{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:46:49Z","timestamp":1740124009847,"version":"3.37.3"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,11,27]],"date-time":"2022-11-27T00:00:00Z","timestamp":1669507200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,11,27]],"date-time":"2022-11-27T00:00:00Z","timestamp":1669507200000},"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":["11971230","12201295"],"award-info":[{"award-number":["11971230","12201295"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20210267","12071234"],"award-info":[{"award-number":["BK20210267","12071234"]}],"id":[{"id":"10.13039\/501100004608","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":[[2023,1]]},"DOI":"10.1007\/s10957-022-02133-9","type":"journal-article","created":{"date-parts":[[2022,11,27]],"date-time":"2022-11-27T11:28:29Z","timestamp":1669548509000},"page":"362-389","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Customized Alternating Direction Methods of Multipliers for Generalized Multi-facility Weber Problem"],"prefix":"10.1007","volume":"196","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8641-9202","authenticated-orcid":false,"given":"Jianlin","family":"Jiang","sequence":"first","affiliation":[]},{"given":"Liyun","family":"Ling","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2040-3363","authenticated-orcid":false,"given":"Yan","family":"Gu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8777-4660","authenticated-orcid":false,"given":"Su","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Yibing","family":"Lv","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,11,27]]},"reference":[{"key":"2133_CR1","doi-asserted-by":"crossref","unstructured":"Blum, E., Oettli, W.: Mathematische Optimierung. Econometrics and Operations Research XX. Springer-Verlag, Berlin (1975)","DOI":"10.1007\/978-3-642-66156-3"},{"issue":"1","key":"2133_CR2","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":"3","key":"2133_CR3","doi-asserted-by":"publisher","first-page":"807","DOI":"10.1137\/100807247","volume":"4","author":"R Chan","year":"2011","unstructured":"Chan, R., Yang, J., Yuan, X.: Alternating direction method for image inpainting in wavelet domain. SIAM J. Imaging Sci. 4(3), 807\u2013826 (2011)","journal-title":"SIAM J. Imaging Sci."},{"key":"2133_CR4","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/s10107-014-0826-5","volume":"155","author":"C Chen","year":"2016","unstructured":"Chen, C., He, B., Ye, Y., Yuan, X.: The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent. Math. Program. 155, 57\u201379 (2016)","journal-title":"Math. Program."},{"key":"2133_CR5","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1090\/mcom\/3104","volume":"86","author":"Y Dai","year":"2017","unstructured":"Dai, Y., Han, D., Yuan, X., Zhang, W.: A sequential updating scheme of the Lagrange multiplier for separable convex programming. Math. Comput. 86, 315\u2013343 (2017)","journal-title":"Math. Comput."},{"key":"2133_CR6","doi-asserted-by":"crossref","unstructured":"Daneshzand, F., Shoeleh, R.: Multifacility location problem. In: Farahani, R.Z., Hekmatfar, M. (eds.) Facility Location: Concepts, Models, Algorithms and Case Studies, pp. 69\u201392. Springer, Berlin (2009)","DOI":"10.1007\/978-3-7908-2151-2_4"},{"issue":"3","key":"2133_CR7","doi-asserted-by":"publisher","first-page":"889","DOI":"10.1007\/s10915-015-0048-x","volume":"66","author":"W Deng","year":"2016","unstructured":"Deng, W., Yin, W.: On the global and linear convergence of the generalized alternating direction method of multipliers. J. Sci. Comput. 66(3), 889\u2013916 (2016)","journal-title":"J. Sci. Comput."},{"key":"2133_CR8","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, 293\u2013318 (1992)","journal-title":"Math. Program."},{"key":"2133_CR9","unstructured":"Esser, E.: Applications of Lagrangian-based alternating direction methods and connections to split Bregman. UCLA CAM Report. 9\u201331 (2009)"},{"issue":"1","key":"2133_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/05695557308974875","volume":"5","author":"JW Eyster","year":"1973","unstructured":"Eyster, J.W., White, J.A., Wierwille, W.W.: On solving multifacility location problems using a hyperboloid approximation procedure. AIIE. Trans. 