{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T09:13:01Z","timestamp":1779268381331,"version":"3.51.4"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2018,2,23]],"date-time":"2018-02-23T00:00:00Z","timestamp":1519344000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001459","name":"Ministry of Education - Singapore","doi-asserted-by":"publisher","award":["R-146-000-194-112"],"award-info":[{"award-number":["R-146-000-194-112"]}],"id":[{"id":"10.13039\/501100001459","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001459","name":"Ministry of Education - Singapore","doi-asserted-by":"publisher","award":["R-146-000-194-112"],"award-info":[{"award-number":["R-146-000-194-112"]}],"id":[{"id":"10.13039\/501100001459","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2019,5]]},"DOI":"10.1007\/s10107-018-1247-7","type":"journal-article","created":{"date-parts":[[2018,2,23]],"date-time":"2018-02-23T06:12:31Z","timestamp":1519366351000},"page":"395-418","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["A block symmetric Gauss\u2013Seidel decomposition theorem for convex composite quadratic programming and its applications"],"prefix":"10.1007","volume":"175","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9275-1965","authenticated-orcid":false,"given":"Xudong","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Defeng","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kim-Chuan","family":"Toh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,2,23]]},"reference":[{"key":"1247_CR1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511624100","volume-title":"Iterative Solution Methods","author":"O Axelsson","year":"1994","unstructured":"Axelsson, O.: Iterative Solution Methods. Cambridge University Press, Cambridge (1994)"},{"key":"1247_CR2","doi-asserted-by":"publisher","first-page":"1298","DOI":"10.1137\/15M1048008","volume":"9","author":"MR Bai","year":"2016","unstructured":"Bai, M.R., Zhang, X.J., Ni, G.Y., Cui, C.F.: An adaptive correction approach for tensor completion. SIAM J. Imaging Sci. 9, 1298\u20131323 (2016)","journal-title":"SIAM J. Imaging Sci."},{"key":"1247_CR3","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/j.dsp.2016.05.006","volume":"55","author":"S Bai","year":"2016","unstructured":"Bai, S., Qi, H.-D.: Tackling the flip ambiguity in wireless sensor network localization and beyond. Digital Signal Process. 55, 85\u201397 (2016)","journal-title":"Digital Signal Process."},{"key":"1247_CR4","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1007\/BF01462238","volume":"52","author":"RE Bank","year":"1988","unstructured":"Bank, R.E., Dupont, T.F., Yserentant, H.: The hierarchical basis multigrid method. Numerische Mathematik 52, 427\u2013458 (1988)","journal-title":"Numerische Mathematik"},{"key":"1247_CR5","doi-asserted-by":"publisher","first-page":"2037","DOI":"10.1137\/120887679","volume":"23","author":"A Beck","year":"2013","unstructured":"Beck, A., Tetruashvili, L.: On the convergence of block coordinate descent type methods. SIAM J. Optim. 23, 2037\u20132060 (2013)","journal-title":"SIAM J. Optim."},{"key":"1247_CR6","volume-title":"Nonlinear Programming","author":"DP Bertsekas","year":"1995","unstructured":"Bertsekas, D.P.: Nonlinear Programming, 2nd edn. Athena Scientific, Belmont (1995)","edition":"2"},{"key":"1247_CR7","unstructured":"Bi, S., Pan, S., Sun, D. F.: Multi-stage convex relaxation approach to noisy structured low-rank matrix recovery, \n                    arXiv:1703.03898\n                    \n                   (2017)"},{"key":"1247_CR8","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/s10107-016-1090-7","volume":"164","author":"C Ding","year":"2017","unstructured":"Ding, C., Qi, H.-D.: Convex optimization learning of faithful Euclidean distance representations in nonlinear dimensionality reduction. Math. Program. 164, 341\u2013381 (2017)","journal-title":"Math. Program."},{"key":"1247_CR9","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/s10589-016-9858-5","volume":"66","author":"C Ding","year":"2017","unstructured":"Ding, C., Qi, H.-D.: Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation. Comput. Optim. Appl. 66, 187\u2013218 (2017)","journal-title":"Comput. Optim. Appl."