{"id":"https://openalex.org/W2076940249","doi":"https://doi.org/10.1137/10081085x","title":"Local Convergence of Exact and Inexact Augmented Lagrangian Methods under the Second-Order Sufficient Optimality Condition","display_name":"Local Convergence of Exact and Inexact Augmented Lagrangian Methods under the Second-Order Sufficient Optimality Condition","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2076940249","doi":"https://doi.org/10.1137/10081085x","mag":"2076940249"},"language":"en","primary_location":{"id":"doi:10.1137/10081085x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/10081085x","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054804948","display_name":"Dami\u00e1n Fern\u00e1ndez","orcid":"https://orcid.org/0000-0002-8254-353X"},"institutions":[{"id":"https://openalex.org/I166401450","display_name":"Universidad Nacional de C\u00f3rdoba","ror":"https://ror.org/056tb7j80","country_code":"AR","type":"education","lineage":["https://openalex.org/I166401450"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"D. Fern\u00e1ndez","raw_affiliation_strings":["FaMAF, Universidad Nacional de C\u00f3rdoba, Medina Allende s/n, 5000 C\u00f3rdoba, Argentina"],"affiliations":[{"raw_affiliation_string":"FaMAF, Universidad Nacional de C\u00f3rdoba, Medina Allende s/n, 5000 C\u00f3rdoba, Argentina","institution_ids":["https://openalex.org/I166401450"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110039123","display_name":"M. V. Solodov","orcid":null},"institutions":[{"id":"https://openalex.org/I4210128604","display_name":"Instituto de Pesquisas Jardim Bot\u00e2nico do Rio de Janeiro","ror":"https://ror.org/033xtdz52","country_code":"BR","type":"archive","lineage":["https://openalex.org/I4210128604"]},{"id":"https://openalex.org/I141883831","display_name":"Instituto Nacional de Matem\u00e1tica Pura e Aplicada","ror":"https://ror.org/028caqe42","country_code":"BR","type":"facility","lineage":["https://openalex.org/I141883831","https://openalex.org/I4210151455"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"M. V. Solodov","raw_affiliation_strings":["IMPA -Instituto de Matem\u00e1tica Pura e Aplicada, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ 22460-320, Brazil"],"affiliations":[{"raw_affiliation_string":"IMPA -Instituto de Matem\u00e1tica Pura e Aplicada, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ 22460-320, Brazil","institution_ids":["https://openalex.org/I141883831","https://openalex.org/I4210128604"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110039123"],"corresponding_institution_ids":["https://openalex.org/I141883831","https://openalex.org/I4210128604"],"apc_list":null,"apc_paid":null,"fwci":10.3149,"has_fulltext":false,"cited_by_count":82,"citation_normalized_percentile":{"value":0.99034335,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"22","issue":"2","first_page":"384","last_page":"407"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8622678518295288},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.785477876663208},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6915392279624939},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.5808868408203125},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.5785265564918518},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5513963103294373},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.5036560893058777},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.470337450504303},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.43656596541404724},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4327061176300049},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4131212532520294},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06836915016174316}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8622678518295288},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.785477876663208},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6915392279624939},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.5808868408203125},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.5785265564918518},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5513963103294373},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.5036560893058777},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.470337450504303},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.43656596541404724},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4327061176300049},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4131212532520294},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06836915016174316},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/10081085x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/10081085x","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.310.2872","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.310.2872","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://pages.cs.wisc.edu/~solodov/fersol10augL.