{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T05:26:21Z","timestamp":1787289981590,"version":"build-2736575974"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T00:00:00Z","timestamp":1785456000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T00:00:00Z","timestamp":1785456000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12222112"],"award-info":[{"award-number":["12222112"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2026,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Mixed sparse optimization has been extensively applied in the modeling of many important problems in various disciplines, in which the sparse structure appears as the inter-group and intra-group manners simultaneously. In this paper, we consider the\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\ell _0$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msub>\n                            <mml:mi>\u2113<\/mml:mi>\n                            <mml:mn>0<\/mml:mn>\n                          <\/mml:msub>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    regularization problem for mixed sparse optimization and investigate its consistency theory. In particular, we first introduce the notions of sparse eigenvalue conditions, one of the weakest regularity conditions in the literature, and discuss their relations with the uniquely solvable property and restricted eigenvalue conditions. Then we establish the oracle property without any regularity condition and provide a recovery bound for the global solutions of the\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\ell _0$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msub>\n                            <mml:mi>\u2113<\/mml:mi>\n                            <mml:mn>0<\/mml:mn>\n                          <\/mml:msub>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    regularized mixed sparse optimization problem under the assumption of sparse eigenvalue condition. Moreover, by virtue of the notion of epi-convergence, an asymptotic analysis is provided to advance the understanding of the convergence of the\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\ell _{2,p}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msub>\n                            <mml:mi>\u2113<\/mml:mi>\n                            <mml:mrow>\n                              <mml:mn>2<\/mml:mn>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mi>p<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    regularization to the\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\ell _{2,0}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msub>\n                            <mml:mi>\u2113<\/mml:mi>\n                            <mml:mrow>\n                              <mml:mn>2<\/mml:mn>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mn>0<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    regularization as\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$p\\rightarrow 0_+$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo>\u2192<\/mml:mo>\n                            <mml:msub>\n                              <mml:mn>0<\/mml:mn>\n                              <mml:mo>+<\/mml:mo>\n                            <\/mml:msub>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , in terms of regularity condition, global solution set and recovery bound, respectively.\n                  <\/jats:p>","DOI":"10.1007\/s10957-026-03070-7","type":"journal-article","created":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T05:30:00Z","timestamp":1785475800000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Recovery Bounds for Cardinality Regularized Optimization Problem"],"prefix":"10.1007","volume":"210","author":[{"given":"Carisa Kwok Wai","family":"Yu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yaohua","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Minghua","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5583-4032","authenticated-orcid":false,"given":"Xiaoqi","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,7,31]]},"reference":[{"issue":"4","key":"3070_CR1","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1214\/12-STS394","volume":"27","author":"F Bach","year":"2012","unstructured":"Bach, F., Jenatton, R., Mairal, J., Obozinski, G.: Structured sparsity through convex optimization. Stat. Sci. 27(4), 450\u2013468 (2012)","journal-title":"Stat. Sci."