},{"key":"1247_CR10","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1007\/s10107-016-1007-5","volume":"161","author":"L Chen","year":"2017","unstructured":"Chen, L., Sun, D.F., Toh, K.-C.: An efficient inexact symmetric Gauss\u2013Seidel based majorized ADMM for high-dimensional convex composite conic programming. Math. Program. 161, 237\u2013270 (2017)","journal-title":"Math. Program."},{"key":"1247_CR11","doi-asserted-by":"publisher","first-page":"1997","DOI":"10.1137\/130949993","volume":"25","author":"O Fercoq","year":"2015","unstructured":"Fercoq, O., Richt\u00e1rik, P.: Accelerated, parallel, and proximal coordinate descent. SIAM J. Optim. 25, 1997\u20132023 (2015)","journal-title":"SIAM J. Optim."},{"key":"1247_CR12","doi-asserted-by":"publisher","first-page":"739","DOI":"10.1137\/16M1085905","volume":"28","author":"O Fercoq","year":"2016","unstructured":"Fercoq, O., Richt\u00e1rik, P.: Optimization in high dimensions via accelerated, parallel, and proximal coordinate descent. SIAM Rev. 28, 739\u2013771 (2016)","journal-title":"SIAM Rev."},{"key":"1247_CR13","unstructured":"Ferreira, J. B., Khoo, Y., Singer, A.: Semidefinite programming approach for the quadratic assignment problem with a sparse graph, \n                    arXiv:1703.09339\n                    \n                   (2017)"},{"key":"1247_CR14","unstructured":"Freund, R. W.: Preconditioning of symmetric, but highly indefinite linear systems, In: Proceedings of 15th imacs world congress on scientific computation modelling and applied mathematics, Berlin, Germany, pp. 551\u2013556 (1997)"},{"key":"1247_CR15","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970937","volume-title":"Iterative Methods for Solving Linear Systems","author":"A Greenbaum","year":"1997","unstructured":"Greenbaum, A.: Iterative Methods for Solving Linear Systems. SIAM, Philadelphia (1997)"},{"key":"1247_CR16","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/S0167-6377(99)00074-7","volume":"26","author":"L Grippo","year":"2000","unstructured":"Grippo, L., Sciandrone, M.: On the convergence of the block nonlinear Gauss\u2013Seidel method under convex constraints. Oper. Res. Lett. 26, 127\u2013136 (2000)","journal-title":"Oper. Res. Lett."},{"key":"1247_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4288-8","volume-title":"Iterative Solutions of Large Sparse Systems of Equations","author":"W Hackbusch","year":"1994","unstructured":"Hackbusch, W.: Iterative Solutions of Large Sparse Systems of Equations. Springer, New York (1994)"},{"key":"1247_CR18","doi-asserted-by":"publisher","unstructured":"Han, D., Sun, D. F., Zhang, L.: Linear rate convergence of the alternating direction method of multipliers for convex composite programming, Math. Oper. Res. (2017). \n                    https:\/\/doi.org\/10.1287\/moor.2017.0875","DOI":"10.1287\/moor.2017.0875"},{"key":"1247_CR19","doi-asserted-by":"publisher","first-page":"1042","DOI":"10.1137\/110847081","volume":"22","author":"KF Jiang","year":"2012","unstructured":"Jiang, K.F., Sun, D.F., Toh, K.-C.: An inexact accelerated proximal gradient method for large scale linearly constrained convex SDP. SIAM J. Optim. 22, 1042\u20131064 (2012)","journal-title":"SIAM J. Optim."},{"key":"1247_CR20","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1137\/140965028","volume":"53","author":"B Kristian","year":"2015","unstructured":"Kristian, B., Sun, H.P.: Preconditioned Douglas\u2013Rachford splitting methods for convex-concave saddle-point problems. SIAM J. Numer. Anal. 53, 421\u2013444 (2015)","journal-title":"SIAM J. Numer. Anal."},{"key":"1247_CR21","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1007\/s10851-015-0564-1","volume":"52","author":"B Kristian","year":"2015","unstructured":"Kristian, B., Sun, H.P.: Preconditioned Douglas\u2013Rachford algorithms for TV-and TGV-regularized variational imaging problems. J. Math. Imaging Vis. 52, 317\u2013344 (2015)","journal-title":"J. Math. Imaging Vis."},{"key":"1247_CR22","unstructured":"Lam, X.Y., Marron, J.S., Sun, D.F., Toh, K.