{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T17:07:04Z","timestamp":1782234424289,"version":"3.54.5"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2016,4,21]],"date-time":"2016-04-21T00:00:00Z","timestamp":1461196800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,4,21]],"date-time":"2016-04-21T00:00:00Z","timestamp":1461196800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1331426"],"award-info":[{"award-number":["1331426"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-15-1-2078"],"award-info":[{"award-number":["N00014-15-1-2078"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2017,1]]},"DOI":"10.1007\/s10107-016-1012-8","type":"journal-article","created":{"date-parts":[[2016,4,21]],"date-time":"2016-04-21T10:05:55Z","timestamp":1461233155000},"page":"365-387","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":44,"title":["Exact augmented Lagrangian duality for mixed integer linear programming"],"prefix":"10.1007","volume":"161","author":[{"given":"Mohammad Javad","family":"Feizollahi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shabbir","family":"Ahmed","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andy","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2016,4,21]]},"reference":[{"issue":"2","key":"1012_CR1","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1137\/S1052623493259215","volume":"7","author":"A Ben-Tal","year":"1997","unstructured":"Ben-Tal, A., Zibulevsky, M.: Penalty\/barrier multiplier methods for convex programming problems. SIAM J. Optim. 7(2), 347\u2013366 (1997)","journal-title":"SIAM J. Optim."},{"key":"1012_CR2","volume-title":"Constrained optimization and Lagrange multiplier methods","author":"DP Bertsekas","year":"1982","unstructured":"Bertsekas, D.P.: Constrained optimization and Lagrange multiplier methods. Academic Press, London (1982)"},{"key":"1012_CR3","volume-title":"Convex analysis and optimization","author":"DP Bertsekas","year":"2003","unstructured":"Bertsekas, D.P., Nedi\u0107, A., Ozdaglar, A.E.: Convex analysis and optimization. Athena Scientific Belmont, Belmont (2003)"},{"issue":"2","key":"1012_CR4","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1016\/0012-365X(77)90028-0","volume":"19","author":"C Blair","year":"1977","unstructured":"Blair, C., Jeroslow, R.: The value function of a mixed integer program: I. Discr. Math. 19(2), 121\u2013138 (1977)","journal-title":"Discr. Math."},{"issue":"1","key":"1012_CR5","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1016\/0012-365X(79)90147-X","volume":"25","author":"C Blair","year":"1979","unstructured":"Blair, C., Jeroslow, R.: The value function of a mixed integer program: II. Discr. Math. 25(1), 7\u201319 (1979)","journal-title":"Discr. Math."},{"issue":"1","key":"1012_CR6","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1007\/BF01583794","volume":"23","author":"C Blair","year":"1982","unstructured":"Blair, C., Jeroslow, R.: The value function of an integer program. Math. Program. 23(1), 237\u2013273 (1982)","journal-title":"Math. Program."},{"issue":"2","key":"1012_CR7","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1007\/s10107-014-0763-3","volume":"150","author":"NL Boland","year":"2015","unstructured":"Boland, N.L., Eberhard, A.C.: On the augmented Lagrangian dual for integer programming. Math. Program. 150(2), 491\u2013509 (2015)","journal-title":"Math. Program."},{"issue":"1","key":"1012_CR8","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":"1","key":"1012_CR9","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/s10957-010-9711-4","volume":"147","author":"RS Burachik","year":"2010","unstructured":"Burachik, R.S., Iusem, A.N., Melo, J.G.: Duality and exact penalization for general augmented lagrangians. J. Optim. Theory Appl. 147(1), 125\u2013140 (2010)","journal-title":"J. Optim. Theory Appl."},{"issue":"4","key":"1012_CR10","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1080\/02331934.2013.830117","volume":"64","author":"RS Burachik","year":"2015","unstructured":"Burachik, R.S., Iusem, A.N., Melo, J.G.: The exact penalty map for nonsmooth and nonconvex optimization. Optimization 64(4), 717\u2013738 (2015)","journal-title":"Optimization"},{"issue":"1","key":"1012_CR11","doi-asserted-by":"publisher","first-page":"33","DOI":"10.3934\/jimo.2005.1.33","volume":"1","author":"RS Burachik","year":"2005","unstructured":"Burachik, R.S., Rubinov, A.: On the absence of duality gap for Lagrange-type functions. J. Ind. Manag. Optim. 