{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T15:50:03Z","timestamp":1776873003921,"version":"3.51.2"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2012,11,18]],"date-time":"2012-11-18T00:00:00Z","timestamp":1353196800000},"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":[[2013,5]]},"DOI":"10.1007\/s10589-012-9515-6","type":"journal-article","created":{"date-parts":[[2012,11,17]],"date-time":"2012-11-17T10:08:12Z","timestamp":1353146892000},"page":"75-111","source":"Crossref","is-referenced-by-count":18,"title":["Combining Lagrangian decomposition and excessive gap smoothing technique for solving large-scale separable convex optimization problems"],"prefix":"10.1007","volume":"55","author":[{"given":"Quoc","family":"Tran\u00a0Dinh","sequence":"first","affiliation":[]},{"given":"Carlo","family":"Savorgnan","sequence":"additional","affiliation":[]},{"given":"Moritz","family":"Diehl","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,11,18]]},"reference":[{"key":"9515_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, New York (1989)"},{"issue":"1","key":"9515_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/2200000016","volume":"3","author":"S. Boyd","year":"2011","unstructured":"Boyd, S., Parikh, N., Chu, E., Peleato, B.: Distributed optimization and statistics via alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1\u2013122 (2011)","journal-title":"Found. Trends Mach. Learn."},{"key":"9515_CR3","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":"9515_CR4","volume-title":"Decomposition Techniques in Mathematical Programming: Engineering and Science Applications","author":"A.J. Connejo","year":"2006","unstructured":"Connejo, A.J., M\u00ednguez, R., Castillo, E., Garc\u00eda-Bertrand, R.: Decomposition Techniques in Mathematical Programming: Engineering and Science Applications. Springer, Berlin (2006)"},{"key":"9515_CR5","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."},{"issue":"3","key":"9515_CR6","doi-asserted-by":"crossref","first-page":"592","DOI":"10.1109\/TAC.2011.2161027","volume":"57","author":"J.C. Duchi","year":"2012","unstructured":"Duchi, J.C., Agarwal, A., Wainwright, M.J.: Dual averaging for distributed optimization: Convergence analysis and network scaling. IEEE Trans. Autom. Control 57(3), 592\u2013606 (2012)","journal-title":"IEEE Trans. Autom. Control"},{"key":"9515_CR7","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/BF01581204","volume":"55","author":"J. Eckstein","year":"1992","unstructured":"Eckstein, J., Bertsekas, D.: 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":"9515_CR8","volume-title":"Finite-Dimensional Variational Inequalities and Complementarity Problems","author":"F. Facchinei","year":"2003","unstructured":"Facchinei, F., Pang, J.-S.: Finite-Dimensional Variational Inequalities and Complementarity Problems, vols.\u00a01\u20132. Springer, Berlin (2003)"},{"issue":"2","key":"9515_CR9","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1137\/090780705","volume":"22","author":"D. Goldfarb","year":"2012","unstructured":"Goldfarb, D., Ma, S.: Fast multiple splitting algorithms for convex optimization. SIAM J. Optim. 22(2), 533\u2013556 (2012)","journal-title":"SIAM J. Optim."},{"key":"9515_CR10","doi-asserted-by":"crossref","first-page":"921","DOI":"10.1016\/j.amc.2003.11.040","volume":"160","author":"A. Hamdi","year":"2005","unstructured":"Hamdi, A.: Two-level primal-dual proximal decomposition technique to solve large-scale optimization problems. Appl. Math. Comput. 160, 921\u2013938 (2005)","journal-title":"Appl. Math. Comput."},{"key":"9515_CR11","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1137\/0326019","volume":"26","author":"S.P. Han","year":"1988","unstructured":"Han, S.P., Lou, G.: A parallel algorithm for a class of convex programs. SIAM J. Control Optim. 26, 345\u2013355 (1988)","journal-title":"SIAM J. Control Optim."},{"issue":"2","key":"9515_CR12","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1137\/060662228","volume":"19","author":"L. Hariharan","year":"2008","unstructured":"Hariharan, L., Pucci, F.D.: Decentralized resource allocation in dynamic networks of agents. SIAM J. Optim. 19(2), 911\u2013940 (2008)","journal-title":"SIAM J. Optim."