{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T05:03:44Z","timestamp":1784869424360,"version":"3.55.0"},"reference-count":57,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100004541","name":"Ministry of Education, India","doi-asserted-by":"publisher","award":["SB23242132MAPMRF00501"],"award-info":[{"award-number":["SB23242132MAPMRF00501"]}],"id":[{"id":"10.13039\/501100004541","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":[[2026,7]]},"DOI":"10.1007\/s10957-026-03050-x","type":"journal-article","created":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T07:27:02Z","timestamp":1782977222000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Golden Ratio Proximal ADMM with Norm Independent Step-Sizes for Separable Convex Optimization"],"prefix":"10.1007","volume":"210","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-1392-0003","authenticated-orcid":false,"given":"Santanu","family":"Soe","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"V.","family":"Vetrivel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,7,2]]},"reference":[{"issue":"2","key":"3050_CR1","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/s10898-018-0697-z","volume":"73","author":"VA Adona","year":"2019","unstructured":"Adona, V.A., Gon\u00e7alves, M.L., Melo, J.G.: Iteration-complexity analysis of a generalized alternating direction method of multipliers. J. Glob. Optim. 73(2), 331\u2013348 (2019)","journal-title":"J. Glob. Optim."},{"issue":"1","key":"3050_CR2","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1080\/02331934.2019.1704754","volume":"70","author":"J Bai","year":"2021","unstructured":"Bai, J., Chang, X., Li, J., Xu, F.: Convergence revisit on generalized symmetric ADMM. Optimization 70(1), 149\u2013168 (2021)","journal-title":"Optimization"},{"issue":"2","key":"3050_CR3","doi-asserted-by":"publisher","first-page":"395","DOI":"10.4208\/nmtma.OA-2025-0066","volume":"19","author":"J Bai","year":"2026","unstructured":"Bai, J., Cui, X., Wu, Z.: A proximal-perturbed Bregman ADMM for solving nonsmooth and nonconvex composite optimization. Numer. Math. Theory Methods Appl. 19(2), 395\u2013422 (2026)","journal-title":"Numer. Math. Theory Methods Appl."},{"issue":"2","key":"3050_CR4","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1007\/s10589-021-00338-8","volume":"81","author":"J Bai","year":"2022","unstructured":"Bai, J., Hager, W.W., Zhang, H.: An inexact accelerated stochastic ADMM for separable convex optimization. Comput. Optim. Appl. 81(2), 479\u2013518 (2022)","journal-title":"Comput. Optim. Appl."},{"issue":"3","key":"3050_CR5","doi-asserted-by":"publisher","first-page":"448","DOI":"10.4208\/csiam-am.SO-2021-0021","volume":"3","author":"J Bai","year":"2022","unstructured":"Bai, J., Han, D., Sun, H., Zhang, H.: Convergence on a symmetric accelerated stochastic ADMM with larger stepsizes. CSIAM Trans. Appl. Math. 3(3), 448\u2013479 (2022)","journal-title":"CSIAM Trans. Appl. Math."},{"issue":"1","key":"3050_CR6","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/s10589-017-9971-0","volume":"70","author":"J Bai","year":"2018","unstructured":"Bai, J., Li, J., Xu, F., Zhang, H.: Generalized symmetric ADMM for separable convex optimization. Comput. Optim. Appl. 70(1), 129\u2013170 (2018)","journal-title":"Comput. Optim. Appl."},{"issue":"3","key":"3050_CR7","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/S0168-1699(99)00046-0","volume":"24","author":"JA Blackard","year":"1999","unstructured":"Blackard, J.A., Dean, D.J.: Comparative accuracies of artificial neural networks and discriminant analysis in predicting forest cover types from cartographic variables. Comput. Electron. Agric. 24(3), 131\u2013151 (1999)","journal-title":"Comput. Electron. Agric."},{"issue":"1","key":"3050_CR8","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1080\/02331934.2014.966306","volume":"64","author":"RI Bo\u0163","year":"2015","unstructured":"Bo\u0163, R.I., Csetnek, E.R.: On the convergence rate of a forward-backward type primal-dual splitting algorithm for convex optimization problems. Optimization 64(1), 5\u201323 (2015)","journal-title":"Optimization"},{"key":"3050_CR9","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/s10444-018-9619-3","volume":"45","author":"RI Bo\u0163","year":"2019","unstructured":"Bo\u0163, R.I., Csetnek, E.R.: ADMM for monotone operators: convergence analysis and rates. Adv. Comput. Math. 45, 327\u2013359 (2019)","journal-title":"Adv. Comput. Math."