{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T16:02:12Z","timestamp":1779897732266,"version":"3.53.1"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2010,9,28]],"date-time":"2010-09-28T00:00:00Z","timestamp":1285632000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Prog. Comp."],"published-print":{"date-parts":[[2010,12]]},"DOI":"10.1007\/s12532-010-0017-1","type":"journal-article","created":{"date-parts":[[2010,9,27]],"date-time":"2010-09-27T05:21:23Z","timestamp":1285564883000},"page":"203-230","source":"Crossref","is-referenced-by-count":264,"title":["Alternating direction augmented Lagrangian methods for semidefinite programming"],"prefix":"10.1007","volume":"2","author":[{"given":"Zaiwen","family":"Wen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Donald","family":"Goldfarb","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wotao","family":"Yin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2010,9,28]]},"reference":[{"key":"17_CR1","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, Upper Saddle River (1989)"},{"key":"17_CR2","unstructured":"Burer, S.: Optimizing a polyhedral-semidefinite relaxation of completely positive programs. Tech. rep, Department of Management Sciences, University of Iowa (2008)"},{"key":"17_CR3","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/s10107-002-0352-8","volume":"95","author":"S. Burer","year":"2003","unstructured":"Burer S., Monteiro R.D.C.: A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization. Math. Program. 95, 329\u2013357 (2003)","journal-title":"Math. Program."},{"key":"17_CR4","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/s10107-004-0564-1","volume":"103","author":"S. Burer","year":"2005","unstructured":"Burer S., Monteiro R.D.C.: Local minima and convergence in low-rank semidefinite programming. Math. Program. 103, 427\u2013444 (2005)","journal-title":"Math. Program."},{"key":"17_CR5","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1007\/s10107-002-0353-7","volume":"95","author":"S. Burer","year":"2003","unstructured":"Burer S., Monteiro R.D.C., Zhang Y.: A computational study of a gradient-based log-barrier algorithm for a class of large-scale SDPs. Math. Program. 95, 359\u2013379 (2003)","journal-title":"Math. Program."},{"key":"17_CR6","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1137\/040609574","volume":"16","author":"S. Burer","year":"2006","unstructured":"Burer S., Vandenbussche D.: Solving lift-and-project relaxations of binary integer programs. SIAM J. Optim. 16, 726\u2013750 (2006)","journal-title":"SIAM J. Optim."},{"key":"17_CR7","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/BF01582566","volume":"64","author":"G. Chen","year":"1994","unstructured":"Chen G., Teboulle M.: A proximal-based decomposition method for convex minimization problems. Math. Program 64, 81\u2013101 (1994)","journal-title":"Math. Program"},{"key":"17_CR8","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"E.D. 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":"17_CR9","unstructured":"Eckstein, J., Bertsekas, D.P.: An alternating direction method for linear programming. LIDS-P, Cambridge, MA, Laboratory for Information and Decision Systems, Massachusetts Institute of Technology (1967)"},{"key":"17_CR10","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/BF01581204","volume":"55","author":"J. Eckstein","year":"1992","unstructured":"Eckstein J., Bertsekas D.P.: On the Douglas\u2013Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 55, 293\u2013318 (1992)","journal-title":"Math. Program."},{"key":"17_CR11","unstructured":"Fortin, M., Glowinski, R.: Augmented Lagrangian methods. In: Studies in Mathematics and its Applications, vol.15. North-Holland Publishing Co., Amsterdam (1983) [Applications to the numerical solution of boundary value problems, Translated from the French by Hunt, B.D., Spicer, C.]"},{"key":"17_CR12","doi-asserted-by":"crossref","unstructured":"Glowinski, R., Le Tallec, P.: Augmented Lagrangian and operator-splitting methods in nonlinear mechanics. In: SIAM Studies in Applied Mathematics, vol. 9. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1989)","DOI":"10.1137\/1.9781611970838"},{"key":"17_CR13","unstructured":"Goldfarb, D., Ma, S.: Fast alternating linearization methods for minimizing the sum of two convex functions. Tech. rep. IEOR, Columbia University (2009)"},{"key":"17_CR14","unstructured":"Goldfarb, D., Ma, S.: Fast multiple splitting algorithms for convex optimization. Tech. rep. IEOR, Columbia University (2009)"},{"key":"17_CR15","doi-asserted-by":"crossref","first-page":"1107","DOI":"10.1137\/070698920","volume":"19","author":"E.T. Hale","year":"2008","unstructured":"Hale E.T., Yin W., Zhang Y.: Fixed-point continuation for l 1-minimization: methodology and convergence. SIAM J. Optim. 19, 1107\u20131130 (2008)","journal-title":"SIAM J. Optim."},{"key":"17_CR16","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s101070100280","volume":"92","author":"B. He","year":"2002","unstructured":"He B., Liao L.-Z., Han D., Yang H.: A new inexact alternating directions method for monotone variational inequalities. Math. Program. 92, 103\u2013118 (2002)","journal-title":"Math. Program."},{"key":"17_CR17","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1023\/A:1004603514434","volume":"106","author":"B.S. He","year":"2000","unstructured":"He B.S., Yang H., Wang S.L.: Alternating direction method with self-adaptive penalty parameters for monotone variational inequalities. J. Optim. Theory Appl. 106, 337\u2013356 (2000)","journal-title":"J. Optim. Theory Appl."},{"key":"17_CR18","doi-asserted-by":"crossref","unstructured":"Hiriart-Urruty, J.-B., Lemar\u00e9chal, C.: Convex analysis and minimization algorithms. I. Fundamentals. In: Grundlehren der Mathematischen Wissenschaften. Fundamental Principles of Mathematical Sciences, vol. 305. Springer, Berlin (1993)","DOI":"10.1007\/978-3-662-02796-7"},{"key":"17_CR19","unstructured":"Johnson, D.S., Trick, M.A. (eds.): Cliques, coloring, and satisfiability. In: DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 26. American Mathematical Society, Providence (1996) [Papers from the workshop held as part of the 2nd DIMACS Implementation Challenge in New Brunswick, NJ, October 11\u201313, 1993]"},{"key":"17_CR20","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1137\/S1052623495288064","volume":"9","author":"K.C. Kiwiel","year":"1999","unstructured":"Kiwiel K.C., Rosa C.H., Ruszczy\u0144ski A.: Proximal decomposition via alternating linearization. SIAM J. Optim. 9, 668\u2013689 (1999)","journal-title":"SIAM J. Optim."},{"key":"17_CR21","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":"17_CR22","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1137\/070704575","volume":"20","author":"J. Malick","year":"2009","unstructured":"Malick J., Povh J., Rendl F., Wiegele A.: Regularization methods for semidefinite programming. SIAM J Optim. 20, 336\u2013356 (2009)","journal-title":"SIAM J Optim."},{"key":"17_CR23","unstructured":"Pataki, G., Schmieta, S.: The dimacs library of semidefinite-quadratic-linear programs. Tech. rep., Center, Columbia University (1999)"},{"key":"17_CR24","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/s00607-006-0182-2","volume":"78","author":"J. Povh","year":"2006","unstructured":"Povh J., Rendl F., Wiegele A.: A boundary point method to solve semidefinite programs. Computing 78, 277\u2013286 (2006)","journal-title":"Computing"},{"key":"17_CR25","unstructured":"Sloane, N.J.A.: Challenge problems: independent sets in graphs. http:\/\/research.att.com\/njas\/doc\/graphs.html"},{"key":"17_CR26","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1017\/S0962492901000071","volume":"10","author":"M.J. Todd","year":"2001","unstructured":"Todd M.J.: Semidefinite optimization. Acta Numer. 10, 515\u2013560 (2001)","journal-title":"Acta Numer."},{"key":"17_CR27","doi-asserted-by":"crossref","first-page":"670","DOI":"10.1137\/S1052623402419819","volume":"14","author":"K.-C. Toh","year":"2003","unstructured":"Toh K.-C.: Solving large scale semidefinite programs via an iterative solver on the augmented systems. SIAM J. Optim. 14, 670\u2013698 (2003)","journal-title":"SIAM J. Optim."},{"key":"17_CR28","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1137\/S1052623495279797","volume":"7","author":"P. Tseng","year":"1997","unstructured":"Tseng P.: Alternating projection-proximal methods for convex programming and variational inequalities. SIAM J. Optim. 