5(1), 1\u20136 (1973)","journal-title":"AIIE. Trans."},{"key":"2133_CR11","volume-title":"Finite-dimensional Variational Inequalities and Complementarity Problems","author":"F Facchinei","year":"2003","unstructured":"Facchinei, F., Pang, J.: Finite-dimensional Variational Inequalities and Complementarity Problems. Springer, New York (2003)"},{"issue":"1","key":"2133_CR12","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 approximations. Comput. Math. Appl. 2(1), 17\u201340 (1976)","journal-title":"Comput. Math. Appl."},{"key":"2133_CR13","doi-asserted-by":"crossref","unstructured":"Glowinski, R., Marrocco, 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. Rev. Fran\u00e7aise Automat. Informat. Recherche Op\u00e9rationnelle S\u00e9r. Rouge Anal. Num\u00e9r. 9, 41\u201376 (1975)","DOI":"10.1051\/m2an\/197509R200411"},{"key":"2133_CR14","first-page":"54","volume":"14","author":"B He","year":"1996","unstructured":"He, B.: A modified projection and contraction method for a class of linear complementarity problems. J. Comput. Math. 14, 54\u201363 (1996)","journal-title":"J. Comput. Math."},{"issue":"2","key":"2133_CR15","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1137\/110822347","volume":"22","author":"B He","year":"2012","unstructured":"He, B., Tao, M., Yuan, X.: Alternating direction method with Gaussian back substitution for separable convex programming. SIAM J. Optim. 22(2), 313\u2013340 (2012)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"2133_CR16","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1023\/A:1004603514434","volume":"106","author":"B He","year":"2000","unstructured":"He, B., Yang, H., Wang, S.: Alternating direction method with self-adaptive penalty parameters for monotone variational inequalities. J. Optim. Theory Appl. 106(2), 337\u2013356 (2000)","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"2133_CR17","doi-asserted-by":"publisher","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":"2133_CR18","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1007\/s10589-013-9564-5","volume":"56","author":"B He","year":"2013","unstructured":"He, B., Yuan, X., Zhang, W.: A customized proximal point algorithm for convex minimization with linear constraints. Comput. Optim. Appl. 56(3), 559\u2013572 (2013)","journal-title":"Comput. Optim. Appl."},{"key":"2133_CR19","doi-asserted-by":"publisher","first-page":"793","DOI":"10.1007\/s10898-019-00796-9","volume":"76","author":"J Jiang","year":"2020","unstructured":"Jiang, J., Zhang, S., Lv, Y., Du, X., Yan, Z.: An ADMM-based location-allocation algorithm for nonconvex constrained multi-source Weber problem under gauge. J. Global Optim. 76, 793\u2013818 (2020)","journal-title":"J. Global Optim."},{"issue":"3","key":"2133_CR20","doi-asserted-by":"publisher","first-page":"1085","DOI":"10.3934\/jimo.2017091","volume":"14","author":"J Jiang","year":"2018","unstructured":"Jiang, J., Zhang, S., Zhang, S., Wen, J.: A variational inequality approach for constrained multifacility Weber problem under gauge. J. Ind. Manag. Optim. 14(3), 1085\u20131104 (2018)","journal-title":"J. Ind. Manag. Optim."},{"issue":"2","key":"2133_CR21","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."},{"key":"2133_CR22","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, 333\u2013373 (2016)","journal-title":"Math. Program."},{"issue":"2","key":"2133_CR23","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1287\/mnsc.25.2.130","volume":"25","author":"RF Love","year":"1979","unstructured":"Love, R.F., Morris, J.G.: Mathematical models of road travel distances. Manag. Sci. 25(2), 130\u2013139 (1979)","journal-title":"Manag. Sci."},{"issue":"2","key":"2133_CR24","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1287\/opre.6.2.232","volume":"6","author":"W Miehle","year":"1958","unstructured":"Miehle, W.: Link-length minimization in networks. Oper. Res. 6(2), 232\u2013243 (1958)","journal-title":"Oper. Res."