},{"issue":"2","key":"3050_CR10","doi-asserted-by":"publisher","first-page":"682","DOI":"10.1287\/moor.2019.1008","volume":"45","author":"RI Bo\u0163","year":"2020","unstructured":"Bo\u0163, R.I., Nguyen, D.K.: The proximal alternating direction method of multipliers in the nonconvex setting: convergence analysis and rates. Math. Oper. Res. 45(2), 682\u2013712 (2020)","journal-title":"Math. Oper. Res."},{"issue":"1","key":"3050_CR11","doi-asserted-by":"publisher","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":"1","key":"3050_CR12","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1007\/s10851-010-0251-1","volume":"40","author":"A Chambolle","year":"2011","unstructured":"Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40(1), 120\u2013145 (2011)","journal-title":"J. Math. Imaging Vis."},{"issue":"2","key":"3050_CR13","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s10915-021-01452-9","volume":"87","author":"X Chang","year":"2021","unstructured":"Chang, X., Yang, J.: A golden ratio primal-dual algorithm for structured convex optimization. J. Sci. Comput. 87(2), 47 (2021)","journal-title":"J. Sci. Comput."},{"issue":"3","key":"3050_CR14","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1007\/s10915-022-02033-0","volume":"93","author":"X Chang","year":"2022","unstructured":"Chang, X., Yang, J.: GRPDA revisited: relaxed condition and connection to Chambolle-Pock\u2019s primal-dual algorithm. J. Sci. Comput. 93(3), 70 (2022)","journal-title":"J. Sci. Comput."},{"key":"3050_CR15","first-page":"23270","volume":"34","author":"L Chapel","year":"2021","unstructured":"Chapel, L., Flamary, R., Wu, H., F\u00e9votte, C., Gasso, G.: Unbalanced optimal transport through non-negative penalized linear regression. Adv. Neural. Inf. Process. Syst. 34, 23270\u201323282 (2021)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"issue":"4","key":"3050_CR16","doi-asserted-by":"publisher","first-page":"2239","DOI":"10.1137\/15100463X","volume":"8","author":"C Chen","year":"2015","unstructured":"Chen, C., Chan, R.H., Ma, S., Yang, J.: Inertial proximal ADMM for linearly constrained separable convex optimization. SIAM J. Imaging Sci. 8(4), 2239\u20132267 (2015)","journal-title":"SIAM J. Imaging Sci."},{"issue":"2","key":"3050_CR17","doi-asserted-by":"publisher","first-page":"676","DOI":"10.1007\/s10957-018-1270-0","volume":"179","author":"C Chen","year":"2018","unstructured":"Chen, C., Chen, Y., Ouyang, Y., Pasiliao, E.: Stochastic accelerated alternating direction method of multipliers with importance sampling. J. Optim. Theory Appl. 179(2), 676\u2013695 (2018)","journal-title":"J. Optim. Theory Appl."},{"key":"3050_CR18","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1007\/s10898-022-01154-y","volume":"87","author":"H Chen","year":"2023","unstructured":"Chen, H., Gu, G., Yang, J.: A golden ratio proximal alternating direction method of multipliers for separable convex optimization. J. Global Optim. 87, 581\u2013602 (2023)","journal-title":"J. Global Optim."},{"issue":"11","key":"3050_CR19","doi-asserted-by":"publisher","first-page":"3090","DOI":"10.1016\/j.jfa.2018.03.008","volume":"274","author":"L Chizat","year":"2018","unstructured":"Chizat, L., Peyr\u00e9, G., Schmitzer, B., Vialard, F.: Unbalanced optimal transport: Dynamic and kantorovich formulations. J. Funct. Anal. 274(11), 3090\u20133123 (2018)","journal-title":"J. Funct. Anal."},{"issue":"1","key":"3050_CR20","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1080\/10556789408805578","volume":"4","author":"J Eckstein","year":"1994","unstructured":"Eckstein, J.: Some saddle-function splitting methods for convex programming. Optim. Methods Softw. 4(1), 75\u201383 (1994)","journal-title":"Optim. Methods Softw."},{"issue":"1","key":"3050_CR21","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/BF01581204","volume":"55","author":"J Eckstein","year":"1992","unstructured":"Eckstein, J., Bertsekas, D.P.: On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 55(1), 293\u2013318 (1992)","journal-title":"Math. Program."},{"key":"3050_CR22","doi-asserted-by":"publisher","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, 17\u201340 (1976)","journal-title":"Comput. Math. Appl."