{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T04:51:07Z","timestamp":1773809467263,"version":"3.50.1"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,4,29]],"date-time":"2024-04-29T00:00:00Z","timestamp":1714348800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,4,29]],"date-time":"2024-04-29T00:00:00Z","timestamp":1714348800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100012165","name":"Key Technologies Research and Development Program","doi-asserted-by":"publisher","award":["2021YFA1000403"],"award-info":[{"award-number":["2021YFA1000403"]}],"id":[{"id":"10.13039\/501100012165","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Nos. U23B2012,11991022"],"award-info":[{"award-number":["Nos. U23B2012,11991022"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2024,9]]},"DOI":"10.1007\/s10898-024-01396-y","type":"journal-article","created":{"date-parts":[[2024,4,29]],"date-time":"2024-04-29T07:02:22Z","timestamp":1714374142000},"page":"93-125","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Subspace Newton method for sparse group $$\\ell _0$$ optimization problem"],"prefix":"10.1007","volume":"90","author":[{"given":"Shichen","family":"Liao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3445-4620","authenticated-orcid":false,"given":"Congying","family":"Han","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tiande","family":"Guo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bonan","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,4,29]]},"reference":[{"issue":"12","key":"1396_CR1","doi-asserted-by":"publisher","first-page":"4203","DOI":"10.1109\/TIT.2005.858979","volume":"51","author":"EJ Candes","year":"2005","unstructured":"Candes, E.J., Tao, T.: Decoding by linear programming. IEEE Trans. Inf. Theory 51(12), 4203\u20134215 (2005). https:\/\/doi.org\/10.1109\/TIT.2005.858979","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"2","key":"1396_CR2","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)","journal-title":"J. Comput. Graph. Stat."},{"key":"1396_CR3","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1016\/j.neucom.2021.10.005","volume":"468","author":"P Zhang","year":"2021","unstructured":"Zhang, P., Wang, R., Xiu, N.: Multinomial logistic regression classifier via $$\\ell _{q,0}$$-proximal newton algorithm. Neurocomputing 468, 148\u2013164 (2021)","journal-title":"Neurocomputing"},{"issue":"1","key":"1396_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1471-2105-14-245","volume":"14","author":"D Lin","year":"2013","unstructured":"Lin, D., Zhang, J., Li, J., Calhoun, V.D., Deng, H.-W., Wang, Y.-P.: Group sparse canonical correlation analysis for genomic data integration. BMC Bioinform. 14(1), 1\u201316 (2013)","journal-title":"BMC Bioinform."},{"issue":"6","key":"1396_CR5","doi-asserted-by":"publisher","first-page":"2028","DOI":"10.1109\/TCBB.2017.2761871","volume":"15","author":"J Li","year":"2018","unstructured":"Li, J., Dong, W., Meng, D.: Grouped gene selection of cancer via adaptive sparse group lasso based on conditional mutual information. IEEE ACM Trans. Comput. Biol. Bioinform. 15(6), 2028\u20132038 (2018). https:\/\/doi.org\/10.1109\/TCBB.2017.2761871","journal-title":"IEEE ACM Trans. Comput. Biol. Bioinform."},{"key":"1396_CR6","unstructured":"Hu, Y., Lu, J., Yang, X., Zhang, K.: Mix sparse optimization: theory and algorithm (2022). https:\/\/www.polyu.edu.hk\/ama\/profile\/xqyang\/mix_sparse2022.pdf"},{"issue":"2","key":"1396_CR7","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1111\/biom.12292","volume":"71","author":"Y Li","year":"2015","unstructured":"Li, Y., Nan, B., Zhu, J.: Multivariate sparse group lasso for the multivariate multiple linear regression with an arbitrary group structure. Biometrics 71(2), 354\u2013363 (2015)","journal-title":"Biometrics"},{"issue":"5","key":"1396_CR8","doi-asserted-by":"publisher","first-page":"1602","DOI":"10.1109\/TCSI.2017.2763969","volume":"65","author":"R