{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T07:10:10Z","timestamp":1751613010687,"version":"3.41.0"},"reference-count":70,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,4,18]],"date-time":"2025-04-18T00:00:00Z","timestamp":1744934400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,4,18]],"date-time":"2025-04-18T00:00:00Z","timestamp":1744934400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2025,7]]},"DOI":"10.1007\/s10898-025-01492-7","type":"journal-article","created":{"date-parts":[[2025,4,18]],"date-time":"2025-04-18T08:09:27Z","timestamp":1744963767000},"page":"737-774","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A dual adaptive algorithm for matrix optimization with sparse group lasso regularization"],"prefix":"10.1007","volume":"92","author":[{"given":"Jinji","family":"Yang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiang","family":"Hu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0391-5033","authenticated-orcid":false,"given":"Chungen","family":"Shen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,4,18]]},"reference":[{"key":"1492_CR1","doi-asserted-by":"crossref","first-page":"6745","DOI":"10.1073\/pnas.96.12.6745","volume":"96","author":"U Alon","year":"1999","unstructured":"Alon, U., Barkai, N., Notterman, D.A., Gish, K.: Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proc. Natl. Acad. Sci. U.S.A. 96, 6745\u20136750 (1999)","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"issue":"1","key":"1492_CR2","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1093\/imanum\/8.1.141","volume":"8","author":"J Barzilai","year":"1988","unstructured":"Barzilai, J., Borwein, J.M.: Two-point step size gradient methods. IMA J. Numer. Anal. 8(1), 141\u2013148 (1988)","journal-title":"IMA J. Numer. Anal."},{"key":"1492_CR3","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611974997","volume-title":"First-Order Methods in Optimization","author":"A Beck","year":"2017","unstructured":"Beck, A.: First-Order Methods in Optimization. SIAM, Philadelphia (2017)"},{"issue":"1","key":"1492_CR4","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1214\/009053607000000758","volume":"36","author":"PJ Bickel","year":"2008","unstructured":"Bickel, P.J., Levina, E.: Regularized estimation of large covariance matrices. Ann. Stat. 36(1), 199\u2013227 (2008)","journal-title":"Ann. Stat."},{"issue":"4","key":"1492_CR5","doi-asserted-by":"crossref","first-page":"1196","DOI":"10.1137\/S1052623497330963","volume":"10","author":"EG Birgin","year":"2000","unstructured":"Birgin, E.G., Mart\u00ednez, J.M., Raydan, M.: Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim. 10(4), 1196\u20131211 (2000)","journal-title":"SIAM J. Optim."},{"key":"1492_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1394-9","volume-title":"Perturbation Analysis of Optimization Problems","author":"JF Bonnans","year":"2000","unstructured":"Bonnans, J.F., Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer-Verlag, New York (2000)"},{"issue":"1","key":"1492_CR7","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1093\/imanum\/drn085","volume":"30","author":"R Borsdorf","year":"2010","unstructured":"Borsdorf, R., Higham, N.J.: A preconditioned Newton algorithm for the nearest correlation matrix. IMA J. Numer. Anal. 30(1), 94\u2013107 (2010)","journal-title":"IMA J. Numer. Anal."},{"issue":"1","key":"1492_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/2200000016","volume":"3","author":"S Boyd","year":"2011","unstructured":"Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1\u2013122 (2011)","journal-title":"Found. Trends Mach. Learn."},{"issue":"2","key":"1492_CR9","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1137\/040609902","volume":"27","author":"S Boyd","year":"2005","unstructured":"Boyd, S., Xiao, L.: Least-squares covariance matrix adjustment. SIAM J. Matrix Anal. Appl. 27(2), 532\u2013546 (2005)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"1","key":"1492_CR10","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1137\/070681235","volume":"19","author":"Z Chan","year":"2008","unstructured":"Chan, Z., Sun, D.: Constraint nondegeneracy, strong regularity, and nonsingularity in semidefinite programming. SIAM J. Optim. 