-C.: Fast algorithms for large scale extended distance weighted discrimination, \n                    arXiv:1604.05473\n                    \n                  . Journal Computational and Graphical Statistics (2016, to appear)"},{"key":"1247_CR23","unstructured":"Li, X.D., Sun, D.F., Toh, K.-C.: QSDPNAL: a two-phase augmented Lagrangian method for convex quadratic semidefinite programming, \n                    arXiv:1512.08872\n                    \n                   (2015)"},{"key":"1247_CR24","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/s10107-014-0850-5","volume":"155","author":"XD Li","year":"2016","unstructured":"Li, X.D., Sun, D.F., 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."},{"key":"1247_CR25","unstructured":"Li, X.D.: A two-phase augmented Lagrangian method for convex composite quadratic programming, PhD thesis, Department of Mathematics, National University of Singapore (2015)"},{"key":"1247_CR26","doi-asserted-by":"publisher","first-page":"408","DOI":"10.1137\/0330025","volume":"30","author":"Z-Q Luo","year":"1992","unstructured":"Luo, Z.-Q., Tseng, P.: On the linear convergence of descent methods for convex essentially smooth minimization. SIAM J. Control Optim. 30, 408\u2013425 (1992)","journal-title":"SIAM J. Control Optim."},{"key":"1247_CR27","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1007\/BF02096261","volume":"46","author":"Z-Q Luo","year":"1993","unstructured":"Luo, Z.-Q., Tseng, P.: Error bounds and convergence analysis of feasible descent methods: a general approach. Ann. Oper. Res. 46, 157\u2013178 (1993)","journal-title":"Ann. Oper. Res."},{"key":"1247_CR28","first-page":"341","volume":"22","author":"Y Nesterov","year":"2012","unstructured":"Nesterov, Y.: Efficiency of coordinate descent methods on huge-scale optimization problems, SIAM. J. Optim. 22, 341\u2013362 (2012)","journal-title":"J. Optim."},{"key":"1247_CR29","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1137\/16M1060182","volume":"27","author":"Y Nesterov","year":"2017","unstructured":"Nesterov, Y., Stich, S.U.: Efficiency of the accelerated coordinate descent method on structured optimization problems. SIAM J. Optim. 27, 110\u2013123 (2017)","journal-title":"SIAM J. Optim."},{"key":"1247_CR30","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719468","volume-title":"Iterative Solution of Nonlinear Equations in Several Variables","author":"JM Ortega","year":"2000","unstructured":"Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. SIAM, Philadelphia (2000)"},{"key":"1247_CR31","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10107-012-0614-z","volume":"144","author":"P Richt\u00e1rik","year":"2014","unstructured":"Richt\u00e1rik, P., Tak\u00e1\u010d, M.: Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function. Math. Program. 144, 1\u201338 (2014)","journal-title":"Math. Program."},{"key":"1247_CR32","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 (1970)"},{"key":"1247_CR33","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1007\/BFb0120929","volume":"14","author":"SM Robinson","year":"1981","unstructured":"Robinson, S.M.: Some continuity properties of polyhedral multifunctions. Math. Program. Study 14, 206\u2013214 (1981)","journal-title":"Math. Program. Study"},{"key":"1247_CR34","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718003","volume-title":"Iterative Methods for Sparse Linear Systems","author":"Y Sadd","year":"2003","unstructured":"Sadd, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia (2003)"},{"key":"1247_CR35","unstructured":"Schmidt, M., Le Roux, N., Bach, F.: Convergence rates of inexact proximal-gradient methods for convex optimization. Advances in neural information processing systems (NIPS), pp. 1458\u20131466 (2011)"},{"key":"1247_CR36","doi-asserted-by":"publisher","first-page":"1072","DOI":"10.1137\/15M1021799","volume":"26","author":"DF Sun","year":"2016","unstructured":"Sun, D.F., Toh, K.-C., Yang, L.Q.: An efficient inexact ABCD method for least squares semidefinite programming. SIAM J. Optim. 26, 1072\u20131100 (2016)","journal-title":"SIAM J. Optim."},{"key":"1247_CR37","doi-asserted-by":"publisher","first-page":"882","DOI":"10.1137\/140964357","volume":"25","author":"DF Sun","year":"2015","unstructured":"Sun, D.F., Toh, K.