{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T14:54:50Z","timestamp":1772636090244,"version":"3.50.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2011,9,13]],"date-time":"2011-09-13T00:00:00Z","timestamp":1315872000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2012,7]]},"DOI":"10.1007\/s10589-011-9429-8","type":"journal-article","created":{"date-parts":[[2011,9,12]],"date-time":"2011-09-12T13:45:52Z","timestamp":1315835152000},"page":"825-843","source":"Crossref","is-referenced-by-count":12,"title":["An efficient simultaneous method for the constrained multiple-sets split feasibility problem"],"prefix":"10.1007","volume":"52","author":[{"given":"Wenxing","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Deren","family":"Han","sequence":"additional","affiliation":[]},{"given":"Xiaoming","family":"Yuan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,9,13]]},"reference":[{"issue":"5","key":"9429_CR1","doi-asserted-by":"crossref","first-page":"3246","DOI":"10.1137\/090754297","volume":"48","author":"H. Attouch","year":"2010","unstructured":"Attouch, H., Brice\u00f1o-Arias, H.L., Combettes, P.L.: A parallel splitting method for coupled monotone inclusions. SIAM J. Control Optim. 48(5), 3246\u20133270 (2010)","journal-title":"SIAM J. Control Optim."},{"key":"9429_CR2","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/BF03007664","volume":"26","author":"J. Baillon","year":"1977","unstructured":"Baillon, J., Haddad, G.: Quelques propri\u00e9t\u00e9s des op\u00e9rateurs angel-born\u00e9s et n-cycliquement monotones. Isr. J. Math. 26, 137\u2013150 (1977)","journal-title":"Isr. J. Math."},{"key":"9429_CR3","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1137\/S0036144593251710","volume":"38","author":"H.H. Bauschke","year":"1996","unstructured":"Bauschke, H.H., Borwein, J.M.: On projection algorithms for solving convex feasibility problems. SIAM Rev. 38, 367\u2013426 (1996)","journal-title":"SIAM Rev."},{"key":"9429_CR4","volume-title":"Parallel and Distributed Computation: Numerical Methods","author":"D.P. Bertsekas","year":"1989","unstructured":"Bertsekas, D.P., Tsitsiklis, J.N.: Parallel and Distributed Computation: Numerical Methods. Prentice-Hall, Englewood Cliffs (1989)"},{"key":"9429_CR5","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1088\/0266-5611\/18\/2\/310","volume":"18","author":"C. Byrne","year":"2002","unstructured":"Byrne, C.: Iterative oblique projection onto convex sets and the split feasibility problem. Inverse Probl. 18, 441\u2013453 (2002)","journal-title":"Inverse Probl."},{"key":"9429_CR6","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1088\/0266-5611\/20\/1\/006","volume":"20","author":"C. Byrne","year":"2004","unstructured":"Byrne, C.: A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse Probl. 20, 103\u2013120 (2004)","journal-title":"Inverse Probl."},{"key":"9429_CR7","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1023\/A:1013349430987","volume":"105","author":"C. Byrne","year":"2001","unstructured":"Byrne, C., Censor, Y.: Proximity function minimization using multiple Bergman projections, with applications to split feasibility and Kullback-Leibler distance minimization. Ann. Oper. Res. 105, 77\u201398 (2001)","journal-title":"Ann. Oper. Res."},{"key":"9429_CR8","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/BF02142692","volume":"8","author":"Y. Censor","year":"1994","unstructured":"Censor, Y., Elfving, T.: A multiprojection algorithm using Bregman projections in a product space. Numer. Algorithms 8, 221\u2013239 (1994)","journal-title":"Numer. Algorithms"},{"key":"9429_CR9","volume-title":"Parallel Optimization: Theory, Algorithms and Applications","author":"Y. Censor","year":"1997","unstructured":"Censor, Y., Zenios, S.A.: Parallel Optimization: Theory, Algorithms and Applications. Oxford University Press, New York (1997)"},{"key":"9429_CR10","doi-asserted-by":"crossref","first-page":"2071","DOI":"10.1088\/0266-5611\/21\/6\/017","volume":"21","author":"Y. Censor","year":"2005","unstructured":"Censor, Y., Elfving, T., Kopf, N., Bortfeld, T.: The multiple-sets split feasibility problem and its applications for inverse problems. Inverse Probl. 21, 2071\u20132084 (2005)","journal-title":"Inverse Probl."