19(1), 370\u2013396 (2008)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"1492_CR11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1961189.1961199","volume":"2","author":"C-C Chang","year":"2011","unstructured":"Chang, C.-C., Lin, C.-J.: LIBSVM: a library for support vector machines. ACM Trans. Intell. Syst. Technol. 2(3), 1\u201327 (2011)","journal-title":"ACM Trans. Intell. Syst. Technol."},{"key":"1492_CR12","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611971309","volume-title":"Optimization and Nonsmooth Analysis","author":"FH Clarke","year":"1990","unstructured":"Clarke, F.H.: Optimization and Nonsmooth Analysis. SIAM, Philadelphia (1990)"},{"key":"1492_CR13","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1016\/j.csda.2014.10.001","volume":"93","author":"Y Cui","year":"2016","unstructured":"Cui, Y., Leng, C., Sun, D.: Sparse estimation of high-dimensional correlation matrices. Comput. Stat. Data Anal. 93, 390\u2013403 (2016)","journal-title":"Comput. Stat. Data Anal."},{"key":"1492_CR14","unstructured":"Deng, Z., Deng, K., Hu, J., Wen, Z.: An augmented Lagrangian primal-dual semismooth newton method for multi-block composite optimization. In: Submission (2023)"},{"issue":"2","key":"1492_CR15","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"ED Dolan","year":"2002","unstructured":"Dolan, E.D., Mor\u00e9, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91(2), 201\u2013213 (2002)","journal-title":"Math. Program."},{"issue":"15","key":"1492_CR16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.laa.2014.07.026","volume":"461","author":"X Duan","year":"2014","unstructured":"Duan, X., Bai, J., Zhang, M., Zhang, X.: On the generalized low rank approximation of the correlation matrices arising in the asset portfolio. Linear Algebra Appl. 461(15), 1\u201317 (2014)","journal-title":"Linear Algebra Appl."},{"issue":"3","key":"1492_CR17","doi-asserted-by":"crossref","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)","journal-title":"Oper. Res. Lett."},{"key":"1492_CR18","volume-title":"Finite-Dimensional Variational Inequalities and Complementarity Problems, vols I and II","author":"F Facchinei","year":"2003","unstructured":"Facchinei, F., Pang, J.-S.: Finite-Dimensional Variational Inequalities and Complementarity Problems, vols I and II. Springer, New York (2003)"},{"key":"1492_CR19","unstructured":"Friedman, J., Hastie, T., Tibshirani, R.: A note on the group lasso and a sparse group lasso. arXiv preprint arXiv:1001.0736 (2010)"},{"issue":"1","key":"1492_CR20","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/0898-1221(76)90003-1","volume":"2","author":"D Gabay","year":"1976","unstructured":"Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Comput. Math. Appl. 2(1), 17\u201340 (1976)","journal-title":"Comput. Math. Appl."},{"issue":"3","key":"1492_CR21","doi-asserted-by":"crossref","first-page":"1432","DOI":"10.1137\/080727075","volume":"31","author":"Y Gao","year":"2009","unstructured":"Gao, Y., Sun, D.: Calibrating least squares semidefinite programming with equality and inequality constraints. SIAM J. Matrix Anal. Appl. 31(3), 1432\u20131457 (2009)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"1492_CR22","first-page":"41","volume":"9","author":"R Glowinski","year":"1975","unstructured":"Glowinski, R., Marrocco, A.: Approximation par \u00e9l\u00e9ments finis daordre un et r\u00e9solution par p\u00e9nalisation-dualit\u00e9 daune classe de probl\u00e9mes non lin\u00e9aires. RAIRO Rech. Op\u00e9r. 9, 41\u201376 (1975)","journal-title":"RAIRO Rech. Op\u00e9r."},{"issue":"4","key":"1492_CR23","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1137\/0723046","volume":"23","author":"L Grippo","year":"1986","unstructured":"Grippo, L., Lampariello, F., Lucidi, S.: A nonmonotone line search technique for Newton\u2019s method. SIAM J. Numer. Anal. 23(4), 707\u2013716 (1986)","journal-title":"SIAM J. Numer. Anal."