{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T18:08:37Z","timestamp":1775066917187,"version":"3.50.1"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,6,25]],"date-time":"2020-06-25T00:00:00Z","timestamp":1593043200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,6,25]],"date-time":"2020-06-25T00:00:00Z","timestamp":1593043200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11771383"],"award-info":[{"award-number":["11771383"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11601095"],"award-info":[{"award-number":["11601095"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100004607","name":"Natural Science Foundation of Guangxi Province","doi-asserted-by":"publisher","award":["2016GXNSFDA380019"],"award-info":[{"award-number":["2016GXNSFDA380019"]}],"id":[{"id":"10.13039\/501100004607","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004607","name":"Natural Science Foundation of Guangxi Province","doi-asserted-by":"publisher","award":["2016GXNSFBA380185"],"award-info":[{"award-number":["2016GXNSFBA380185"]}],"id":[{"id":"10.13039\/501100004607","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":[[2020,7]]},"DOI":"10.1007\/s10957-020-01697-8","type":"journal-article","created":{"date-parts":[[2020,6,25]],"date-time":"2020-06-25T09:02:27Z","timestamp":1593075747000},"page":"226-247","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Monotone Splitting Sequential Quadratic Optimization Algorithm with Applications in Electric Power Systems"],"prefix":"10.1007","volume":"186","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3254-4278","authenticated-orcid":false,"given":"Jinbao","family":"Jian","sequence":"first","affiliation":[]},{"given":"Chen","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Jianghua","family":"Yin","sequence":"additional","affiliation":[]},{"given":"Linfeng","family":"Yang","sequence":"additional","affiliation":[]},{"given":"Guodong","family":"Ma","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,6,25]]},"reference":[{"issue":"2","key":"1697_CR1","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1090\/S0002-9947-1956-0084194-4","volume":"82","author":"J Douglas","year":"1956","unstructured":"Douglas, J., Rachford, H.H.: On the numerical solution of the heat conduction problem in two and three space variables. Trans. Am. Math. Soc. 82(2), 421\u2013439 (1956)","journal-title":"Trans. Am. Math. Soc."},{"issue":"6","key":"1697_CR2","doi-asserted-by":"publisher","first-page":"964","DOI":"10.1137\/0716071","volume":"16","author":"PL Lions","year":"1979","unstructured":"Lions, P.L., Mercier, B.: Splitting algorithms for the sum of two nonlinear operators. SIAM J. Numer. Anal. 16(6), 964\u2013979 (1979)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"1697_CR3","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 with the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1\u2013122 (2011)","journal-title":"Found. Trends Mach. Learn."},{"issue":"2","key":"1697_CR4","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1137\/110836936","volume":"50","author":"BS He","year":"2012","unstructured":"He, B.S., Yuan, X.M.: On the $${\\rm O}(1\/n)$$ convergence rate of the Douglas\u2013Rachford alternating direction method. SIAM J. Numer. Anal. 50(2), 700\u2013709 (2012)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"1697_CR5","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1007\/s00211-014-0673-6","volume":"130","author":"BS He","year":"2015","unstructured":"He, B.S., Yuan, X.M.: On non-ergodic convergence rate of Douglas\u2013Rachford alternating direction method of multipliers. Numer. Math. 130(3), 567\u2013577 (2015)","journal-title":"Numer. Math."},{"issue":"3","key":"1697_CR6","doi-asserted-by":"publisher","first-page":"1467","DOI":"10.1137\/15M1044448","volume":"9","author":"BS He","year":"2016","unstructured":"He, B.S., Ma, F., Yuan, X.M.: Convergence study on the symmetric version of ADMM with larger step sizes. SIAM J. Imaging Sci. 9(3), 1467\u20131501 (2016)","journal-title":"SIAM J. Imaging Sci."},{"issue":"3","key":"1697_CR7","doi-asserted-by":"publisher","first-page":"1011","DOI":"10.1137\/13090849X","volume":"24","author":"BS He","year":"2014","unstructured":"He, B.S., Liu, H., Wang, Z.R., Yuan, X.M.: A strictly contractive Peaceman\u2013Rachford splitting method for convex programming. SIAM J. Optim. 