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7200000286102295}],"awards":[{"id":"https://openalex.org/G146285273","display_name":null,"funder_award_id":"FAPERJ","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320322749","display_name":"Funda\u00e7\u00e3o Carlos Chagas Filho de Amparo \u00e0 Pesquisa do Estado do Rio de Janeiro","ror":"https://ror.org/03kk0s825"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W147998453","https://openalex.org/W189195062","https://openalex.org/W368078881","https://openalex.org/W1543439990","https://openalex.org/W1669104078","https://openalex.org/W1982203621","https://openalex.org/W1983585148","https://openalex.org/W1984848663","https://openalex.org/W1986490170","https://openalex.org/W1987995897","https://openalex.org/W1996701679","https://openalex.org/W2022853838","https://openalex.org/W2026689197","https://openalex.org/W2037091587","https://openalex.org/W2042613327","https://openalex.org/W2057624533","https://openalex.org/W2067758385","https://openalex.org/W2074465099","https://openalex.org/W2075572180","https://openalex.org/W2079004067","https://openalex.org/W2079693963","https://openalex.org/W2084478514","https://openalex.org/W2085881836","https://openalex.org/W2099959094","https://openalex.org/W2127012596","https://openalex.org/W2149416133","https://openalex.org/W2155865164","https://openalex.org/W2611293703","https://openalex.org/W3029645440","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2015060724","https://openalex.org/W2058578573","https://openalex.org/W2012871340","https://openalex.org/W3046535663","https://openalex.org/W4313189992","https://openalex.org/W3035320230","https://openalex.org/W4317581747","https://openalex.org/W4287694146","https://openalex.org/W3105202832","https://openalex.org/W2017965889"],"abstract_inverted_index":{"We":[0],"establish":[1],"local":[2],"convergence":[3,7,148,181,207],"and":[4,57,164,208],"rate":[5,182],"of":[6,8,39,67,92,167,184,206,223,227],"the":[9,15,19,29,47,52,59,68,74,78,86,90,95,99,112,122,134,154,172,179,185,189,195,203,210,224,229],"classical":[10,75],"augmented":[11],"Lagrangian":[12],"algorithm":[13],"under":[14,219],"sole":[16],"assumption":[17,62],"that":[18,178,218],"dual":[20],"starting":[21,118],"point":[22],"is":[23,106,183],"close":[24],"to":[25,82,107,158,160,200],"a":[26,64],"multiplier":[27,80,124],"satisfying":[28],"second-order":[30,69,135],"sufficient":[31,70,136],"optimality":[32,137],"condition.":[33,71],"In":[34,171],"particular,":[35],"no":[36],"constraint":[37,55,109],"qualifications":[38],"any":[40],"kind":[41],"are":[42,115,125,156,169],"needed.":[43],"Previous":[44,192],"literature":[45],"on":[46],"subject":[48],"required,":[49],"in":[50],"addition,":[51],"linear":[53],"independence":[54],"qualification":[56],"either":[58],"strict":[60],"complementarity":[61],"or":[63],"stronger":[65,113,211],"version":[66],"That":[72],"said,":[73],"results":[76],"allow":[77],"initial":[79],"estimate":[81],"be":[83],"far":[84,120],"from":[85,121],"optimal":[87,123],"one,":[88],"at":[89],"expense":[91],"proportionally":[93],"increasing":[94],"threshold":[96],"value":[97],"for":[98,139,194],"penalty":[100,140,230],"parameters.":[101],"Although":[102],"our":[103,128,220],"primary":[104],"goal":[105],"avoid":[108],"qualifications,":[110],"if":[111,153],"assumptions":[114,212,221],"introduced,":[116],"then":[117],"points":[119],"allowed":[126,157],"within":[127],"analysis":[129],"as":[130,188],"well.":[131],"Using":[132],"only":[133],"condition,":[138],"parameters":[141,155,231],"large":[142],"enough":[143],"we":[144,175,216],"prove":[145],"primal-dual":[146,190],"Q-linear":[147],"rate,":[149],"which":[150],"becomes":[151],"superlinear":[152],"go":[159],"infinity.":[161],"Both":[162],"exact":[163,173],"inexact":[165],"solutions":[166],"subproblems":[168],"considered.":[170],"case,":[174],"further":[176],"show":[177,217],"primal":[180,196],"same":[186],"Q-order":[187],"rate.":[191],"assertions":[193],"sequence":[197],"all":[198],"had":[199],"do":[201],"with":[202],"weaker":[204],"R-rate":[205],"required":[209],"cited":[213],"above.":[214],"Finally,":[215],"one":[222],"popular":[225],"rules":[226],"controlling":[228],"ensures":[232],"their":[233],"boundedness.":[234]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
