","volume":"146","author":"J Bolte","year":"2014","unstructured":"Bolte, J., Sabach, S., Teboulle, M.: Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Math. Program. 146(1), 459\u2013494 (2014)","journal-title":"Math. Program."},{"issue":"4","key":"1907_CR6","doi-asserted-by":"publisher","first-page":"1205","DOI":"10.1137\/050644641","volume":"17","author":"J Bolte","year":"2007","unstructured":"Bolte, J., Daniilidis, A., Lewis, A.: The \u0142ojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems. SIAM J. Optim. 17(4), 1205\u20131223 (2007). https:\/\/doi.org\/10.1137\/050644641","journal-title":"SIAM J. Optim."},{"issue":"5\u20136","key":"1907_CR7","doi-asserted-by":"publisher","first-page":"877","DOI":"10.1007\/s00041-008-9045-x","volume":"14","author":"EJ Candes","year":"2008","unstructured":"Candes, E.J., Wakin, M.B., Boyd, S.P.: Enhancing sparsity by reweighted $$\\ell _1$$ minimization. J. Fourier Anal. Appl. 14(5\u20136), 877\u2013905 (2008)","journal-title":"J. Fourier Anal. Appl."},{"key":"1907_CR8","doi-asserted-by":"publisher","first-page":"1528","DOI":"10.1137\/120871390","volume":"23","author":"X Chen","year":"2013","unstructured":"Chen, X., Niu, L., Yuan, Y.X.: Optimality conditions and a smoothing trust region newton method for nonlipschitz optimization. SIAM J. Optim. 23, 1528\u20131552 (2013)","journal-title":"SIAM J. Optim."},{"key":"1907_CR9","unstructured":"Chen, X., Zhou, W.: Convergence of reweighted $$\\ell _1$$ minimization algorithms and unique solution of truncated lp minimization. The Hong Kong Polytechnic University, Department of Applied Mathematics (2010)"},{"issue":"1","key":"1907_CR10","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1111\/j.1467-9868.2009.00723.x","volume":"72","author":"H Chun","year":"2010","unstructured":"Chun, H., Kele\u015f, S.: Sparse partial least squares regression for simultaneous dimension reduction and variable selection. J. R. Stat. Soc. Ser. B (Statistical Methodology) 72(1), 3\u201325 (2010)","journal-title":"J. R. Stat. Soc. Ser. B (Statistical Methodology)"},{"issue":"12","key":"1907_CR11","doi-asserted-by":"publisher","first-page":"2980","DOI":"10.1109\/TIP.2007.909318","volume":"16","author":"MA Figueiredo","year":"2007","unstructured":"Figueiredo, M.A., Bioucas-Dias, J.M., Nowak, R.D.: Majorization-minimization algorithms for wavelet-based image restoration. IEEE Trans. Image Process. 16(12), 2980\u20132991 (2007)","journal-title":"IEEE Trans. Image Process."},{"issue":"2","key":"1907_CR12","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1007\/s10107-011-0470-2","volume":"129","author":"D Ge","year":"2011","unstructured":"Ge, D., Jiang, X., Ye, Y.: A note on the complexity of $$\\ell _p$$ minimization. Math. Program. 129(2), 285\u2013299 (2011)","journal-title":"Math. Program."},{"issue":"4","key":"1907_CR13","doi-asserted-by":"publisher","first-page":"853","DOI":"10.1007\/s10898-020-00955-3","volume":"79","author":"Y Hu","year":"2021","unstructured":"Hu, Y., Li, C., Meng, K., Yang, X.: Linear convergence of inexact descent method and inexact proximal gradient algorithms for lower-order regularization problems. J. Global Optim. 79(4), 853\u2013883 (2021)","journal-title":"J. Global Optim."},{"issue":"1","key":"1907_CR14","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1137\/090775397","volume":"21","author":"MJ Lai","year":"2011","unstructured":"Lai, M.J., Wang, J.: An unconstrained $$ \\ell _q $$ minimization with $$0<q\\le 1$$ for sparse solution of underdetermined linear systems. SIAM J. Optim. 21(1), 82\u2013101 (2011)","journal-title":"SIAM J. Optim."},{"issue":"5","key":"1907_CR15","doi-asserted-by":"publisher","first-page":"1199","DOI":"10.1007\/s10208-017-9366-8","volume":"18","author":"G Li","year":"2018","unstructured":"Li, G., Pong, T.K.: Calculus of the exponent of kurdyka-\u0142ojasiewicz inequality and its applications to linear convergence of first-order methods. Found. Comput. Math. 18(5), 1199\u20131232 (2018)","journal-title":"Found. Comput. Math."