},{"key":"9515_CR13","author":"B.S. He","year":"2011","unstructured":"He, B.S., Tao, M., Xu, M.H., Yuan, X.M.: Alternating directions based contraction method for generally separable linearly constrained convex programming problems. Optimization (2011). doi: 10.1080\/02331934.2011.611885","journal-title":"Optimization"},{"key":"9515_CR14","first-page":"349","volume":"106","author":"B.S. He","year":"2000","unstructured":"He, B.S., Yang, H., Wang, S.L.: Alternating directions method with self-adaptive penalty parameters for monotone variational inequalities. J. Optim. Theory Appl. 106, 349\u2013368 (2000)","journal-title":"J. Optim. Theory Appl."},{"key":"9515_CR15","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1137\/110836936","volume":"50","author":"B.S. He","year":"2012","unstructured":"He, B.S., Yuan, X.M.: On the O(1\/n) convergence rate of the Douglas\u2013Rachford alternating direction method. SIAM J. Numer. Anal. 50, 700\u2013709 (2012)","journal-title":"SIAM J. Numer. Anal."},{"issue":"5\u20136","key":"9515_CR16","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1080\/02331930108844546","volume":"49","author":"K. Holmberg","year":"2001","unstructured":"Holmberg, K.: Experiments with primal-dual decomposition and subgradient methods for the uncapacitated facility location problem. Optimization 49(5\u20136), 495\u2013516 (2001)","journal-title":"Optimization"},{"issue":"3","key":"9515_CR17","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1080\/10556780500098565","volume":"21","author":"K. Holmberg","year":"2006","unstructured":"Holmberg, K., Kiwiel, K.C.: Mean value cross decomposition for nonlinear convex problem. Optim. Methods Softw. 21(3), 401\u2013417 (2006)","journal-title":"Optim. Methods Softw."},{"key":"9515_CR18","unstructured":"Kojima, M., Megiddo, N., Mizuno, S., et\u00a0al.: Horizontal and vertical decomposition in interior point methods for linear programs. Technical report, Information Sciences, Tokyo Institute of Technology, Tokyo (1993)"},{"key":"9515_CR19","unstructured":"Lenoir, A., Mahey, P.: Accelerating convergence of a separable augmented Lagrangian algorithm. Technical report, LIMOS\/RR-07-14, pp. 1\u201334 (2007)"},{"key":"9515_CR20","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1287\/trsc.7.4.297","volume":"7","author":"R.F. Love","year":"1973","unstructured":"Love, R.F., Kraemer, S.A.: A dual decomposition method for minimizing transportation costs in multifacility location problems. Transp. Sci. 7, 297\u2013316 (1973)","journal-title":"Transp. Sci."},{"issue":"4","key":"9515_CR21","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1137\/0802028","volume":"2","author":"S. Mehrotra","year":"1992","unstructured":"Mehrotra, S.: On the implementation of a primal-dual interior point method. SIAM J. Optim. 2(4), 575\u2013601 (1992)","journal-title":"SIAM J. Optim."},{"issue":"11","key":"9515_CR22","doi-asserted-by":"crossref","first-page":"2674","DOI":"10.1109\/TAC.2008.2007159","volume":"53","author":"I. Necoara","year":"2008","unstructured":"Necoara, I., Suykens, J.A.K.: Applications of a smoothing technique to decomposition in convex optimization. IEEE Trans. Autom. Control 53(11), 2674\u20132679 (2008)","journal-title":"IEEE Trans. Autom. Control"},{"key":"9515_CR23","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1109\/TAC.2008.2009515","volume":"54","author":"A. Ned\u00edc","year":"2009","unstructured":"Ned\u00edc, A., Ozdaglar, A.: Distributed subgradient methods for multi-agent optimization. IEEE Trans. Autom. Control 54, 48\u201361 (2009)","journal-title":"IEEE Trans. Autom. Control"},{"key":"9515_CR24","first-page":"543","volume":"269","author":"Y. Nesterov","year":"1983","unstructured":"Nesterov, Y.: A method for unconstrained convex minimization problem with the rate of convergence o(1\/k 2). Dokl. Akad. Nauk SSSR 269, 543\u2013547 (1983) (Translated as Soviet Math. Dokl.)","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"9515_CR25","series-title":"Applied Optimization","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-8853-9","volume-title":"Introductory Lectures on Convex Optimization: A Basic Course","author":"Y. Nesterov","year":"2004","unstructured":"Nesterov, Y.: Introductory Lectures on Convex Optimization: A Basic Course. Applied Optimization, vol. 87. Kluwer Academic, Dordrecht (2004)"},{"issue":"1","key":"9515_CR26","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1137\/S1052623403422285","volume":"16","author":"Y. Nesterov","year":"2005","unstructured":"Nesterov, Y.: Excessive gap technique in nonsmooth convex minimization. SIAM J. Optim. 16(1), 235\u2013249 (2005)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"9515_CR27","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s10107-004-0552-5","volume":"103","author":"Y. Nesterov","year":"2005","unstructured":"Nesterov, Y.: Smooth minimization of non-smooth functions. Math. Program. 