1(1), 33 (2005)","journal-title":"J. Ind. Manag. Optim."},{"issue":"2","key":"1012_CR12","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1137\/050647621","volume":"18","author":"RS Burachik","year":"2007","unstructured":"Burachik, R.S., Rubinov, A.: Abstract convexity and augmented Lagrangians. SIAM J. Optim. 18(2), 413\u2013436 (2007)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"1012_CR13","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1137\/0329027","volume":"29","author":"JV Burke","year":"1991","unstructured":"Burke, J.V.: Calmness and exact penalization. SIAM J. Control Optim. 29(2), 493\u2013497 (1991)","journal-title":"SIAM J. Control Optim."},{"issue":"4","key":"1012_CR14","doi-asserted-by":"publisher","first-page":"968","DOI":"10.1137\/0329054","volume":"29","author":"JV Burke","year":"1991","unstructured":"Burke, J.V.: An exact penalization viewpoint of constrained optimization. SIAM J. Control Optim. 29(4), 968\u2013998 (1991)","journal-title":"SIAM J. Control Optim."},{"issue":"2","key":"1012_CR15","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1287\/moor.1.2.165","volume":"1","author":"FH Clarke","year":"1976","unstructured":"Clarke, F.H.: A new approach to Lagrange multipliers. Math. Oper. Res. 1(2), 165\u2013174 (1976)","journal-title":"Math. Oper. Res."},{"issue":"1","key":"1012_CR16","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.ijepes.2015.04.009","volume":"73","author":"MJ Feizollahi","year":"2015","unstructured":"Feizollahi, M.J., Costley, M., Ahmed, S., Grijalva, S.: Large-scale decentralized unit commitment. Int. J. Electr. Power Energy Syst. 73(1), 97\u2013106 (2015)","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"1012_CR17","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1007\/BFb0120690","volume":"2","author":"AM Geoffrion","year":"1974","unstructured":"Geoffrion, A.M.: Lagrangean relaxation for integer programming. Math. Program. Study 2, 82\u2013114 (1974)","journal-title":"Math. Program. Study"},{"issue":"3","key":"1012_CR18","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1287\/moor.28.3.533.16395","volume":"28","author":"X Huang","year":"2003","unstructured":"Huang, X., Yang, X.: A unified augmented lagrangian approach to duality and exact penalization. Math. Oper. Res. 28(3), 533\u2013552 (2003)","journal-title":"Math. Oper. Res."},{"key":"1012_CR19","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511983658","volume-title":"Mathematical programs with equilibrium constraints","author":"ZQ Luo","year":"1996","unstructured":"Luo, Z.Q., Pang, J.S., Ralph, D.: Mathematical programs with equilibrium constraints. Cambridge University Press, Cambridge (1996)"},{"issue":"1","key":"1012_CR20","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/BF01585518","volume":"7","author":"RR Meyer","year":"1974","unstructured":"Meyer, R.R.: On the existence of optimal solutions to integer and mixed-integer programming problems. Math. Program. 7(1), 223\u2013235 (1974)","journal-title":"Math. Program."},{"issue":"3\u20134","key":"1012_CR21","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/BF01262932","volume":"16","author":"RR Meyer","year":"1975","unstructured":"Meyer, R.R.: Integer and mixed-integer programming models: general properties. J. Optim. Theory Appl. 16(3\u20134), 191\u2013206 (1975)","journal-title":"J. Optim. Theory Appl."},{"issue":"4","key":"1012_CR22","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1007\/s10898-006-9122-0","volume":"40","author":"A Nedi\u0107","year":"2008","unstructured":"Nedi\u0107, A., Ozdaglar, A.: A geometric framework for nonconvex optimization duality using augmented Lagrangian functions. J. Global Optim. 40(4), 545\u2013573 (2008)","journal-title":"J. Global Optim."},{"issue":"3","key":"1012_CR23","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1287\/moor.1070.0296","volume":"33","author":"A Nedic","year":"2008","unstructured":"Nedic, A., Ozdaglar, A.: Separation of nonconvex sets with general augmenting functions. Math. Oper. Res. 33(3), 587\u2013605 (2008)","journal-title":"Math. Oper. Res."