{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:43:51Z","timestamp":1787341431049,"version":"build-2736575974"},"reference-count":54,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["2013\/07375-0"],"award-info":[{"award-number":["2013\/07375-0"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["2013\/05475-7"],"award-info":[{"award-number":["2013\/05475-7"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["303013\/2013-3"],"award-info":[{"award-number":["303013\/2013-3"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["306986\/2016-7"],"award-info":[{"award-number":["306986\/2016-7"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["302915\/2016-8"],"award-info":[{"award-number":["302915\/2016-8"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>Mathematical programs with complementarity constraints (MPCCs) are difficult optimization problems that do not satisfy the majority of the usual constraint qualifications (CQs) for standard nonlinear optimization. Despite this fact, classical methods behave well when applied to MPCCs. Recently, Izmailov, Solodov, and Uskov proved that first order augmented Lagrangian methods, under a natural adaption of the linear independence constraint qualification to the MPCC setting (MPCC-LICQ), converge to strongly stationary (S-stationary) points, if the multiplier sequence is bounded. If the multiplier sequence is not bounded, only Clarke stationary (C-stationary) points are recovered. In this paper we improve this result in two ways. For the case of bounded multipliers we are able replace the MPCC-LICQ assumption by the much weaker MPCC-relaxed positive linear dependence condition (MPCC-RCLPD). For the case with unbounded multipliers, building upon results from Scholtes, Anitescu, and others, we show that a second order augmented Lagrangian method converges to points that are at least Mordukhovich stationary (M-stationary) but we still need the more stringent MPCC-LICQ assumption. Numerical tests, validating the theory, are also presented.<\/jats:p>","DOI":"10.1137\/17m1125698","type":"journal-article","created":{"date-parts":[[2018,9,20]],"date-time":"2018-09-20T10:06:42Z","timestamp":1537438002000},"page":"2574-2600","source":"Crossref","is-referenced-by-count":22,"title":["Convergence Properties of a Second Order Augmented Lagrangian Method for Mathematical Programs with Complementarity Constraints"],"prefix":"10.1137","volume":"28","author":[{"given":"Roberto","family":"Andreani","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9224-9051","authenticated-orcid":true,"given":"Leonardo D.","family":"Secchin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paulo J. S.","family":"Silva","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,9,20]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-009-9240-y"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/060654797"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s001860400410"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1080\/02331930903578700"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drx011"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-011-0456-0"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/15M1008488"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/040606855"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623402401221"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-006-0005-4"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1080\/10556780701577730"},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"E. G. Birgin and J. M. Mart\u00ednez,\n                      Practical Augmented Lagrangian Methods for Constrained Optimization\n                      , Fundam. Algorithms 10, SIAM, Philadelphia, PA, 2014,https:\/\/doi.org\/10.1137\/1.9781611973365.","DOI":"10.1137\/1.9781611973365"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019928808826"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-011-9396-0"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/23.4.539"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1080\/0233193031000149894"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/s10107990015a"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144595285963"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1080\/02331930500342591"},{"key":"atypb20","first-page":"111","author":"Flegel M. L.","year":"2006","journal-title":"MA"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/s11228-006-0033-5"},{"key":"atypb22","unstructured":"R. Fletcher and S. Leyffer,\n                      Numerical Experience with Solving MPECs as NLPs\n                      , Numerical Analysis Report 210, University of Dundee, 2002."},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623402407382"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-012-0228-x"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2015.03.001"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1007\/BF00927673"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1080\/10556788.2010.535170"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-011-0488-5"},{"key":"atypb29","unstructured":"A Collection of Fortran Codes for Large Scale Scientific Computation\n                      , HSL Mathematical Software Library, Didcot, 2016,http:\/\/www.hsl.rl.ac.uk(accessed 10 November 2016)."},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-004-5154-0"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1137\/120868359"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1137\/070705490"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1007\/s13675-015-0044-9"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1137\/090774975"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1137\/100802487"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1287\/moor.2014.0667"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1137\/040621065"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-004-5024-z"},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-004-0543-6"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-009-9642-0"},{"key":"atypb41","doi-asserted-by":"crossref","unstructured":"Z.Q. Luo, J.S. Pang, and D. Ralph,\n                      Mathematical Programs with Equilibrium Constraints\n                      , Cambridge University Press, Cambridge, 1996,https:\/\/doi.org\/10.1017\/CBO9780511983658.","DOI":"10.1017\/CBO9780511983658"},{"key":"atypb42","doi-asserted-by":"crossref","unstructured":"J. Outrata, M. Kocvara, and J. Zowe,\n                      Nonsmooth Approach to Optimization Problems with Equilibrium Constraints\n                      , 1st ed., Nonconvex Optim. Appl. 28, Springer, New York, 1998,https:\/\/doi.org\/10.1007\/978-1-4757-2825-5.","DOI":"10.1007\/978-1-4757-2825-5"},{"key":"atypb43","first-page":"177","volume":"35","author":"Outrata J. V.","year":"1999","journal-title":"Kybernetika"},{"key":"atypb44","doi-asserted-by":"publisher","DOI":"10.1137\/070688742"},{"key":"atypb45","first-page":"283","author":"M. J.","year":"1969","journal-title":"New York"},{"key":"atypb46","unstructured":"A. Ramos,\n                      Mathematical Programs with Equilibrium Constraints: A Sequential Optimality Condition, New Constraint Qualifications and Algorithmic Consequences\n                      ,http:\/\/www.optimization-online.org\/DB_HTML\/2016\/04\/5423.html, 2016."},{"key":"atypb47","doi-asserted-by":"publisher","DOI":"10.1137\/0312021"},{"key":"atypb48","doi-asserted-by":"publisher","DOI":"10.1287\/moor.25.1.1.15213"},{"key":"atypb49","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623499361233"},{"key":"atypb50","doi-asserted-by":"publisher","DOI":"10.1137\/090748883"},{"key":"atypb51","doi-asserted-by":"publisher","DOI":"10.1016\/j.trb.2015.08.013"},{"key":"atypb52","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2005.03.027"},{"key":"atypb53","doi-asserted-by":"publisher","DOI":"10.1080\/1055678041001697659"},{"key":"atypb54","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2004.10.032"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M1125698","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:19:34Z","timestamp":1787339974000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M1125698"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":54,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/17M1125698"],"URL":"https:\/\/doi.org\/10.1137\/17m1125698","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}