},{"key":"1492_CR24","first-page":"2004","volume":"17","author":"I Guyon","year":"2003","unstructured":"Guyon, I., Gunn, S., Hur, A.B., Dror, G.: Result analysis of the nips: feature selection challenge. Adv. Neural Inf. Process. Syst. 17, 2004 (2003)","journal-title":"Adv. Neural Inf. Process. Syst."},{"issue":"2","key":"1492_CR25","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1137\/110836936","volume":"50","author":"B He","year":"2012","unstructured":"He, B., Yuan, X.: On the O(1\/n) convergence rate of the Douglas-Rachford alternating direction method. SIAM J. Numer. Anal. 50(2), 700\u2013709 (2012)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"1492_CR26","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1007\/s00211-014-0673-6","volume":"130","author":"B He","year":"2015","unstructured":"He, B., Yuan, X.: On non-ergodic convergence rate of Douglas\u2013Rachford alternating direction method of multipliers. Numer. Math. 130(3), 567\u2013577 (2015)","journal-title":"Numer. Math."},{"key":"1492_CR27","unstructured":"Hu, J., Tian, T., Pan, S., Wen, Z.: On the local convergence of the semismooth Newton method for composite optimization. arXiv preprint arXiv:2211.01127 (2022)"},{"key":"1492_CR28","doi-asserted-by":"crossref","unstructured":"Jacob, L., Obozinski, G., Vert, J.P.: Group lasso with overlap and graph lasso. In: Proceedings of the 26th Annual International Conference on Machine Learning, pp. 433\u2013440 (2009)","DOI":"10.1145\/1553374.1553431"},{"key":"1492_CR29","unstructured":"Krizhevsky, A., Hinton, G., et al.: Learning multiple layers of features from tiny images. Technical report (2009)"},{"key":"1492_CR30","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1023\/B:COAP.0000026881.96694.32","volume":"28","author":"H-D Li","year":"2004","unstructured":"Li, H.-D., Fukushima, M., Qi, L., Yamashita, N.: Regularized Newton methods for convex minimization problems with singular solutions. Comput. Optim. Appl. 28, 131\u2013147 (2004)","journal-title":"Comput. Optim. Appl."},{"key":"1492_CR31","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/s12532-010-0020-6","volume":"2","author":"L Li","year":"2010","unstructured":"Li, L., Toh, K.-C.: An inexact interior point method for l1-regularized sparse covariance selection. Math. Program. Comput. 2, 291\u2013315 (2010)","journal-title":"Math. Program. Comput."},{"key":"1492_CR32","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.csda.2018.07.011","volume":"128","author":"P Li","year":"2018","unstructured":"Li, P., Xiao, Y.: An efficient algorithm for sparse inverse covariance matrix estimation based on dual formulation. Comput. Stat. Data Anal. 128, 292\u2013307 (2018)","journal-title":"Comput. Stat. Data Anal."},{"issue":"4","key":"1492_CR33","doi-asserted-by":"crossref","first-page":"1641","DOI":"10.1137\/090771181","volume":"21","author":"Q Li","year":"2011","unstructured":"Li, Q., Qi, H.: A sequential semismooth Newton method for the nearest low-rank correlation matrix problem. SIAM J. Optim. 21(4), 1641\u20131666 (2011)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"1492_CR34","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1137\/16M106340X","volume":"27","author":"J Liang","year":"2017","unstructured":"Liang, J., Fadili, J., Peyr\u00e9, G.: Activity identification and local linear convergence of forward-backward-type methods. SIAM J. Optim. 27(1), 408\u2013437 (2017)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"1492_CR35","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1080\/10618600.2013.782818","volume":"23","author":"H Liu","year":"2014","unstructured":"Liu, H., Wang, L., Zhao, T.: Sparse covariance matrix estimation with eigenvalue constraints. J. Comput. Graph. Stat. 23(2), 439\u2013459 (2014)","journal-title":"J. Comput. Graph. Stat."},{"issue":"4","key":"1492_CR36","first-page":"1","volume":"37","author":"X Liu","year":"2022","unstructured":"Liu, X., Shen, C., Wang, L.: A dual active-set proximal Newton algorithm for sparse approximation of correlation matrices. Optim. Methods Soft. 37(4), 1\u201325 (2022)","journal-title":"Optim. Methods Soft."