Matsuoka","year":"2017","unstructured":"Matsuoka, R., Kyochi, S., Ono, S., Okuda, M.: Joint sparsity and order optimization based on admm with non-uniform group hard thresholding. IEEE Trans. Circuits Syst. I Regul. Pap. 65(5), 1602\u20131613 (2017)","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"issue":"1","key":"1396_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/19M1304799","volume":"14","author":"L Pan","year":"2021","unstructured":"Pan, L., Chen, X.: Group sparse optimization for images recovery using capped folded concave functions. SIAM J. Imaging Sci. 14(1), 1\u201325 (2021)","journal-title":"SIAM J. Imaging Sci."},{"issue":"3","key":"1396_CR10","doi-asserted-by":"publisher","first-page":"1614","DOI":"10.1137\/21M1443455","volume":"32","author":"W Li","year":"2022","unstructured":"Li, W., Bian, W., Toh, K.-C.: Difference-of-convex algorithms for a class of sparse group $$\\ell _0$$ regularized optimization problems. SIAM J. Optim. 32(3), 1614\u20131641 (2022)","journal-title":"SIAM J. Optim."},{"key":"1396_CR11","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1007\/s10479-019-03189-z","volume":"284","author":"J Chen","year":"2020","unstructured":"Chen, J., Dai, G., Zhang, N.: An application of sparse-group lasso regularization to equity portfolio optimization and sector selection. Ann. Oper. Res. 284, 243\u2013262 (2020)","journal-title":"Ann. Oper. Res."},{"key":"1396_CR12","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1214\/07-EJS008","volume":"1","author":"F Bunea","year":"2007","unstructured":"Bunea, F., Tsybakov, A., Wegkamp, M.: Sparsity oracle inequalities for the lasso. Electron. J. Stat. 1, 169\u2013194 (2007)","journal-title":"Electron. J. Stat."},{"issue":"1","key":"1396_CR13","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1137\/080716542","volume":"2","author":"A Beck","year":"2009","unstructured":"Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1), 183\u2013202 (2009)","journal-title":"SIAM J. Imaging Sci."},{"issue":"11","key":"1396_CR14","doi-asserted-by":"publisher","first-page":"1413","DOI":"10.1002\/cpa.20042","volume":"57","author":"I Daubechies","year":"2004","unstructured":"Daubechies, I., Defrise, M., De Mol, C.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 57(11), 1413\u20131457 (2004)","journal-title":"Commun. Pure Appl. Math."},{"key":"1396_CR15","doi-asserted-by":"publisher","first-page":"7253","DOI":"10.1109\/TPAMI.2021.3092177","volume":"44","author":"H Wang","year":"2019","unstructured":"Wang, H., Shao, Y., Zhou, S., Zhang, C., Xiu, N.: Support vector machine classifier via $$l_{0\/1}$$ soft-margin loss. IEEE Trans. Pattern Anal. Mach. Intell. 44, 7253\u20137265 (2019)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"1396_CR16","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/s10957-016-0934-x","volume":"170","author":"A Beck","year":"2015","unstructured":"Beck, A., Vaisbourd, Y.: The sparse principal component analysis problem: optimality conditions and algorithms. J. Optim. Theory Appl. 170, 119\u2013143 (2015)","journal-title":"J. Optim. Theory Appl."},{"key":"1396_CR17","doi-asserted-by":"publisher","first-page":"1593","DOI":"10.1109\/TSP.2022.3156911","volume":"70","author":"S Zhou","year":"2021","unstructured":"Zhou, S., Luo, Z., Xiu, N., Li, G.Y.: Computing one-bit compressive sensing via double-sparsity constrained optimization. IEEE Trans. Signal Process. 70, 1593\u20131608 (2021)","journal-title":"IEEE Trans. Signal Process."},{"key":"1396_CR18","doi-asserted-by":"publisher","first-page":"807","DOI":"10.1007\/s10463-012-0396-3","volume":"65","author":"X Shen","year":"2013","unstructured":"Shen, X., Pan, W., Zhu, Y., Zhou, H.: On constrained and regularized high-dimensional regression. Ann. Inst. Stat. Math. 65, 807\u2013832 (2013)","journal-title":"Ann. Inst. Stat. Math."