},{"key":"9429_CR11","doi-asserted-by":"crossref","first-page":"2353","DOI":"10.1088\/0031-9155\/51\/10\/001","volume":"51","author":"Y. Censor","year":"2006","unstructured":"Censor, Y., Bortfeld, T., Martin, B., Trofimov, A.: A unified approach for inversion problems in intensity-modulated radiation therapy. Phys. Med. Biol. 51, 2353\u20132365 (2006)","journal-title":"Phys. Med. Biol."},{"key":"9429_CR12","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/S1076-5670(08)70157-5","volume":"95","author":"P.L. Combettes","year":"1996","unstructured":"Combettes, P.L.: The convex feasibility problem in image recovery. Adv. Imaging Electron Phys. 95, 155\u2013270 (1996)","journal-title":"Adv. Imaging Electron Phys."},{"key":"9429_CR13","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/978-1-4613-3632-7_7","volume-title":"Large Scale Optimization: State of the Art","author":"J. Eckstein","year":"1994","unstructured":"Eckstein, J., Fukushima, M.: Some reformulation and applications of the alternating directions method of multipliers. In: Hager, W.W., et al. (eds.) Large Scale Optimization: State of the Art, pp. 115\u2013134. Kluwer Academic, Dordrecht (1994)"},{"key":"9429_CR14","volume-title":"Finite-Dimensional Variational Inequalities and Complementarity Problems, vols.\u00a0I and\u00a0II","author":"F. Facchinei","year":"2003","unstructured":"Facchinei, F., Pang, J.S.: Finite-Dimensional Variational Inequalities and Complementarity Problems, vols.\u00a0I and\u00a0II. Springer, Berlin (2003)"},{"key":"9429_CR15","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/BF00247655","volume":"2","author":"M. Fukushima","year":"1992","unstructured":"Fukushima, M.: Application of the alternating directions method of multipliers to separable convex programming problems. Comput. Optim. Appl. 2, 93\u2013111 (1992)","journal-title":"Comput. Optim. Appl."},{"key":"9429_CR16","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/S0168-2024(08)70034-1","volume-title":"Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems","author":"D. Gabay","year":"1983","unstructured":"Gabay, D.: Applications of the method of multipliers to variational inequalities. In: Fortin, M., Glowinski, R. (eds.) Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems, pp. 299\u2013331. North-Holland, Amsterdam (1983)"},{"key":"9429_CR17","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 approximations. Comput. Math. Appl. 2, 17\u201340 (1976)","journal-title":"Comput. Math. Appl."},{"key":"9429_CR18","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970838","volume-title":"Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics","author":"R. Glowinski","year":"1989","unstructured":"Glowinski, R., Le Tallec, P.: Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics. SIAM, Philadelphia (1989)"},{"key":"9429_CR19","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/s10957-006-9060-5","volume":"132","author":"D.R. Han","year":"2007","unstructured":"Han, D.R.: Inexact operator splitting methods with self-adaptive strategy for variational inequality problems. J. Optim. Theory Appl. 132, 227\u2013243 (2007)","journal-title":"J. Optim. Theory Appl."},{"key":"9429_CR20","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s00211-008-0181-7","volume":"111","author":"D.R. Han","year":"2008","unstructured":"Han, D.R., Xu, W., Yang, H.: An operator splitting method for variational inequalities with partially unknown mappings. Numer. Math. 111, 207\u2013237 (2008)","journal-title":"Numer. Math."},{"key":"9429_CR21","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/s10589-007-9109-x","volume":"42","author":"B.S. He","year":"2009","unstructured":"He, B.S.: Parallel splitting augmented Lagrangian methods for monotone structured variational inequalities. Comput. Optim. Appl. 42, 195\u2013212 (2009)","journal-title":"Comput. Optim. Appl."},{"key":"9429_CR22","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s101070100280","volume":"92","author":"B.S. He","year":"2002","unstructured":"He, B.S., Liao, L.Z., Han, D.R., Yang, H.: A new inexact alternating direction method for monotone variational inequalities. Math. Program. 92, 103\u2013118 (2002)","journal-title":"Math. Program."},{"key":"9429_CR23","first-page":"693","volume":"24","author":"B.S. He","year":"2006","unstructured":"He, B.S., Liao, L.Z., Qian, M.J.: Alternating projection based prediction-correction method for structured variational inequalities. J. Comput. Math. 24, 693\u2013710 (2006)","journal-title":"J. Comput. Math."