},{"key":"2133_CR25","unstructured":"Minkowski, H.: Theorie der Konvexen K\u00f6rper. Gesammelte Abhandlungen. Teubner, Berlin (1911)"},{"issue":"1","key":"2133_CR26","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1137\/S1052623403425629","volume":"15","author":"A Nemirovski","year":"2004","unstructured":"Nemirovski, A.: Prox-method with rate of convergence $$O(1\/t)$$ for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems. SIAM J. Optim. 15(1), 229\u2013251 (2004)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"2133_CR27","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1111\/j.1467-9787.1977.tb00511.x","volume":"17","author":"LM Ostresh","year":"1977","unstructured":"Ostresh, L.M.: The multifacility location problem: applications and descent theorems. J. Regional Sci. 17(3), 409\u2013419 (1977)","journal-title":"J. Regional Sci."},{"issue":"11","key":"2133_CR28","doi-asserted-by":"publisher","first-page":"2233","DOI":"10.1109\/TPAMI.2011.282","volume":"34","author":"Y Peng","year":"2012","unstructured":"Peng, Y., Ganesh, A., Wright, J., Xu, W., Ma, Y.: RASL: Robust alignment by sparse and low-rank decomposition for linearly correlated images. IEEE Trans. Pattern Anal. Mach. Intell. 34(11), 2233\u20132246 (2012)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"2133_CR29","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1007\/978-1-4419-7572-0_16","volume-title":"Foundations of Location Analysis","author":"F Plastria","year":"2011","unstructured":"Plastria, F.: The Weiszfeld algorithm: proof, amendments, and extensions. In: Eiselt, H.A., Marianov, V. (eds.) Foundations of Location Analysis, vol. 155, pp. 357\u2013389. Springer, New York (2011)"},{"issue":"1","key":"2133_CR30","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1287\/opre.40.1.188","volume":"40","author":"J Rosen","year":"1992","unstructured":"Rosen, J., Xue, G.: On the convergence of Miehle\u2019s algorithm for the Euclidean multifacility location problem. Oper. Res. 40(1), 188\u2013191 (1992)","journal-title":"Oper. Res."},{"issue":"6","key":"2133_CR31","doi-asserted-by":"publisher","first-page":"1164","DOI":"10.1287\/opre.41.6.1164","volume":"41","author":"J Rosen","year":"1993","unstructured":"Rosen, J., Xue, G.: On the convergence of a hyperboloid approximation procedure for the perturbed Euclidean multifacility location problem. Oper. Res. 41(6), 1164\u20131171 (1993)","journal-title":"Oper. Res."},{"issue":"3","key":"2133_CR32","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/j.jvcir.2009.10.006","volume":"21","author":"S Setzer","year":"2010","unstructured":"Setzer, S., Steidl, G., Teuber, T.: Deblurring Poissonian images by split Bregman techniques. J. Vis. Commun. Image R. 21(3), 193\u2013199 (2010)","journal-title":"J. Vis. Commun. Image R."},{"issue":"1","key":"2133_CR33","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."},{"key":"2133_CR34","first-page":"355","volume":"43","author":"E Weiszfeld","year":"1937","unstructured":"Weiszfeld, E.: Sur le point pour lequel la somme des distances de $$n$$ points donn\u00e9s est minimum. Tohoku Math. J. 43, 355\u2013386 (1937)","journal-title":"Tohoku Math. J."},{"issue":"1","key":"2133_CR35","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 $$l_1$$-problems in compressive sensing. SIAM J. Sci. Comput. 33(1), 250\u2013278 (2011)","journal-title":"SIAM 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\/s10957-022-02133-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-022-02133-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-022-02133-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T16:39:31Z","timestamp":1673282371000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-022-02133-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,27]]},"references-count":35,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,1]]}},"alternative-id":["2133"],"URL":"https:\/\/doi.org\/10.1007\/s10957-022-02133-9","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"type":"print","value":"0022-3239"},{"type":"electronic","value":"1573-2878"}],"subject":[],"published":{"date-parts":[[2022,11,27]]},"assertion":[{"value":"16 April 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 November 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 November 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}