},{"issue":"R2","key":"3050_CR23","first-page":"41","volume":"9","author":"R Glowinski","year":"1975","unstructured":"Glowinski, R., Marroco, A.: Sur l\u2019approximation, par \u00e9l\u00e9ments finis d\u2019ordre un, et la r\u00e9solution, par p\u00e9nalisation-dualit\u00e9 d\u2019une classe de probl\u00e8mes de Dirichlet non lin\u00e9aires. RAIRO Anal. Num\u00e9r. 9(R2), 41\u201376 (1975)","journal-title":"RAIRO Anal. Num\u00e9r."},{"issue":"2","key":"3050_CR24","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1137\/080725891","volume":"2","author":"T Goldstein","year":"2009","unstructured":"Goldstein, T., Osher, S.: The split Bregman method for $$\\ell _1$$-regularized problems. SIAM J. Imaging Sci. 2(2), 323\u2013343 (2009)","journal-title":"SIAM J. Imaging Sci."},{"issue":"2","key":"3050_CR25","doi-asserted-by":"publisher","first-page":"448","DOI":"10.1007\/s10957-018-1232-6","volume":"177","author":"ML Gon\u00e7alves","year":"2018","unstructured":"Gon\u00e7alves, M.L., Alves, M.M., Melo, J.G.: Pointwise and ergodic convergence rates of a variable metric proximal alternating direction method of multipliers. J. Optim. Theory Appl. 177(2), 448\u2013478 (2018)","journal-title":"J. Optim. Theory Appl."},{"key":"3050_CR26","doi-asserted-by":"crossref","unstructured":"Hallac, D., Leskovec, J., Boyd, S.: Network lasso: Clustering and optimization in large graphs. In: Proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining, pp. 387\u2013396. (2015)","DOI":"10.1145\/2783258.2783313"},{"issue":"2","key":"3050_CR27","doi-asserted-by":"publisher","first-page":"622","DOI":"10.1287\/moor.2017.0875","volume":"43","author":"D Han","year":"2018","unstructured":"Han, D., Sun, D., Zhang, L.: Linear rate convergence of the alternating direction method of multipliers for convex composite programming. Math. Oper. Res. 43(2), 622\u2013637 (2018)","journal-title":"Math. Oper. Res."},{"issue":"1","key":"3050_CR28","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1007\/s101070100280","volume":"92","author":"B He","year":"2002","unstructured":"He, B., Liao, L.Z., Han, D., Yang, H.: A new inexact alternating directions method for monotone variational inequalities. Math. Program. 92(1), 103\u2013118 (2002)","journal-title":"Math. Program."},{"issue":"3","key":"3050_CR29","doi-asserted-by":"publisher","first-page":"1204","DOI":"10.1007\/s10915-015-0060-1","volume":"66","author":"B He","year":"2016","unstructured":"He, B., Xu, H.K., Yuan, X.: On the proximal jacobian decomposition of alm for multiple-block separable convex minimization problems and its relationship to admm. J. Sci. Comput. 66(3), 1204\u20131217 (2016)","journal-title":"J. Sci. Comput."},{"issue":"3","key":"3050_CR30","doi-asserted-by":"publisher","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-Rachford alternating direction method of multipliers. Numer. Math. 130(3), 567\u2013577 (2015)","journal-title":"Numer. Math."},{"issue":"5","key":"3050_CR31","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/BF00927673","volume":"4","author":"MR Hestenes","year":"1969","unstructured":"Hestenes, M.R.: Multiplier and gradient methods. J. Optim. Theory Appl. 4(5), 303\u2013320 (1969)","journal-title":"J. Optim. Theory Appl."},{"key":"3050_CR32","volume-title":"Matrix Analysis","author":"RA Horn","year":"2013","unstructured":"Horn, R.A., Johnson, C.R.: Matrix Analysis, 2nd edn. Cambridge University Press, Cambridge (2013)","edition":"2"},{"key":"3050_CR33","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/s11590-025-02212-6","volume":"20","author":"B Li","year":"2026","unstructured":"Li, B., Liu, P., Shao, H., Wu, T., Xu, J.: A proximal alternating direction method of multipliers with a proximal-perturbed lagrangian function for nonconvex and nonsmooth structured optimization. Optim. Lett. 20, 109\u2013122 (2026)","journal-title":"Optim. Lett."},{"issue":"2","key":"3050_CR34","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1007\/s10915-018-0893-5","volume":"79","author":"H Li","year":"2019","unstructured":"Li, H., Lin, Z.: Accelerated alternating direction method of multipliers: an optimal $$O(1\/k)$$ nonergodic analysis. J. Sci. Comput. 79(2), 671\u2013699 (2019)","journal-title":"J. Sci. Comput."