},{"issue":"4","key":"1492_CR37","doi-asserted-by":"crossref","first-page":"2000","DOI":"10.1137\/080742531","volume":"31","author":"Z Lu","year":"2010","unstructured":"Lu, Z.: Adaptive first-order methods for general sparse inverse covariance selection. SIAM J. Matrix Anal. Appl. 31(4), 2000\u20132016 (2010)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"1","key":"1492_CR38","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1137\/0802004","volume":"2","author":"Z-Q Luo","year":"1992","unstructured":"Luo, Z.-Q., Tseng, P.: Error bound and convergence analysis of matrix splitting algorithms for the affine variational inequality problem. SIAM J. Optim. 2(1), 43\u201354 (1992)","journal-title":"SIAM J. Optim."},{"key":"1492_CR39","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1137\/S0895479802413856","volume":"26","author":"J Malick","year":"2005","unstructured":"Malick, J.: A dual approach to semidefinite least-squares problems. SIAM J. Matrix Anal. Appl. 26, 272\u2013284 (2005)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"1492_CR40","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1007\/s10107-005-0629-9","volume":"104","author":"F Meng","year":"2005","unstructured":"Meng, F., Sun, D., Zhao, G.: Semismoothness of solutions to generalized equations and the Moreau\u2013Yosida regularization. Math. Program. 104, 561\u2013581 (2005)","journal-title":"Math. Program."},{"issue":"6","key":"1492_CR41","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1080\/02331934.2015.1105225","volume":"66","author":"BS Mordukhovich","year":"2017","unstructured":"Mordukhovich, B.S., Nam, N.M.: Geometric approach to convex subdifferential calculus. Optimization 66(6), 839\u2013873 (2017)","journal-title":"Optimization"},{"key":"1492_CR42","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/s10589-020-00166-2","volume":"76","author":"T Nakagaki","year":"2020","unstructured":"Nakagaki, T., Fukuda, M., Kim, S., Yamashita, M.: A dual spectral projected gradient method for log-determinant semidefinite problems. Comput. Optim. Appl. 76, 33\u201368 (2020)","journal-title":"Comput. Optim. Appl."},{"issue":"1","key":"1492_CR43","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1287\/moor.28.1.39.14258","volume":"28","author":"J-S Pang","year":"2003","unstructured":"Pang, J.-S., Sun, D., Sun, J.: Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems. Math. Oper. Res. 28(1), 39\u201363 (2003)","journal-title":"Math. Oper. Res."},{"issue":"2","key":"1492_CR44","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1137\/050624509","volume":"28","author":"H Qi","year":"2006","unstructured":"Qi, H., Sun, D.: A quadratically convergent Newton method for computing the nearest correlation matrix. SIAM J. Matrix Anal. Appl. 28(2), 360\u2013385 (2006)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"1492_CR45","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1287\/moor.18.1.227","volume":"18","author":"L Qi","year":"1993","unstructured":"Qi, L.: Convergence analysis of some algorithms for solving nonsmooth equations. Math. Oper. Res. 18, 227\u2013244 (1993)","journal-title":"Math. Oper. Res."},{"key":"1492_CR46","doi-asserted-by":"crossref","unstructured":"Qi, L., Sun, D.: A survey of some nonsmooth equations and smoothing Newton methods. In: Progress in Optimization, vol. 30, pp. 121\u2013146, Springer (1999)","DOI":"10.1007\/978-1-4613-3285-5_7"},{"key":"1492_CR47","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/BF01581275","volume":"58","author":"L Qi","year":"1993","unstructured":"Qi, L., Sun, J.: A nonsmooth version of Newton\u2019s method. Math. Program. 58, 353\u2013367 (1993)","journal-title":"Math. Program."},{"issue":"1","key":"1492_CR48","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1137\/S1052623494266365","volume":"7","author":"M Raydan","year":"1997","unstructured":"Raydan, M.: The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem. SIAM J. Optim. 7(1), 26\u201333 (1997)","journal-title":"SIAM J. Optim."