},{"issue":"1","key":"3070_CR2","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. Imag. Sci. 2(1), 183\u2013202 (2009)","journal-title":"SIAM J. Imag. Sci."},{"key":"3070_CR3","doi-asserted-by":"publisher","first-page":"1705","DOI":"10.1214\/08-AOS620","volume":"37","author":"PJ Bickel","year":"2009","unstructured":"Bickel, P.J., Ritov, Y., Tsybakov, A.B.: Simultaneous analysis of Lasso and Dantzig selector. Ann. Stat. 37, 1705\u20131732 (2009)","journal-title":"Ann. Stat."},{"issue":"5","key":"3070_CR4","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(5), 629\u2013654 (2008)","journal-title":"J. Fourier Anal. Appl."},{"issue":"3","key":"3070_CR5","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1016\/j.acha.2009.04.002","volume":"27","author":"T Blumensath","year":"2009","unstructured":"Blumensath, T., Davies, M.E.: Iterative hard thresholding for compressed sensing. Appl. Comput. Harmon. Anal. 27(3), 265\u2013274 (2009)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"3070_CR6","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"},{"key":"3070_CR7","doi-asserted-by":"publisher","first-page":"4203","DOI":"10.1109\/TIT.2005.858979","volume":"51","author":"E Cand\u00e8s","year":"2005","unstructured":"Cand\u00e8s, E., Tao, T.: Decoding by linear programming. IEEE Trans. Inf. Theory 51, 4203\u20134215 (2005)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"3070_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1088\/0266-5611\/24\/3\/035020","volume":"24","author":"R Chartrand","year":"2008","unstructured":"Chartrand, R., Staneva, V.: Restricted isometry properties and nonconvex compressive sensing. Inverse Prob. 24, 1\u201314 (2008)","journal-title":"Inverse Prob."},{"key":"3070_CR9","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":"3070_CR10","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1137\/S003614450037906X","volume":"43","author":"SS Chen","year":"2001","unstructured":"Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM Rev. 43, 129\u2013159 (2001)","journal-title":"SIAM Rev."},{"issue":"5","key":"3070_CR11","doi-asserted-by":"publisher","first-page":"2832","DOI":"10.1137\/090761471","volume":"32","author":"X Chen","year":"2010","unstructured":"Chen, X., Xu, F., Ye, Y.: Lower bound theory of nonzero entries in solutions of $$\\ell _2$$-$$\\ell _p$$ minimization. SIAM J. Sci. Comput. 32(5), 2832\u20132852 (2010)","journal-title":"SIAM J. Sci. Comput."},{"issue":"4","key":"3070_CR12","doi-asserted-by":"publisher","first-page":"1168","DOI":"10.1137\/050626090","volume":"4","author":"P Combettes","year":"2005","unstructured":"Combettes, P., Wajs, V.: Signal recovery by proximal forward-backward splitting. Multiscale Model. Simul. 4(4), 1168\u20131200 (2005)","journal-title":"Multiscale Model. Simul."},{"key":"3070_CR13","doi-asserted-by":"publisher","first-page":"1413","DOI":"10.1002\/cpa.20042","volume":"57","author":"I Daubechies","year":"2004","unstructured":"Daubechies, I., Defrise, M., Mol, C.D.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 57, 1413\u20131457 (2004)","journal-title":"Commun. Pure Appl. Math."},{"issue":"6","key":"3070_CR14","doi-asserted-by":"publisher","first-page":"797","DOI":"10.1002\/cpa.20132","volume":"59","author":"DL Donoho","year":"2006","unstructured":"Donoho, D.L.: For most large underdetermined systems of linear equations the minimal $$\\ell _1$$-norm solution is also the sparsest solution. Commun. Pure Appl. Math. 59(6), 797\u2013829 (2006)","journal-title":"Commun. Pure Appl. Math."},{"issue":"4","key":"3070_CR15","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. Imag. Sci. 6(4), 2010\u20132046 (2013)","journal-title":"SIAM J. Imag. Sci."},{"issue":"2","key":"3070_CR16","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1016\/j.acha.2020.04.002","volume":"49","author":"X Feng","year":"2020","unstructured":"Feng, X., Yan, S., Wu, C.: The $$\\ell _{2, q}$$ regularized group sparse optimization: Lower bound theory, recovery bound and algorithms. Appl. Comput. Harmon. Anal. 49(2), 381\u2013414 (2020)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"3070_CR17","doi-asserted-by":"crossref","unstructured":"Fullwood, M, Liu, M., Pan, Y., Liu, J., Xu, H., Mohamed,Y., Orlov, Y., Velkov, S., Ho, A., Mei, P.,Chew, E., Huang, P., Welboren, W.,Han, Y., Ooi, H., Ariyaratne, P., Vega, V., Luo, Y., Tan, P., Choy, P., Wansa,K., Zhao, B., Lim, K.,Leow, S., Yow, J., Joseph, R., Li, H., Desai, K.,Thomsen, J., Lee, Y., Karuturi, K., Herve, T., Bourque, G., Stunnenberg, H.,Ruan, X.,Cacheux-Rataboul, V., Sung, W., Liu, E., Wei, C., Cheung, E., Ruan,Y An oestrogen-receptor-$$\\alpha $$-bound human chromatin interactome. Nature 462, 58\u201364 (2009)","DOI":"10.1038\/nature08497"},{"key":"3070_CR18","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/s10107-024-02068-1","volume":"211","author":"Y Hu","year":"2025","unstructured":"Hu, Y., Hu, X., Yang, X.: On convergence of iterative thresholding algorithms to approximate sparse solution for composite nonconvex optimization. Math. Program. 