24(3), 1011\u20131040 (2014)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"1697_CR8","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1137\/110849468","volume":"23","author":"RDC Monteiro","year":"2013","unstructured":"Monteiro, R.D.C., Svaiter, B.F.: Iteration-complexity of block-decomposition algorithms and the alternating direction method of multipliers. SIAM J. Optim. 23(1), 475\u2013507 (2013)","journal-title":"SIAM J. Optim."},{"issue":"1\u20132","key":"1697_CR9","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1007\/s10107-012-0530-2","volume":"141","author":"D Goldfarb","year":"2013","unstructured":"Goldfarb, D., Ma, S.Q., Scheinberg, K.: Fast alternating linearization methods for minimizing the sum of two convex functions. Math. Program. 141(1\u20132), 349\u2013382 (2013)","journal-title":"Math. Program."},{"issue":"3","key":"1697_CR10","doi-asserted-by":"publisher","first-page":"1588","DOI":"10.1137\/120896219","volume":"7","author":"T Goldstein","year":"2014","unstructured":"Goldstein, T., O\u2019Donoghue, B., Setzer, S., Baraniuk, R.: Fast alternating direction optimization methods. SIAM J. Imaging Sci. 7(3), 1588\u20131623 (2014)","journal-title":"SIAM J. Imaging Sci."},{"issue":"1","key":"1697_CR11","first-page":"3836","volume":"26","author":"MY Hong","year":"2014","unstructured":"Hong, M.Y., Luo, Z.Q., Razaviyayn, M.: Convergence analysis of alternating direction method of multipliers for a family of nonconvex problems. SIAM J. Optim. 26(1), 3836\u20133840 (2014)","journal-title":"SIAM J. Optim."},{"issue":"4","key":"1697_CR12","doi-asserted-by":"publisher","first-page":"2434","DOI":"10.1137\/140998135","volume":"25","author":"GY Li","year":"2015","unstructured":"Li, G.Y., 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":"1","key":"1697_CR13","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/s10915-018-0757-z","volume":"78","author":"Y Wang","year":"2019","unstructured":"Wang, Y., Yin, W.T., Zeng, J.S.: Global convergence of ADMM in nonconvex nonsmooth optimization. J. Sci. Comput. 78(1), 29\u201363 (2019)","journal-title":"J. Sci. Comput."},{"key":"1697_CR14","unstructured":"Wilson, R.B.: A simplicial method for concave programming. Ph.D. dissertation, Harvard Business School, Boston (1963)"},{"issue":"3","key":"1697_CR15","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1007\/BF01580879","volume":"35","author":"M Fukushima","year":"1986","unstructured":"Fukushima, M.: A successive quadratic programming algorithm with global and superlinear convergence properties. Math. Program. 35(3), 253\u2013264 (1986)","journal-title":"Math. Program."},{"issue":"1","key":"1697_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10107-007-0180-y","volume":"118","author":"MV Solodov","year":"2009","unstructured":"Solodov, M.V.: Global convergence of an SQP method without boundedness assumptions on any of the iterative sequences. Math. Program. Ser. A 118(1), 1\u201312 (2009)","journal-title":"Math. Program. Ser. A"},{"issue":"4","key":"1697_CR17","doi-asserted-by":"publisher","first-page":"934","DOI":"10.1137\/0325051","volume":"25","author":"ER Panier","year":"1987","unstructured":"Panier, E.R., Tits, A.L.: A superlinearly convergent feasible method for the solution of inequality constrained optimization problems. SIAM J. Control Optim. 25(4), 934\u2013950 (1987)","journal-title":"SIAM J. Control Optim."},{"issue":"2","key":"1697_CR18","doi-asserted-by":"publisher","first-page":"1220","DOI":"10.1016\/j.nonrwa.2008.01.001","volume":"10","author":"ZB Zhu","year":"2009","unstructured":"Zhu, Z.B., Jian, J.B.: An efficient feasible SQP algorithm for inequality constrained optimization. Nonlinear Anal. Real World Appl. 10(2), 1220\u20131228 (2009)","journal-title":"Nonlinear Anal. Real World Appl."},{"issue":"3\u20134","key":"1697_CR19","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1080\/01630560802000918","volume":"29","author":"JB Jian","year":"2008","unstructured":"Jian, J.B., Tang, C.M., Hu, Q.J., Zheng, H.Y.: A new superlinearly convergent strongly subfeasible sequential quadratic programming algorithm for inequality constrained optimization. Numer. Funct. Anal. Optim. 29(3\u20134), 376\u2013409 (2008)","journal-title":"Numer. Funct. Anal. Optim."