},{"issue":"8","key":"3050_CR35","doi-asserted-by":"publisher","first-page":"2160","DOI":"10.1007\/s10114-025-4144-z","volume":"41","author":"P Liu","year":"2025","unstructured":"Liu, P., Jian, J., Shao, H., Wang, X., Wang, X.: A half-proximal symmetric splitting method for non-convex separable optimization. Acta Math. Sin. Engl. Ser. 41(8), 2160\u20132194 (2025)","journal-title":"Acta Math. Sin. Engl. Ser."},{"issue":"2","key":"3050_CR36","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1007\/s10255-023-1048-5","volume":"39","author":"PJ Liu","year":"2023","unstructured":"Liu, P.J., Jian, J.B., Ma, G.D.: A Bregman-style partially symmetric alternating direction method of multipliers for nonconvex multi-block optimization. Acta Math. Sin. Engl. Ser. 39(2), 354\u2013380 (2023)","journal-title":"Acta Math. Sin. Engl. Ser."},{"issue":"2","key":"3050_CR37","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1007\/s40305-023-00535-8","volume":"12","author":"PJ Liu","year":"2024","unstructured":"Liu, P.J., Jian, J.B., Shao, H., Wang, X.Q., Xu, J.W., Wu, X.Y.: A Bregman-style improved ADMM and its linearized version in the nonconvex setting: convergence and rate analyses. J. Oper. Res. Soc. China 12(2), 298\u2013340 (2024)","journal-title":"J. Oper. Res. Soc. China"},{"key":"3050_CR38","unstructured":"Nesterov, Y.E.: A method of solving a convex programming problem with convergence rate $$O(1\/k^2)$$. Dokl. Akad. Nauk SSSR 269, 543\u2013547 (1983)"},{"issue":"1","key":"3050_CR39","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1137\/14095697X","volume":"8","author":"Y Ouyang","year":"2015","unstructured":"Ouyang, Y., Chen, Y., Lan, G., Pasiliao, E., Jr.: An accelerated linearized alternating direction method of multipliers. SIAM J. Imaging Sci. 8(1), 644\u2013681 (2015)","journal-title":"SIAM J. Imaging Sci."},{"issue":"3","key":"3050_CR40","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1016\/S0167-7152(96)00140-X","volume":"33","author":"RK Pace","year":"1997","unstructured":"Pace, R.K., Barry, R.: Sparse spatial autoregressions. Stat. Probab. Lett. 33(3), 291\u2013297 (1997)","journal-title":"Stat. Probab. Lett."},{"key":"3050_CR41","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1016\/j.cam.2018.09.053","volume":"354","author":"A Padcharoen","year":"2019","unstructured":"Padcharoen, A., Kumam, P., Mart\u00ednez-Moreno, J.: Augmented lagrangian method for TV-$$\\ell _1$$-$$\\ell _2$$ based colour image restoration. J. Comput. Appl. Math. 354, 507\u2013519 (2019)","journal-title":"J. Comput. Appl. Math."},{"issue":"3","key":"3050_CR42","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1561\/2400000003","volume":"1","author":"N Parikh","year":"2014","unstructured":"Parikh, N., Boyd, S.: Proximal algorithms. Found. Trends Optim. 1(3), 127\u2013239 (2014)","journal-title":"Proximal algorithms. Found. Trends Optim."},{"issue":"5\u20136","key":"3050_CR43","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1561\/2200000073","volume":"11","author":"G Peyr\u00e9","year":"2019","unstructured":"Peyr\u00e9, G., Cuturi, M.: Computational optimal transport. Found. Trends Mach. Learn. 11(5\u20136), 355\u2013607 (2019). https:\/\/doi.org\/10.1561\/2200000073","journal-title":"Found. Trends Mach. Learn."},{"key":"3050_CR44","first-page":"283","volume-title":"Optimization","author":"MJD Powell","year":"1969","unstructured":"Powell, M.J.D.: A method for nonlinear constraints in minimization problems. In: Fletcher, R. (ed.) Optimization, pp. 283\u2013298. Academic Press, London (1969)"},{"key":"3050_CR45","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton, NJ (1970)"},{"issue":"1","key":"3050_CR46","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1137\/130910774","volume":"24","author":"R Shefi","year":"2014","unstructured":"Shefi, R., Teboulle, M.: Rate of convergence analysis of decomposition methods based on the proximal method of multipliers for convex minimization. SIAM J. Optim. 24(1), 269\u2013297 (2014)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"3050_CR47","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1214\/aoms\/1177729893","volume":"21","author":"J Sherman","year":"1950","unstructured":"Sherman, J., Morrison, W.J.: Adjustment of an inverse matrix corresponding to a change in one element of a given matrix. Ann. Math. Stat. 21(1), 124\u2013127 (1950)","journal-title":"Ann. Math. Stat."