},{"key":"1492_CR49","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/BFb0121018","volume":"22","author":"SM Robinson","year":"1984","unstructured":"Robinson, S.M.: Local structure of feasible sets in nonlinear programming, part II: nondegeneracy. Math. Program. Study 22, 217\u2013230 (1984)","journal-title":"Math. Program. Study"},{"key":"1492_CR50","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970524","volume-title":"Conjugate Duality and Optimization","author":"RT Rockafellar","year":"1974","unstructured":"Rockafellar, R.T.: Conjugate Duality and Optimization. SIAM, Philadelphia (1974)"},{"key":"1492_CR51","doi-asserted-by":"crossref","unstructured":"Rockafellar, R.T., Wets, R.J.B.: Variational Analysis, No. 317 in the series Grundlehren der Mathematischen Wissenschaften, Springer, Berlin, Heidelberg (1998)","DOI":"10.1007\/978-3-642-02431-3"},{"issue":"16","key":"1492_CR52","doi-asserted-by":"crossref","first-page":"4623","DOI":"10.1080\/02331934.2021.1958809","volume":"71","author":"C Shen","year":"2022","unstructured":"Shen, C., Mi, L., Zhang, L.-H.: An active-set proximal quasi-newton algorithm for $$\\ell _1$$-regularized minimization over a sphere constraint. Optimization 71(16), 4623\u20134664 (2022)","journal-title":"Optimization"},{"key":"1492_CR53","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10589-020-00228-5","volume":"78","author":"C Shen","year":"2021","unstructured":"Shen, C., Wang, Y., Xue, W., Zhang, L.-H.: An accelerated active-set algorithm for a quadratic semidefinite program with general constraints. Comput. Optim. Appl. 78, 1\u201342 (2021)","journal-title":"Comput. Optim. Appl."},{"key":"1492_CR54","doi-asserted-by":"crossref","unstructured":"Shen, C., Yang, W., Yu, Z., Zhang, L.-H.: A nonmonotone active-set semismooth Newton method for matrix approximation with group regularization. J. Sci. Comput. 103, 62 (2025)","DOI":"10.1007\/s10915-025-02877-2"},{"issue":"4","key":"1492_CR55","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1287\/moor.1060.0195","volume":"31","author":"D Sun","year":"2006","unstructured":"Sun, D.: The strong second-order sufficient condition and constraint nondegeneracy in nonlinear semidefinite programming and their implications. Math. Oper. Res. 31(4), 761\u2013776 (2006)","journal-title":"Math. Oper. Res."},{"issue":"1","key":"1492_CR56","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1287\/moor.27.1.150.342","volume":"27","author":"D Sun","year":"2002","unstructured":"Sun, D., Sun, J.: Semi-smooth matrix valued functions. Math. Oper. Res. 27(1), 150\u2013169 (2002)","journal-title":"Math. Oper. Res."},{"issue":"3","key":"1492_CR57","first-page":"250","volume":"13","author":"W Sun","year":"1995","unstructured":"Sun, W.: Generalized Newton\u2019s method for LC$$^1$$ unconstrained optimization. J. Comput. Math. 13(3), 250\u2013258 (1995)","journal-title":"J. Comput. Math."},{"issue":"3","key":"1492_CR58","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1080\/10556788.2013.829057","volume":"29","author":"B Wang","year":"2014","unstructured":"Wang, B., Zhang, L.: Calibrating low-rank correlation matrix problem: an SCA-based approach. Optim. Methods Soft. 29(3), 561\u2013582 (2014)","journal-title":"Optim. Methods Soft."},{"issue":"2","key":"1492_CR59","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1007\/s10589-015-9812-y","volume":"64","author":"C Wang","year":"2016","unstructured":"Wang, C.: On how to solve large-scale log-determinant optimization problems. Comput. Optim. Appl. 64(2), 489\u2013511 (2016)","journal-title":"Comput. Optim. Appl."},{"issue":"6","key":"1492_CR60","doi-asserted-by":"crossref","first-page":"2994","DOI":"10.1137\/090772514","volume":"20","author":"C Wang","year":"2010","unstructured":"Wang, C., Sun, D., Toh, K.-C.: Solving log-determinant optimization problems by a Newton-CG primal proximal point algorithm. SIAM J. Optim. 