-C., Yang, L.Q.: A convergent 3-block semi-proximal alternating direction method of multipliers for conic programming with 4-type constraints. SIAM J. Optim. 25, 882\u2013915 (2015)","journal-title":"SIAM J. Optim."},{"key":"1247_CR38","unstructured":"Sun, J.: On monotropic piecewise qudratic programming, PhD Thesis, Department of Mathematics, University of Washington, Seattle (1986)"},{"key":"1247_CR39","doi-asserted-by":"publisher","first-page":"144","DOI":"10.1007\/s10957-016-0867-4","volume":"170","author":"R Tappenden","year":"2016","unstructured":"Tappenden, R., Richt\u00e1rik, R., Gondzio, J.: Inexact coordinate descent: complexity and preconditioning. J. Optim. Theory Appl. 170, 144\u2013176 (2016)","journal-title":"J. Optim. Theory Appl."},{"key":"1247_CR40","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1023\/A:1017501703105","volume":"109","author":"P Tseng","year":"2001","unstructured":"Tseng, P.: Convergence of a block coordinate descent method for nondifferentiable minimization. J. Optim. Theory Appl. 109, 475\u2013494 (2001)","journal-title":"J. Optim. Theory Appl."},{"key":"1247_CR41","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1007\/s10107-010-0394-2","volume":"125","author":"P Tseng","year":"2010","unstructured":"Tseng, P., Yun, S.: A coordinate gradient descent method for nonsmooth separable minimization. Math. Program. 125, 387\u2013423 (2010)","journal-title":"Math. Program."},{"key":"1247_CR42","volume-title":"Matrix Iterative Analysis","author":"RS Varga","year":"2009","unstructured":"Varga, R.S.: Matrix Iterative Analysis. Springer, Berlin (2009)"},{"key":"1247_CR43","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1137\/16M1055323","volume":"27","author":"B Wen","year":"2017","unstructured":"Wen, B., Chen, X., Pong, T.K.: Linear convergence of proximal gradient algorithm with extrapolation for a class of nonconvex nonsmooth minimization problems. SIAM J. Optim. 27, 124\u2013145 (2017)","journal-title":"SIAM J. Optim."},{"key":"1247_CR44","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1007\/s10107-014-0800-2","volume":"152","author":"L Xiao","year":"2015","unstructured":"Xiao, L., Lu, Z.: On the complexity analysis of randomized block-coordinate descent methods. Math. Program. 152, 615\u2013642 (2015)","journal-title":"Math. Program."},{"key":"1247_CR45","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1016\/S0001-8708(77)80029-7","volume":"23","author":"DM Young","year":"1997","unstructured":"Young, D.M.: On the accelerated SSOR method for solving large linear systems. Adv. Math. 23, 215\u2013217 (1997)","journal-title":"Adv. Math."},{"key":"1247_CR46","unstructured":"Zhang, X., Xu, C., Zhang, Y., Zhu, T., Cheng, L.: Multivariate regression with grossly corrupted observations: a robust approach and its applications, \n                    arXiv:1701.02892\n                    \n                   (2017)"},{"key":"1247_CR47","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1007\/s10107-016-1100-9","volume":"165","author":"ZR Zhou","year":"2017","unstructured":"Zhou, Z.R., So, A.M.-C.: A unified approach to error bounds for structured convex optimization problems. Math. Program. 165, 689\u2013728 (2017)","journal-title":"Math. Program."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-018-1247-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-018-1247-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-018-1247-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,24]],"date-time":"2019-04-24T08:19:08Z","timestamp":1556093948000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-018-1247-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,23]]},"references-count":47,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2019,5]]}},"alternative-id":["1247"],"URL":"https:\/\/doi.org\/10.1007\/s10107-018-1247-7","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,2,23]]},"assertion":[{"value":"24 May 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 February 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 February 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}