},{"key":"9429_CR24","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/s10957-009-9619-z","volume":"145","author":"Z.K. Jiang","year":"2010","unstructured":"Jiang, Z.K., Yuan, X.M.: New parallel descent-like method for solving a class of variational inequalities. J. Optim. Theory Appl. 145, 311\u2013323 (2010)","journal-title":"J. Optim. Theory Appl."},{"key":"9429_CR25","first-page":"29","volume":"83","author":"S. Kontogiorgis","year":"1998","unstructured":"Kontogiorgis, S., Meyer, R.R.: A variable-penalty alternating directions method for convex optimization. Math. Program. 83, 29\u201353 (1998)","journal-title":"Math. Program."},{"key":"9429_CR26","doi-asserted-by":"crossref","first-page":"1655","DOI":"10.1088\/0266-5611\/21\/5\/009","volume":"21","author":"B. Qu","year":"2005","unstructured":"Qu, B., Xiu, N.H.: A note on the CQ algorithm for the split feasibility problem. Inverse Probl. 21, 1655\u20131665 (2005)","journal-title":"Inverse Probl."},{"key":"9429_CR27","doi-asserted-by":"crossref","first-page":"1218","DOI":"10.1016\/j.laa.2007.03.002","volume":"428","author":"B. Qu","year":"2008","unstructured":"Qu, B., Xiu, N.H.: A new halfspace-relaxation projection method for the split feasibility problem. Linear Algebra Appl. 428, 1218\u20131229 (2008)","journal-title":"Linear Algebra Appl."},{"key":"9429_CR28","first-page":"464","volume-title":"Lecture Notes in Comput. Sci.","author":"S. Setzer","year":"2009","unstructured":"Setzer, S.: Split Bregman algorithm, Douglas-Rachford splitting and frame shrinkage. In: Lecture Notes in Comput. Sci., vol. 5567, pp.\u00a0464\u2013476 (2009)"},{"key":"9429_CR29","doi-asserted-by":"crossref","first-page":"2021","DOI":"10.1088\/0266-5611\/22\/6\/007","volume":"22","author":"H.K. Xu","year":"2006","unstructured":"Xu, H.K.: A variable Krasnosel\u2019ski\u0131\u030c-Mann algorithm and the multiple-set split feasibility problem. Inverse Probl. 22, 2021\u20132034 (2006)","journal-title":"Inverse Probl."},{"key":"9429_CR30","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1088\/0266-5611\/20\/4\/014","volume":"20","author":"Q.Z. Yang","year":"2004","unstructured":"Yang, Q.Z.: The relaxed CQ algorithm solving the split feasibility problem. Inverse Probl. 20, 1261\u20131266 (2004)","journal-title":"Inverse Probl."},{"key":"9429_CR31","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1080\/10556780600552693","volume":"22","author":"C.H. Ye","year":"2007","unstructured":"Ye, C.H., Yuan, X.M.: A descent method for structured monotone variational inequalities. Optim. Methods Softw. 22, 329\u2013338 (2007)","journal-title":"Optim. Methods Softw."},{"key":"9429_CR32","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/s10589-009-9293-y","volume":"49","author":"X.M. Yuan","year":"2011","unstructured":"Yuan, X.M.: An improved proximal alternating direction method for structured variational inequalities. Comput. Optim. Appl. 49, 17\u201329 (2011)","journal-title":"Comput. Optim. Appl."},{"key":"9429_CR33","doi-asserted-by":"crossref","unstructured":"Zhang, W.X., Han, D.R., Li, Z.B.: A self-adaptive projection method for solving the multiple-sets split feasibility problem. Inverse Probl. 25. doi: 10.1088\/0266-5611\/25\/11\/115001","DOI":"10.1088\/0266-5611\/25\/11\/115001"},{"key":"9429_CR34","doi-asserted-by":"crossref","first-page":"1791","DOI":"10.1088\/0266-5611\/21\/5\/017","volume":"21","author":"J.L. Zhao","year":"2005","unstructured":"Zhao, J.L., Yang, Q.Z.: Several solution methods for the split feasibility problem. Inverse Probl. 21, 1791\u20131799 (2005)","journal-title":"Inverse Probl."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-011-9429-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-011-9429-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-011-9429-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T07:36:41Z","timestamp":1559288201000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-011-9429-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,9,13]]},"references-count":34,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,7]]}},"alternative-id":["9429"],"URL":"https:\/\/doi.org\/10.1007\/s10589-011-9429-8","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,9,13]]}}}