},{"key":"1012_CR24","unstructured":"Ralphs, T.K., Hassanzadeh, A.: On the value function of a mixed integer linear optimization problem and an algorithm for its construction. Technical report, Laboratory for Computational Optimization at Lehigh (CORL), Department of Industrial and Systems Engineering. Lehigh University, Technical Report 14T-004 (2014)"},{"issue":"2","key":"1012_CR25","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1137\/0312021","volume":"12","author":"RT Rockafellar","year":"1974","unstructured":"Rockafellar, R.T.: Augmented Lagrange multiplier functions and duality in nonconvex programming. SIAM J. Control 12(2), 268\u2013285 (1974)","journal-title":"SIAM J. Control"},{"key":"1012_CR26","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-02431-3","volume-title":"Variational analysis","author":"RT Rockafellar","year":"1998","unstructured":"Rockafellar, R.T., Wets, R.J.B.: Variational analysis, vol. 317. Springer, Heidelberg (1998)"},{"issue":"5","key":"1012_CR27","doi-asserted-by":"publisher","first-page":"931","DOI":"10.1080\/1055678021000066058","volume":"17","author":"A Rubinov","year":"2002","unstructured":"Rubinov, A., Yang, X., Bagirov, A.: Penalty functions with a small penalty parameter. Optim. Methods Softw. 17(5), 931\u2013964 (2002)","journal-title":"Optim. Methods Softw."},{"issue":"1","key":"1012_CR28","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1137\/S1052623497326095","volume":"10","author":"AM Rubinov","year":"1999","unstructured":"Rubinov, A.M., Glover, B.M., Yang, X.: Decreasing functions with applications to penalization. SIAM J. Optim. 10(1), 289\u2013313 (1999)","journal-title":"SIAM J. Optim."},{"issue":"4","key":"1012_CR29","doi-asserted-by":"publisher","first-page":"775","DOI":"10.1287\/moor.27.4.775.295","volume":"27","author":"AM Rubinov","year":"2002","unstructured":"Rubinov, A.M., Huang, X., Yang, X.: The zero duality gap property and lower semicontinuity of the perturbation function. Math. Oper. Res. 27(4), 775\u2013791 (2002)","journal-title":"Math. Oper. Res."},{"key":"1012_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-9172-0","volume-title":"Lagrange-type functions in constrained non-convex optimization","author":"AM Rubinov","year":"2003","unstructured":"Rubinov, A.M., Yang, X.: Lagrange-type functions in constrained non-convex optimization, vol. 85. Springer Science and Business Media, Heidelberg (2003)"},{"key":"1012_CR31","doi-asserted-by":"crossref","unstructured":"Sun, X.A., Phan, D., Ghosh, S.: Fully decentralized AC optimal power flow algorithms. IEEE power and energy society general meeting, July 21\u201325 (2013)","DOI":"10.1109\/PESMG.2013.6672864"},{"issue":"4","key":"1012_CR32","doi-asserted-by":"publisher","first-page":"740","DOI":"10.1287\/moor.2013.0591","volume":"38","author":"CY Wang","year":"2013","unstructured":"Wang, C.Y., Yang, X.Q., Yang, X.M.: Nonlinear augmented Lagrangian and duality theory. Math. Oper. Res. 38(4), 740\u2013760 (2013)","journal-title":"Math. Oper. Res."},{"key":"1012_CR33","volume-title":"Integer and combinatorial optimization. Wiley series in discrete mathematics and optimization","author":"LA Wolsey","year":"1999","unstructured":"Wolsey, L.A., Nemhauser, G.L.: Integer and combinatorial optimization. Wiley series in discrete mathematics and optimization. Wiley, London (1999)"},{"issue":"4","key":"1012_CR34","doi-asserted-by":"publisher","first-page":"1119","DOI":"10.1137\/S1052623400371806","volume":"11","author":"X Yang","year":"2001","unstructured":"Yang, X., Huang, X.: A nonlinear Lagrangian approach to constrained optimization problems. SIAM J. Optim. 11(4), 1119\u20131144 (2001)","journal-title":"SIAM J. Optim."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-016-1012-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-016-1012-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-016-1012-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-016-1012-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,16]],"date-time":"2020-05-16T16:19:13Z","timestamp":1589645953000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-016-1012-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4,21]]},"references-count":34,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["1012"],"URL":"https:\/\/doi.org\/10.1007\/s10107-016-1012-8","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,4,21]]},"assertion":[{"value":"13 August 2015","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 April 2016","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 April 2016","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}