{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T19:25:47Z","timestamp":1783625147658,"version":"3.55.0"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2023,7,18]],"date-time":"2023-07-18T00:00:00Z","timestamp":1689638400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,7,18]],"date-time":"2023-07-18T00:00:00Z","timestamp":1689638400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971149"],"award-info":[{"award-number":["11971149"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271217"],"award-info":[{"award-number":["12271217"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s11590-023-02041-5","type":"journal-article","created":{"date-parts":[[2023,7,18]],"date-time":"2023-07-18T19:02:35Z","timestamp":1689706955000},"page":"1173-1200","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Convergence analysis of generalized ADMM with majorization for linearly constrained composite convex optimization"],"prefix":"10.1007","volume":"18","author":[{"given":"Hongwu","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haibin","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7503-4585","authenticated-orcid":false,"given":"Yunhai","family":"Xiao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6870-1458","authenticated-orcid":false,"given":"Peili","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,7,18]]},"reference":[{"key":"2041_CR1","unstructured":"Chen, C.: Numerical algorithms for a class of matrix norm approximation problems. Nanjing University, (2012)"},{"key":"2041_CR2","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/s10589-016-9864-7","volume":"66","author":"L Chen","year":"2017","unstructured":"Chen, L., Sun, D., Toh, K.-C.: A note on the convergence of ADMM for linearly constrained convex optimization problems. Comput. Optim. Appl. 66, 327\u2013343 (2017)","journal-title":"Comput. Optim. Appl."},{"key":"2041_CR3","doi-asserted-by":"crossref","unstructured":"Clarke, Frank H.: Optimization and nonsmooth analysis. SIAM, (1990)","DOI":"10.1137\/1.9781611971309"},{"key":"2041_CR4","doi-asserted-by":"publisher","first-page":"1013","DOI":"10.1007\/s10957-016-0877-2","volume":"169","author":"Y Cui","year":"2016","unstructured":"Cui, Y., Li, X., Sun, D., Toh, K.-C.: On the convergence properties of a majorized alternating direction method of multipliers for linearly constrained convex optimization problems with coupled objective functions. J. Optim. Theory Appl. 169, 1013\u20131041 (2016)","journal-title":"J. Optim. Theory Appl."},{"key":"2041_CR5","doi-asserted-by":"publisher","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, 201\u2013213 (2002)","journal-title":"Math. Program."},{"key":"2041_CR6","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. Pogram. 55, 293\u2013318 (1992)","journal-title":"Math. Pogram."},{"issue":"3","key":"2041_CR7","doi-asserted-by":"publisher","first-page":"946","DOI":"10.1137\/110853996","volume":"34","author":"M Fazel","year":"2013","unstructured":"Fazel, M., Pong, T., Sun, D., Tseng, P.: Hankel matrix rank minimization with applications to system identification and realization. SIAM J. Matric. Anal. Appl. 34(3), 946\u2013977 (2013)","journal-title":"SIAM J. Matric. Anal. Appl."},{"key":"2041_CR8","unstructured":"Fortin, M., Glowinski, R.: Augmented Lagrangian methods: applications to the numerical solution of boundary-value problems. Elsevier, (2000)"},{"key":"2041_CR9","doi-asserted-by":"crossref","unstructured":"Gabay, D.: Applications of the method of multipliers to variational inequalities. In Studies in mathematics and its applications, volume\u00a015, pages 299\u2013331. Elsevier, (1983)","DOI":"10.1016\/S0168-2024(08)70034-1"},{"issue":"1","key":"2041_CR10","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(1), 17\u201340 (1976)","journal-title":"Comput. Math. Appl."},{"key":"2041_CR11","doi-asserted-by":"crossref","unstructured":"Glowinski, R.: On alternating direction methods of multipliers: a historical perspective. Modeling, simulation and optimization for science and technology, pages 59\u201382, (2014)","DOI":"10.1007\/978-94-017-9054-3_4"},{"issue":"3","key":"2041_CR12","doi-asserted-by":"publisher","first-page":"833","DOI":"10.1287\/moor.2019.1010","volume":"45","author":"M Hong","year":"2020","unstructured":"Hong, M., Chang, T.-H., Wang, X., Razaviyayn, M., Ma, S., Luo, Z.-Q.: A block successive upper-bound minimization method of multipliers for linearly constrained convex optimization. Math. Operat. Res. 45(3), 833\u2013861 (2020)","journal-title":"Math. Operat. Res."},{"issue":"2","key":"2041_CR13","doi-asserted-by":"publisher","first-page":"922","DOI":"10.1137\/140999025","volume":"26","author":"M Li","year":"2016","unstructured":"Li, M., Sun, D., Toh, K.-C.: A majorized admm with indefinite proximal terms for linearly constrained convex composite optimization. SIAM J. Optim. 26(2), 922\u2013950 (2016)","journal-title":"SIAM J. Optim."},{"issue":"1\u20132","key":"2041_CR14","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/s10107-014-0850-5","volume":"155","author":"X Li","year":"2016","unstructured":"Li, X., Sun, D., Toh, K.-C.: A schur complement based semi-proximal admm for convex quadratic conic programming and extensions. Math. Program. 155(1\u20132), 333\u2013373 (2016)","journal-title":"Math. Program."},{"key":"2041_CR15","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1007\/s10107-018-1247-7","volume":"175","author":"X Li","year":"2019","unstructured":"Li, X., Sun, D., Toh, K.-C.: A block symmetric Gauss\u2013Seidel decomposition theorem for convex composite quadratic programming and its applications. Math. Program. 175, 395\u2013418 (2019)","journal-title":"Math. Program."},{"key":"2041_CR16","unstructured":"Qin, C., Xiao, Y., Li, P.: A majorized-generalized alternating direction method of multipliers for convex composite programming. arXiv preprint arXiv:2111.12519, (2021)"},{"key":"2041_CR17","doi-asserted-by":"crossref","unstructured":"Rockafellar, R\u00a0Tyrrell.: Convex analysis, volume\u00a018. Princeton university press, (1970)","DOI":"10.1515\/9781400873173"},{"issue":"2","key":"2041_CR18","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1287\/moor.1.2.97","volume":"1","author":"RT Rockafellar","year":"1976","unstructured":"Rockafellar, R.T.: Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Math. Oper. Res. 1(2), 97\u2013116 (1976)","journal-title":"Math. Oper. Res."},{"key":"2041_CR19","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1007\/s12532-018-0134-9","volume":"10","author":"Y Xiao","year":"2018","unstructured":"Xiao, Y., Chen, L., Li, D.: A generalized alternating direction method of multipliers with semi-proximal terms for convex composite conic programming. Math. Program. Comput. 10, 533\u2013555 (2018)","journal-title":"Math. Program. Comput."}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-023-02041-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11590-023-02041-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-023-02041-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,18]],"date-time":"2024-05-18T03:35:38Z","timestamp":1716003338000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11590-023-02041-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,18]]},"references-count":19,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["2041"],"URL":"https:\/\/doi.org\/10.1007\/s11590-023-02041-5","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,18]]},"assertion":[{"value":"6 April 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 June 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 July 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}