7, 951\u2013965 (1997)","journal-title":"SIAM J. Optim."},{"key":"17_CR29","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1137\/1038003","volume":"38","author":"L. Vandenberghe","year":"1996","unstructured":"Vandenberghe L., Boyd S.: Semidefinite programming. SIAM Rev. 38, 49\u201395 (1996)","journal-title":"SIAM Rev."},{"key":"17_CR30","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1137\/080724265","volume":"1","author":"Y. Wang","year":"2008","unstructured":"Wang Y., Yang J., Yin W., Zhang Y.: A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Imaging Sci. 1, 248\u2013272 (2008)","journal-title":"SIAM J. Imaging Sci."},{"key":"17_CR31","unstructured":"Wen, Z., Goldfarb, D., Ma, S., Scheinberg, K.: Row by row methods for semidefinite program ming. Technical report, Department of IEOR, Columbia University (2009)"},{"key":"17_CR32","unstructured":"Wiegele, A.: Biq mac library\u2014a collection of max-cut and quadratic 0-1 programming instances of medium size. Technical report (2007)"},{"key":"17_CR33","doi-asserted-by":"crossref","unstructured":"Wolkowicz, H., Saigal, R., Vandenberghe, L. (eds.): Handbook of semidefinite programming: theory, algorithms, and applications. In: International Series in Operations Research & Management Science, vol. 27. Kluwer, Boston (2000)","DOI":"10.1007\/978-1-4615-4381-7"},{"key":"17_CR34","unstructured":"Yang, J., Yuan, X.: An inexact alternating direction method for trace norm regularized least squares problem. Technical report, Department of Mathematics, Nanjing University (2010)"},{"key":"17_CR35","unstructured":"Yang, J., Zhang, Y.: Alternating direction algorithms for l1-problems in compressive sensing. Technical report, Rice University (2009)"},{"key":"17_CR36","doi-asserted-by":"crossref","first-page":"2842","DOI":"10.1137\/080732894","volume":"31","author":"J. Yang","year":"2008","unstructured":"Yang J., Zhang Y., Yin W.: An efficient tvl1 algorithm for deblurring multichannel images corrupted by impulsive noise. SIAM J. Sci. Comput. 31, 2842\u20132865 (2008)","journal-title":"SIAM J. Sci. Comput."},{"key":"17_CR37","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1080\/10556780600552693","volume":"22","author":"C. Ye","year":"2007","unstructured":"Ye C., Yuan X.: A descent method for structured monotone variational inequalities. Optimi Methods Softw 22, 329\u2013338 (2007)","journal-title":"Optimi Methods Softw"},{"key":"17_CR38","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/j.cam.2005.07.002","volume":"193","author":"Z. Yu","year":"2006","unstructured":"Yu Z.: Solving semidefinite programming problems via alternating direction methods. J. Comput. Appl. Math. 193, 437\u2013445 (2006)","journal-title":"J. Comput. Appl. Math."},{"key":"17_CR39","unstructured":"Yuan, X.: Alternating direction methods for sparse covariance selection. Technical report, Department of Mathematics, Hong Kong Baptist University (2009)"},{"key":"17_CR40","unstructured":"Zhang, Y.: User\u2019s guide for yall1: Your algorithms for l1 optimization. Technical report, Rice Univer sity (2009)"},{"key":"17_CR41","doi-asserted-by":"crossref","first-page":"1737","DOI":"10.1137\/080718206","volume":"20","author":"X. Zhao","year":"2010","unstructured":"Zhao X., Sun D., Toh K.: A newton-cg augmented lagrangian method for semidefinite programming. SIAM J. Optim. 20, 1737\u20131765 (2010)","journal-title":"SIAM J. Optim."}],"container-title":["Mathematical Programming Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12532-010-0017-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12532-010-0017-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12532-010-0017-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,12]],"date-time":"2020-06-12T04:57:15Z","timestamp":1591937835000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12532-010-0017-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9,28]]},"references-count":41,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2010,12]]}},"alternative-id":["17"],"URL":"https:\/\/doi.org\/10.1007\/s12532-010-0017-1","relation":{},"ISSN":["1867-2949","1867-2957"],"issn-type":[{"value":"1867-2949","type":"print"},{"value":"1867-2957","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,9,28]]}}}