},{"key":"1907_CR16","unstructured":"Li, Q., Zhou, Y., Liang, Y., Varshney, P.K.: Convergence analysis of proximal gradient with momentum for nonconvex optimization. In: Proceedings of the 34th International Conference on Machine Learning-Volume 70, pp. 2111\u20132119. JMLR. org, Sydney, Australia (2017)"},{"key":"1907_CR17","doi-asserted-by":"crossref","unstructured":"Lu, C., Wei, Y., Lin, Z., Yan, S.: Proximal iteratively reweighted algorithm with multiple splitting for nonconvex sparsity optimization. In: Twenty-Eighth AAAI Conference on Artificial Intelligence. AAAI Press, Qu\u00e9bec, Canada (2014)","DOI":"10.1609\/aaai.v28i1.8897"},{"issue":"1\u20132","key":"1907_CR18","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1007\/s10107-013-0722-4","volume":"147","author":"Z Lu","year":"2014","unstructured":"Lu, Z.: Iterative reweighted minimization methods for $$\\ell _p$$ regularized unconstrained nonlinear programming. Math. Program. 147(1\u20132), 277\u2013307 (2014)","journal-title":"Math. Program."},{"key":"1907_CR19","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511983658","volume-title":"Mathematical Programs with Equilibrium Constraints","author":"ZQ Luo","year":"1996","unstructured":"Luo, Z.Q., Pang, J.S., Ralph, D.: Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge (1996)"},{"key":"1907_CR20","doi-asserted-by":"crossref","unstructured":"Portilla, J.: Image restoration through l0 analysis-based sparse optimization in tight frames. In: 2009 16th IEEE International Conference on Image Processing (ICIP), pp. 3909\u20133912. IEEE, IEEE Press, Cairo, Egypt (2009)","DOI":"10.1109\/ICIP.2009.5413975"},{"key":"1907_CR21","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/j.neucom.2017.02.029","volume":"241","author":"S Scardapane","year":"2017","unstructured":"Scardapane, S., Comminiello, D., Hussain, A., Uncini, A.: Group sparse regularization for deep neural networks. Neurocomputing 241, 81\u201389 (2017)","journal-title":"Neurocomputing"},{"issue":"4","key":"1907_CR22","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1007\/s10898-017-0507-z","volume":"68","author":"T Sun","year":"2017","unstructured":"Sun, T., Jiang, H., Cheng, L.: Global convergence of proximal iteratively reweighted algorithm. J. Global Optim. 68(4), 815\u2013826 (2017)","journal-title":"J. Global Optim."},{"key":"1907_CR23","unstructured":"Wang, F.: Study on the kurdyka\u2013\u0142ojasiewicz exponents of $$\\ell _p$$ regularization functions (in chinese). Master thesis, Southwestern University of Finance and Economics (2021)"},{"key":"1907_CR24","doi-asserted-by":"publisher","first-page":"2639","DOI":"10.1007\/s11590-020-01685-x","volume":"15","author":"H Wang","year":"2021","unstructured":"Wang, H., Zeng, H., Wang, J.: Relating lp regularization and reweighted l1 regularization. Optim. Lett. 15, 2639\u20132660 (2021)","journal-title":"Optim. Lett."},{"key":"1907_CR25","unstructured":"Wang, H., Zhang, F., Wu, Q., Hu, Y., Shi, Y.: Nonconvex and nonsmooth sparse optimization via adaptively iterative reweighted methods. arXiv preprint arXiv:1810.10167 (2018)"},{"issue":"1","key":"1907_CR26","doi-asserted-by":"publisher","first-page":"A536","DOI":"10.1137\/140952363","volume":"37","author":"P Yin","year":"2015","unstructured":"Yin, P., Lou, Y., He, Q., Xin, J.: Minimization of 1\u20132 for compressed sensing. SIAM J. Sci. Comput. 37(1), A536\u2013A563 (2015)","journal-title":"SIAM J. Sci. Comput."},{"key":"1907_CR27","doi-asserted-by":"crossref","unstructured":"Yu, P., Li, G., Pong, T.K.: Kurdyka-\u0142ojasiewicz exponent via inf-projection. Found. Comput. Math. pp. 1\u201347 (2021)","DOI":"10.1007\/s10208-021-09528-6"},{"key":"1907_CR28","unstructured":"Zhou, Y., Yu, Y., Dai, W., Liang, Y., Xing, E.: On convergence of model parallel proximal gradient algorithm for stale synchronous parallel system. In: Artificial Intelligence and Statistics, pp. 713\u2013722. JMLR, Cadiz, Spain (2016)"}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-022-01907-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11590-022-01907-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-022-01907-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T23:06:47Z","timestamp":1675984007000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11590-022-01907-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,26]]},"references-count":28,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,3]]}},"alternative-id":["1907"],"URL":"https:\/\/doi.org\/10.1007\/s11590-022-01907-4","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"type":"print","value":"1862-4472"},{"type":"electronic","value":"1862-4480"}],"subject":[],"published":{"date-parts":[[2022,7,26]]},"assertion":[{"value":"30 October 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 June 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 July 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}