},{"issue":"3","key":"3050_CR48","doi-asserted-by":"publisher","first-page":"1355","DOI":"10.1007\/s10589-025-00761-1","volume":"93","author":"S Soe","year":"2026","unstructured":"Soe, S., Tam, M.K., Vetrivel, V.: The golden ratio primal-dual algorithm with two new stepsize rules for convex-concave saddle point problems. Comput. Optim. Appl. 93(3), 1355\u20131399 (2026)","journal-title":"Comput. Optim. Appl."},{"issue":"1","key":"3050_CR49","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1137\/100781894","volume":"21","author":"M Tao","year":"2011","unstructured":"Tao, M., Yuan, X.: Recovering low-rank and sparse components of matrices from incomplete and noisy observations. SIAM J. Optim. 21(1), 57\u201381 (2011)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"3050_CR50","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. R. Stat. Soc. Ser. B (Methodol.) 58(1), 267\u2013288 (1996)","journal-title":"J. R. Stat. Soc. Ser. B (Methodol.)"},{"key":"3050_CR51","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/058","volume-title":"Topics in Optimal Transportation, Graduate Studies in Mathematics","author":"C Villani","year":"2003","unstructured":"Villani, C.: Topics in Optimal Transportation, Graduate Studies in Mathematics, vol. 58. American Mathematical Society, Providence, RI (2003)"},{"issue":"3","key":"3050_CR52","doi-asserted-by":"publisher","first-page":"839","DOI":"10.1007\/s10589-025-00647-2","volume":"90","author":"X Wang","year":"2025","unstructured":"Wang, X., Shao, H., Wu, T.: A convex combined symmetric alternating direction method of multipliers for separable optimization. Comput. Optim. Appl. 90(3), 839\u2013880 (2025)","journal-title":"Comput. Optim. Appl."},{"issue":"5","key":"3050_CR53","doi-asserted-by":"publisher","first-page":"A2792","DOI":"10.1137\/110833543","volume":"34","author":"X Wang","year":"2012","unstructured":"Wang, X., Yuan, X.: The linearized alternating direction method of multipliers for Dantzig selector. SIAM J. Sci. Comput. 34(5), A2792\u2013A2811 (2012)","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"3050_CR54","doi-asserted-by":"publisher","first-page":"1459","DOI":"10.1137\/16M1082305","volume":"27","author":"Y Xu","year":"2017","unstructured":"Xu, Y.: Accelerated first-order primal-dual proximal methods for linearly constrained composite convex programming. SIAM J. Optim. 27(3), 1459\u20131484 (2017)","journal-title":"SIAM J. Optim."},{"issue":"281","key":"3050_CR55","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1090\/S0025-5718-2012-02598-1","volume":"82","author":"J Yang","year":"2013","unstructured":"Yang, J., Yuan, X.: Linearized augmented lagrangian and alternating direction methods for nuclear norm minimization. Math. Comp. 82(281), 301\u2013329 (2013)","journal-title":"Math. Comp."},{"issue":"3","key":"3050_CR56","doi-asserted-by":"publisher","first-page":"895","DOI":"10.1007\/s10957-023-02336-8","volume":"200","author":"C Yin","year":"2024","unstructured":"Yin, C., Yang, J.: Golden ratio proximal gradient ADMM for distributed composite convex optimization. J. Optim. Theory Appl. 200(3), 895\u2013922 (2024)","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"3050_CR57","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1007\/s10915-011-9507-1","volume":"51","author":"X Yuan","year":"2012","unstructured":"Yuan, X.: Alternating direction method for covariance selection models. J. Sci. Comput. 51(2), 261\u2013273 (2012)","journal-title":"J. Sci. Comput."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-026-03050-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-026-03050-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-026-03050-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T04:50:54Z","timestamp":1784868654000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-026-03050-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7]]},"references-count":57,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,7]]}},"alternative-id":["3050"],"URL":"https:\/\/doi.org\/10.1007\/s10957-026-03050-x","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7]]},"assertion":[{"value":"23 September 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 June 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 July 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that there are no conflicts of interest in this paper.","order":1,"name":"Ethics","label":"Conflicts of Interest","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"18"}}