211, 181\u2013206 (2025)","journal-title":"Math. Program."},{"issue":"9","key":"3070_CR19","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ad617d","volume":"40","author":"Y Hu","year":"2024","unstructured":"Hu, Y., Hu, X., Yu, C.K.W., Qin, J.: Joint sparse optimization: Lower-order regularization method and application in cell fate conversion. Inverse Prob. 40(9), 095003 (2024)","journal-title":"Inverse Prob."},{"issue":"30","key":"3070_CR20","first-page":"1","volume":"18","author":"Y Hu","year":"2017","unstructured":"Hu, Y., Li, C., Meng, K., Qin, J., Yang, X.: Group sparse optimization via $$\\ell _{p, q}$$ regularization. J. Mach. Learn. Res. 18(30), 1\u201352 (2017)","journal-title":"J. Mach. Learn. Res."},{"key":"3070_CR21","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1007\/s10898-024-01441-w","volume":"91","author":"Y Hu","year":"2025","unstructured":"Hu, Y., Lu, J., Yang, X., Zhang, K.: Iterative mix thresholding algorithm with continuation technique for mix sparse optimization and application. J. Global Optim. 91, 511\u2013534 (2025)","journal-title":"J. Global Optim."},{"issue":"4","key":"3070_CR22","doi-asserted-by":"publisher","first-page":"1978","DOI":"10.1214\/09-AOS778","volume":"38","author":"J Huang","year":"2010","unstructured":"Huang, J., Zhang, T.: The benefit of group sparsity. Ann. Stat. 38(4), 1978\u20132004 (2010)","journal-title":"Ann. Stat."},{"issue":"1","key":"3070_CR23","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1137\/090775397","volume":"21","author":"M Lai","year":"2011","unstructured":"Lai, M., 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":"6","key":"3070_CR24","doi-asserted-by":"publisher","DOI":"10.1093\/bib\/bbac402","volume":"23","author":"RWT Leung","year":"2022","unstructured":"Leung, R.W.T., Jiang, X., Zong, X., Zhang, Y., Hu, X., Hu, Y., Qin, J.: CORN - Condition Orientated Regulatory Networks: bridging conditions to gene networks. Brief. Bioinform. 23(6), bbac402 (2022)","journal-title":"Brief. Bioinform."},{"issue":"4","key":"3070_CR25","doi-asserted-by":"publisher","first-page":"2434","DOI":"10.1137\/140998135","volume":"25","author":"G Li","year":"2015","unstructured":"Li, G., Pong, T.K.: Global convergence of splitting methods for nonconvex composite optimization. SIAM J. Optim. 25(4), 2434\u20132460 (2015)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"3070_CR26","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":"4","key":"3070_CR27","doi-asserted-by":"publisher","first-page":"2448","DOI":"10.1137\/100808071","volume":"23","author":"Z Lu","year":"2013","unstructured":"Lu, Z., Zhang, Y.: Sparse approximation via penalty decomposition methods. SIAM J. Optim. 23(4), 2448\u20132478 (2013)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"3070_CR28","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1214\/07-AOS582","volume":"37","author":"N Meinshausen","year":"2009","unstructured":"Meinshausen, N., Yu, B.: Lasso-type recovery of sparse representations for high-dimensional data. Ann. Stat. 37(1), 246\u2013270 (2009)","journal-title":"Ann. Stat."},{"issue":"1","key":"3070_CR29","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. Imag. Sci. 14(1), 1\u201325 (2021)","journal-title":"SIAM J. Imag. Sci."},{"key":"3070_CR30","doi-asserted-by":"publisher","first-page":"220","DOI":"10.1016\/j.neunet.2019.05.011","volume":"118","author":"DN Phan","year":"2019","unstructured":"Phan, D.N., Thi, H.A.L.: Group variable selection via $$\\ell _{p,0}$$ regularization and application to optimal scoring. Neural Netw. 118, 220\u2013234 (2019)","journal-title":"Neural Netw."},{"issue":"6","key":"3070_CR31","doi-asserted-by":"publisher","DOI":"10.1093\/bib\/bbab311","volume":"22","author":"J Qin","year":"2021","unstructured":"Qin, J., Hu, Y., Yao, J.-C., Leung, R.W.T., Zhou, Y., Qin, Y., Wang, J.: Cell fate conversion prediction by group sparse optimization method utilizing single-cell and bulk OMICs data. Brief. Bioinform. 