20(6), 2994\u20133013 (2010)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"1492_CR61","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1007\/s40305-021-00351-y","volume":"9","author":"Y Xiao","year":"2021","unstructured":"Xiao, Y., Li, P., Lu, S.: Sparse estimation of high-dimensional inverse covariance matrices with explicit eigenvalue constraints. J. Oper. Res. Soc. China 9(3), 543\u2013568 (2021)","journal-title":"J. Oper. Res. Soc. China"},{"issue":"500","key":"1492_CR62","doi-asserted-by":"crossref","first-page":"1480","DOI":"10.1080\/01621459.2012.725386","volume":"107","author":"L Xue","year":"2012","unstructured":"Xue, L., Ma, S., Zou, H.: Positive definite $$\\ell _1$$ penalized estimation of large covariance matrices. J. Am. Stat. Assoc. 107(500), 1480\u20131491 (2012)","journal-title":"J. Am. Stat. Assoc."},{"issue":"2","key":"1492_CR63","doi-asserted-by":"crossref","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."},{"key":"1492_CR64","unstructured":"Yu, Y.L.: On decomposing the proximal map. In: Proceedings of the 26th International Conference on Neural Information Processing Systems, vol. 1, pp. 91\u201399 (2013)"},{"key":"1492_CR65","first-page":"1999","volume":"13","author":"G Yuan","year":"2012","unstructured":"Yuan, G., Ho, C.-H., Lin, C.-J.: An improved GLMNET for $$l_1$$-regularized logistic regression. J. Mach. Learn. Res. 13, 1999\u20132030 (2012)","journal-title":"J. Mach. Learn. Res."},{"issue":"1\u20132","key":"1492_CR66","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/s10107-018-1280-6","volume":"174","author":"M-C Yue","year":"2019","unstructured":"Yue, M.-C., Zhou, Z., So, A.M.-C.: A family of inexact SQA methods for non-smooth convex minimization with provable convergence guarantees based on the Luo\u2013Tseng error bound property. Math. Program. 174(1\u20132), 327\u2013358 (2019)","journal-title":"Math. Program."},{"issue":"1","key":"1492_CR67","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s10107-018-1329-6","volume":"179","author":"Y Zhang","year":"2020","unstructured":"Zhang, Y., Zhang, N., Sun, D., Toh, K.-C.: An efficient Hessian based algorithm for solving large-scale sparse group lasso problems. Math. Program. 179(1), 223\u2013263 (2020)","journal-title":"Math. Program."},{"issue":"3","key":"1492_CR68","doi-asserted-by":"crossref","first-page":"2197","DOI":"10.1137\/19M1267830","volume":"30","author":"Y Zhang","year":"2020","unstructured":"Zhang, Y., Zhang, N., Sun, D., Toh, K.-C.: A proximal point dual Newton algorithm for solving group graphical lasso problems. SIAM J. Optim. 30(3), 2197\u20132220 (2020)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"1492_CR69","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/s10589-006-6446-0","volume":"35","author":"B Zhou","year":"2006","unstructured":"Zhou, B., Gao, L., Dai, Y.: Gradient methods with adaptive step-sizes. Comput. Optim. Appl. 35(1), 69\u201386 (2006)","journal-title":"Comput. Optim. Appl."},{"issue":"8","key":"1492_CR70","doi-asserted-by":"crossref","first-page":"1798","DOI":"10.1109\/TMM.2017.2689918","volume":"19","author":"Y Zhou","year":"2017","unstructured":"Zhou, Y., Han, J., Yuan, X., Wei, Z., Hong, R.: Inverse sparse group lasso model for robust object tracking. IEEE Trans. Multimed. 19(8), 1798\u20131810 (2017)","journal-title":"IEEE Trans. Multimed."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-025-01492-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10898-025-01492-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-025-01492-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T06:49:50Z","timestamp":1751611790000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10898-025-01492-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,18]]},"references-count":70,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,7]]}},"alternative-id":["1492"],"URL":"https:\/\/doi.org\/10.1007\/s10898-025-01492-7","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[2025,4,18]]},"assertion":[{"value":"1 June 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 March 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 April 2025","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 declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}