},{"key":"1396_CR19","unstructured":"Pati, Y.C., Rezaiifar, R., Krishnaprasad, P.S.: Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition. In: Proceedings of the 27th Asilomar Conference on Signals Systems, and Computers, pp. 40\u201344 (1993)"},{"issue":"3","key":"1396_CR20","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1016\/j.acha.2008.07.002","volume":"26","author":"D Needell","year":"2009","unstructured":"Needell, D., Tropp, J.A.: Cosamp: iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmon. Anal. 26(3), 301\u2013321 (2009)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"2","key":"1396_CR21","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1109\/JSTSP.2010.2042411","volume":"4","author":"T Blumensath","year":"2010","unstructured":"Blumensath, T., Davies, M.E.: Normalized iterative hard thresholding: guaranteed stability and performance. IEEE J. Sel. Top. Signal Process. 4(2), 298\u2013309 (2010)","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"1396_CR22","doi-asserted-by":"publisher","first-page":"1480","DOI":"10.1137\/120869778","volume":"23","author":"A Beck","year":"2013","unstructured":"Beck, A., Eldar, Y.C.: Sparsity constrained nonlinear optimization: optimality conditions and algorithms. SIAM J. Optim. 23, 1480\u20131509 (2013)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"1396_CR23","first-page":"6027","volume":"18","author":"X Yuan","year":"2017","unstructured":"Yuan, X., Li, P., Zhang, T.: Gradient hard thresholding pursuit. J. Mach. Learn. Res. 18(1), 6027\u20136069 (2017)","journal-title":"J. Mach. Learn. Res."},{"key":"1396_CR24","first-page":"12","volume":"22","author":"S Zhou","year":"2019","unstructured":"Zhou, S., Xiu, N., Qi, H.: Global and quadratic convergence of newton hard-thresholding pursuit. J. Mach. Learn. Res. 22, 12\u201311245 (2019)","journal-title":"J. Mach. Learn. Res."},{"key":"1396_CR25","doi-asserted-by":"publisher","first-page":"629","DOI":"10.1007\/s00041-008-9035-z","volume":"14","author":"T Blumensath","year":"2008","unstructured":"Blumensath, T., Davies, M.E.: Iterative thresholding for sparse approximations. J. Fourier Anal. Appl. 14, 629\u2013654 (2008)","journal-title":"J. Fourier Anal. Appl."},{"issue":"3","key":"1396_CR26","doi-asserted-by":"publisher","first-page":"1607","DOI":"10.1137\/151003714","volume":"8","author":"E Soubies","year":"2015","unstructured":"Soubies, E., Blanc-F\u00e9raud, L., Aubert, G.: A continuous exact $$\\ell _0$$ penalty (cel0) for least squares regularized problem. SIAM J. Imaging Sci. 8(3), 1607\u20131639 (2015)","journal-title":"SIAM J. Imaging Sci."},{"issue":"2","key":"1396_CR27","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1214\/15-AOS1388","volume":"44","author":"D Bertsimas","year":"2016","unstructured":"Bertsimas, D., King, A., Mazumder, R.: Best subset selection via a modern optimization lens. Ann. Stat. 44(2), 813\u2013852 (2016)","journal-title":"Ann. Stat."},{"issue":"4","key":"1396_CR28","doi-asserted-by":"publisher","first-page":"769","DOI":"10.1007\/s10898-019-00830-w","volume":"76","author":"W Cheng","year":"2020","unstructured":"Cheng, W., Chen, Z., Hu, Q.: An active set Barzilar\u2013Borwein algorithm for $$\\ell _0$$ regularized optimization. J. Glob. Optim. 76(4), 769\u2013791 (2020)","journal-title":"J. Glob. Optim."},{"issue":"1","key":"1396_CR29","doi-asserted-by":"publisher","first-page":"858","DOI":"10.1137\/18M1186009","volume":"58","author":"W Bian","year":"2020","unstructured":"Bian, W., Chen, X.: A smoothing proximal gradient algorithm for nonsmooth convex regression with cardinality penalty. SIAM J. Numer. Anal. 58(1), 858\u2013883 (2020)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"1396_CR30","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/30\/1\/015001","volume":"30","author":"K Ito","year":"2013","unstructured":"Ito, K., Kunisch, K.: A variational approach to sparsity optimization based on Lagrange multiplier theory. Inverse Probl. 30(1), 015001 (2013)","journal-title":"Inverse Probl."},{"issue":"1","key":"1396_CR31","first-page":"403","volume":"19","author":"J Huang","year":"2018","unstructured":"Huang, J., Jiao, Y., Liu, Y., Lu, X.: A constructive approach to l0 penalized regression. J. Mach. Learn. Res. 19(1), 403\u2013439 (2018)","journal-title":"J. Mach. Learn. Res."