22(6), bbab311 (2021)","journal-title":"Brief. Bioinform."},{"key":"3070_CR32","volume-title":"Variational Analysis","author":"RT Rockafellar","year":"2009","unstructured":"Rockafellar, R.T., Wets, R.J.B.: Variational Analysis. Springer Science & Business Media, Berlin (2009)"},{"key":"3070_CR33","doi-asserted-by":"publisher","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. Roy. Stat. Soc. B 58, 267\u2013288 (1996)","journal-title":"J. Roy. Stat. Soc. B"},{"issue":"5","key":"3070_CR34","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/aa6699","volume":"33","author":"J Wang","year":"2017","unstructured":"Wang, J., Hu, Y., Li, C., Yao, J.-C.: Linear convergence of CQ algorithms and applications in gene regulatory network inference. Inverse Prob. 33(5), 055017 (2017)","journal-title":"Inverse Prob."},{"key":"3070_CR35","doi-asserted-by":"publisher","first-page":"1013","DOI":"10.1109\/TNNLS.2012.2197412","volume":"23","author":"Z Xu","year":"2012","unstructured":"Xu, Z., Chang, X., Xu, F., Zhang, H.: $${L}_{1\/2}$$ regularization: A thresholding representation theory and a fast solver. IEEE Trans. Neural Netw. Learn. Sys 23, 1013\u20131027 (2012)","journal-title":"IEEE Trans. Neural Netw. Learn. Sys"},{"issue":"2","key":"3070_CR36","doi-asserted-by":"publisher","first-page":"857","DOI":"10.1137\/120864192","volume":"23","author":"J Yang","year":"2013","unstructured":"Yang, J., Sun, D., Toh, K.-C.: A proximal point algorithm for log-determinant optimization with group Lasso regularization. SIAM J. Optim. 23(2), 857\u2013893 (2013)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"3070_CR37","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1137\/090777761","volume":"33","author":"J Yang","year":"2011","unstructured":"Yang, J., Zhang, Y.: Alternating direction algorithms for $$\\ell _1$$-problems in compressive sensing. SIAM J. Sci. Comput. 33(1), 250\u2013278 (2011)","journal-title":"SIAM J. Sci. Comput."},{"issue":"9","key":"3070_CR38","doi-asserted-by":"publisher","first-page":"2104","DOI":"10.1109\/TPAMI.2013.17","volume":"35","author":"L Yuan","year":"2013","unstructured":"Yuan, L., Liu, J., Ye, J.: Efficient methods for overlapping group Lasso. IEEE Trans. Pattern Anal. Mach. Intell. 35(9), 2104\u20132116 (2013)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"1","key":"3070_CR39","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1111\/j.1467-9868.2005.00532.x","volume":"68","author":"M Yuan","year":"2007","unstructured":"Yuan, M., Lin, Y.: Model selection and estimation in regression with grouped variables. J. Roy. Stat. Soc. B 68(1), 49\u201367 (2007)","journal-title":"J. Roy. Stat. Soc. B"},{"issue":"4","key":"3070_CR40","doi-asserted-by":"publisher","first-page":"1567","DOI":"10.1214\/07-AOS520","volume":"36","author":"C-H Zhang","year":"2008","unstructured":"Zhang, C.-H., Huang, J.: The sparsity and bias of the Lasso selection in high-dimensional linear regression. Ann. Stat. 36(4), 1567\u20131594 (2008)","journal-title":"Ann. Stat."},{"key":"3070_CR41","first-page":"1081","volume":"11","author":"T Zhang","year":"2010","unstructured":"Zhang, T.: Analysis of multi-stage convex relaxation for sparse regularization. J. Mach. Learn. Res. 11, 1081\u20131107 (2010)","journal-title":"J. Mach. Learn. Res."},{"issue":"8","key":"3070_CR42","doi-asserted-by":"publisher","first-page":"1798","DOI":"10.1109\/TMM.2017.2689918","volume":"19","author":"Y Zhou","year":"2017","unstructured":"Zhou, Y., Han, J.H., Yuan, X.H., Wei, Z.C., Hong, R.C.: Inverse sparse group Lasso model for robust object tracking. IEEE Trans. Multimedia 19(8), 1798\u20131810 (2017)","journal-title":"IEEE Trans. Multimedia"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-026-03070-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-026-03070-7","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-026-03070-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T05:08:45Z","timestamp":1787288925000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-026-03070-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,31]]},"references-count":42,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,8]]}},"alternative-id":["3070"],"URL":"https:\/\/doi.org\/10.1007\/s10957-026-03070-7","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,31]]},"assertion":[{"value":"6 December 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 July 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 July 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"35"}}