},{"issue":"3","key":"1697_CR20","doi-asserted-by":"publisher","first-page":"755","DOI":"10.1007\/s10589-019-00087-9","volume":"73","author":"E B\u00f6rgens","year":"2019","unstructured":"B\u00f6rgens, E., Kanzow, C.: Regularized Jacobi-type ADMM-methods for a class of separable convex optimization problems in Hilbert spaces. Comput. Optim. Appl. 73(3), 755\u2013790 (2019)","journal-title":"Comput. Optim. Appl."},{"key":"1697_CR21","first-page":"144","volume-title":"Numerical Analysis, Dundee, 1977, Lecture Notes in Mathematics 630","author":"MJD Powell","year":"1978","unstructured":"Powell, M.J.D.: A fast algorithm for nonlinearly constrained optimization calculations. In: Watson, G.A. (ed.) Numerical Analysis, Dundee, 1977, Lecture Notes in Mathematics 630, pp. 144\u2013157. Springer, Berlin (1978)"},{"key":"1697_CR22","volume-title":"Fast Algorithms for Smoothth Constrained Optimization-Theoretical Analysis and Mumerical Experiments","author":"JB Jian","year":"2010","unstructured":"Jian, J.B.: Fast Algorithms for Smoothth Constrained Optimization-Theoretical Analysis and Mumerical Experiments. Science Press, Beijing (2010)"},{"key":"1697_CR23","volume-title":"Power Generation, Operation, and Control","author":"AJ Wood","year":"2014","unstructured":"Wood, A.J., Wollenberg, B.F., Shebl\u00e9, G.B.: Power Generation, Operation, and Control. Wiley, New York (2014)"},{"issue":"5","key":"1697_CR24","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1016\/j.ijepes.2009.11.002","volume":"32","author":"A Theerthamalai","year":"2010","unstructured":"Theerthamalai, A., Maheswarapu, S.: An effective non-iterative \u201c$$\\lambda $$-logic based\u201d algorithm for economic dispatch of generators with cubic fuel cost function. Int. J. Electr. Power Energy Syst. 32(5), 539\u2013542 (2010)","journal-title":"Int. J. Electr. Power Energy Syst."},{"issue":"1","key":"1697_CR25","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/s00521-016-2335-3","volume":"28","author":"I Ziane","year":"2017","unstructured":"Ziane, I., Benhamida, F., Graa, A.: Simulated annealing algorithm for combined economic and emission power dispatch using max\/max price penalty factor. Neural Comput. Appl. 28(1), 197\u2013205 (2017)","journal-title":"Neural Comput. Appl."},{"issue":"3","key":"1697_CR26","doi-asserted-by":"publisher","first-page":"1325","DOI":"10.1109\/59.260861","volume":"8","author":"D Walters","year":"1993","unstructured":"Walters, D., Sheble, G.: Genetic algorithm solution of economic dispatch with valve point loading. IEEE Trans. Power Syst. 8(3), 1325\u20131332 (1993)","journal-title":"IEEE Trans. Power Syst."},{"issue":"2","key":"1697_CR27","doi-asserted-by":"publisher","first-page":"710","DOI":"10.1109\/TPWRS.2014.2330577","volume":"30","author":"J Zhan","year":"2015","unstructured":"Zhan, J., Wu, Q.H., Guo, C., Zhou, X.: Economic dispatch with non-smooth objectives\u2013part I: local minimum analysis. IEEE Trans. Power Syst. 30(2), 710\u2013721 (2015)","journal-title":"IEEE Trans. Power Syst."},{"key":"1697_CR28","unstructured":"Wang, H., Banerjee, A.: Bregman alternating direction method of multipliers. In: Advances in Neural Information Processing Systems 27 (NIPS 2014), pp. 2816\u20132824. Curran Associates (2014)"},{"key":"1697_CR29","unstructured":"Wang, F.H., Xu, Z.B., Xu, H.K.: Convergence of Bregman alternating direction method with multipliers for nonconvex composite problems. arXiv:1410.8625 (2014)"},{"key":"1697_CR30","unstructured":"OPTI Toolbok\u2014a free MATLAB toolbox for optimization. https:\/\/www.inverseproblem.co.nz\/OPTI\/index.php\/Main\/HomePage"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-020-01697-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-020-01697-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-020-01697-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,25]],"date-time":"2021-06-25T00:33:04Z","timestamp":1624581184000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-020-01697-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,25]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,7]]}},"alternative-id":["1697"],"URL":"https:\/\/doi.org\/10.1007\/s10957-020-01697-8","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,25]]},"assertion":[{"value":"27 October 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 May 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 June 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}