},{"key":"1396_CR32","doi-asserted-by":"publisher","first-page":"1541","DOI":"10.1007\/s11075-021-01085-x","volume":"88","author":"S Zhou","year":"2021","unstructured":"Zhou, S., Pan, L., Xiu, N.: Newton method for $$\\ell _0$$-regularized optimization. Numer. Algorithms 88, 1541\u20131570 (2021)","journal-title":"Numer. Algorithms"},{"key":"1396_CR33","unstructured":"Nocedal, J., Wright, S.J.: Numerical optimization. In: Fundamental Statistical Inference (2018)"},{"issue":"3","key":"1396_CR34","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/0167-6377(94)00059-F","volume":"17","author":"F Facchinei","year":"1995","unstructured":"Facchinei, F.: Minimization of sc1 functions and the Maratos effect. Oper. Res. Lett. 17(3), 131\u2013137 (1995). https:\/\/doi.org\/10.1016\/0167-6377(94)00059-F","journal-title":"Oper. Res. Lett."},{"key":"1396_CR35","doi-asserted-by":"crossref","unstructured":"Yang, J., Leung, H.C.M., Yiu, S.-M., Cai, Y., Chin, F.Y.L.: Intra- and inter-sparse multiple output regression with application on environmental microbial community study. In: 2013 IEEE International Conference on Bioinformatics Biomedicine, pp. 404\u2013409 (2013)","DOI":"10.1109\/BIBM.2013.6732526"},{"issue":"4","key":"1396_CR36","doi-asserted-by":"publisher","first-page":"2010","DOI":"10.1137\/13090540X","volume":"6","author":"E Esser","year":"2013","unstructured":"Esser, E., Lou, Y., Xin, J.: A method for finding structured sparse solutions to nonnegative least squares problems with applications. SIAM J. Imaging Sci. 6(4), 2010\u20132046 (2013)","journal-title":"SIAM J. Imaging Sci."},{"key":"1396_CR37","doi-asserted-by":"publisher","first-page":"998","DOI":"10.1109\/TSP.2016.2630028","volume":"65","author":"Y Jiao","year":"2016","unstructured":"Jiao, Y., Jin, B., Lu, X.: Group sparse recovery via the $$\\ell ^0(\\ell ^2)$$ penalty: theory and algorithm. IEEE Trans. Signal Process. 65, 998\u20131012 (2016)","journal-title":"IEEE Trans. Signal Process."},{"key":"1396_CR38","doi-asserted-by":"publisher","first-page":"3042","DOI":"10.1109\/TSP.2010.2044837","volume":"58","author":"YC Eldar","year":"2009","unstructured":"Eldar, Y.C., Kuppinger, P., B\u00f6lcskei, H.: Block-sparse signals: uncertainty relations and efficient recovery. IEEE Trans. Signal Process. 58, 3042\u20133054 (2009)","journal-title":"IEEE Trans. Signal Process."},{"key":"1396_CR39","doi-asserted-by":"publisher","first-page":"890","DOI":"10.1137\/080714488","volume":"31","author":"E Berg","year":"2008","unstructured":"Berg, E., Friedlander, M.P.: Probing the pareto frontier for basis pursuit solutions. SIAM J. Sci. Comput. 31, 890\u2013912 (2008)","journal-title":"SIAM J. Sci. Comput."},{"key":"1396_CR40","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1214\/12-STS392","volume":"27","author":"J Huang","year":"2012","unstructured":"Huang, J., Breheny, P.J., Ma, S.: A selective review of group selection in high-dimensional models. Stat. Sci. 27, 4 (2012)","journal-title":"Stat. Sci."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-024-01396-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10898-024-01396-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-024-01396-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,10]],"date-time":"2024-08-10T08:13:58Z","timestamp":1723277638000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10898-024-01396-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,29]]},"references-count":40,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["1396"],"URL":"https:\/\/doi.org\/10.1007\/s10898-024-01396-y","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,29]]},"assertion":[{"value":"1 October 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 March 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 April 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}