103(1), 127\u2013152 (2005)","journal-title":"Math. Program."},{"issue":"2","key":"9515_CR28","doi-asserted-by":"crossref","first-page":"630","DOI":"10.1137\/S0097539704446232","volume":"37","author":"G. Neveen","year":"2007","unstructured":"Neveen, G., Jochen, K.: Faster and simpler algorithms for multicommodity flow and other fractional packing problems. SIAM J. Comput. 37(2), 630\u2013652 (2007)","journal-title":"SIAM J. Comput."},{"key":"9515_CR29","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1287\/moor.20.3.634","volume":"20","author":"A. Ruszczy\u0144ski","year":"1995","unstructured":"Ruszczy\u0144ski, A.: On convergence of an augmented Lagrangian decomposition method for sparse convex optimization. Math. Oper. Res. 20, 634\u2013656 (1995)","journal-title":"Math. Oper. Res."},{"key":"9515_CR30","first-page":"1511","volume-title":"Proceedings European Control Conference (ECC)","author":"S. Samar","year":"2007","unstructured":"Samar, S., Boyd, S., Gorinevsky, D.: Distributed estimation via dual decomposition. In: Proceedings European Control Conference (ECC), Kos, Greece, pp. 1511\u20131516 (2007)"},{"key":"9515_CR31","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/BF01586091","volume":"32","author":"J.E. Spingarn","year":"1985","unstructured":"Spingarn, J.E.: Applications of the method of partial inverses to convex programming: decomposition. Math. Program. Ser. A 32, 199\u2013223 (1985)","journal-title":"Math. Program. Ser. A"},{"key":"9515_CR32","unstructured":"Tran-Dinh, Q., Necoara, I., Savorgnan, C., Diehl, M.: An inexact perturbed path-following method for Lagrangian decomposition in large-scale separable convex optimization. Int. Report 12-181, ESATSISTA, KU Leuven, Belgium (2012). SIAM J. Optim., accepted"},{"issue":"4","key":"9515_CR33","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(4), 951\u2013965 (1997)","journal-title":"SIAM J. Optim."},{"issue":"10","key":"9515_CR34","doi-asserted-by":"crossref","first-page":"4825","DOI":"10.1109\/TSP.2008.927460","volume":"56","author":"P. Tsiaflakis","year":"2008","unstructured":"Tsiaflakis, P., Diehl, M., Moonen, M.: Distributed spectrum management algorithms for multi-user DSL networks. IEEE Trans. Signal Process. 56(10), 4825\u20134843 (2008)","journal-title":"IEEE Trans. Signal Process."},{"issue":"4","key":"9515_CR35","doi-asserted-by":"crossref","first-page":"2230","DOI":"10.1109\/TSP.2009.2039825","volume":"58","author":"P. Tsiaflakis","year":"2010","unstructured":"Tsiaflakis, P., Necoara, I., Suykens, J.A.K., Moonen, M.: Improved dual decomposition based optimization for DSL dynamic spectrum management. IEEE Trans. Signal Process. 58(4), 2230\u20132245 (2010)","journal-title":"IEEE Trans. Signal Process."},{"key":"9515_CR36","unstructured":"Vania, D.S.E.: Finding approximate solutions for large scale linear programs. Ph.D. Thesis, No. 18188, ETH, Zurich (2009)"},{"key":"9515_CR37","unstructured":"Venkat, A.N.: Distributed model predictive control: theory and applications. Ph.D. Thesis, University of Wisconsin-Madison (2006)"},{"issue":"1","key":"9515_CR38","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/s10107-004-0559-y","volume":"106","author":"A. W\u00e4chter","year":"2006","unstructured":"W\u00e4chter, A., Biegler, L.T.: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math. Program. 106(1), 25\u201357 (2006)","journal-title":"Math. Program."},{"key":"9515_CR39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10107-003-0471-x","volume":"102","author":"G. Zhao","year":"2005","unstructured":"Zhao, G.: A Lagrangian dual method with self-concordant barriers for multistage stochastic convex programming. Math. Program. 102, 1\u201324 (2005)","journal-title":"Math. Program."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-012-9515-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-012-9515-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-012-9515-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T11:36:43Z","timestamp":1559302603000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-012-9515-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11,18]]},"references-count":39,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,5]]}},"alternative-id":["9515"],"URL":"https:\/\/doi.org\/10.1007\/s10589-012-9515-6","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,11,18]]}}}