{"id":"https://openalex.org/W2089447917","doi":"https://doi.org/10.1137/050647621","title":"Abstract Convexity and Augmented Lagrangians","display_name":"Abstract Convexity and Augmented Lagrangians","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2089447917","doi":"https://doi.org/10.1137/050647621","mag":"2089447917"},"language":"en","primary_location":{"id":"doi:10.1137/050647621","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050647621","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/A5075925642","display_name":"Regina S. Burachik","orcid":"https://orcid.org/0000-0003-1332-6213"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Regina Sandra Burachik","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108208587","display_name":"Alex Rubinov","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alex Rubinov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8707,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.85801998,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"18","issue":"2","first_page":"413","last_page":"436"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9991999864578247,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9957000017166138,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.9023030996322632},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.7623050212860107},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.742778480052948},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.7093770503997803},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7076602578163147},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.6441173553466797},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5329293608665466},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5008471012115479},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4751933813095093},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.42553600668907166},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.4092821180820465},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.2816062271595001},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17934325337409973},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1457710564136505}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.9023030996322632},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.7623050212860107},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.742778480052948},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.7093770503997803},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7076602578163147},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.6441173553466797},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5329293608665466},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5008471012115479},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4751933813095093},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.42553600668907166},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4092821180820465},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2816062271595001},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17934325337409973},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1457710564136505},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/050647621","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050647621","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:vital:155","is_oa":false,"landing_page_url":"http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/61647","pdf_url":null,"source":{"id":"https://openalex.org/S4306400234","display_name":"FedUni ResearchOnline (Federation University Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210158496","host_organization_name":"Australian Federation of University Women \u2013 South Australia","host_organization_lineage":["https://openalex.org/I4210158496"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.606.7586","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.606.7586","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.maths.unisa.edu.au/~yalcin/regina/papers/Burachik-Rubinov-2006-a.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.49000000953674316,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W573706636","https://openalex.org/W580782046","https://openalex.org/W1514382660","https://openalex.org/W1551360398","https://openalex.org/W1556819741","https://openalex.org/W1566027928","https://openalex.org/W1577338488","https://openalex.org/W1595225922","https://openalex.org/W1601741115","https://openalex.org/W1986490170","https://openalex.org/W2009398741","https://openalex.org/W2012757448","https://openalex.org/W2017727320","https://openalex.org/W2019329666","https://openalex.org/W2052431132","https://openalex.org/W2067243588","https://openalex.org/W2076744267","https://openalex.org/W2123014493","https://openalex.org/W2133374626","https://openalex.org/W2200834864","https://openalex.org/W2229034016","https://openalex.org/W2626963867","https://openalex.org/W3158532942"],"related_works":["https://openalex.org/W2315802443","https://openalex.org/W2155425983","https://openalex.org/W2089042254","https://openalex.org/W4220928172","https://openalex.org/W2172478086","https://openalex.org/W2017727320","https://openalex.org/W2133374626","https://openalex.org/W2031363992","https://openalex.org/W4297948077","https://openalex.org/W1984850688"],"abstract_inverted_index":{"The":[0],"ultimate":[1],"goal":[2],"of":[3,23,31,57],"this":[4],"paper":[5],"is":[6],"to":[7,69],"demonstrate":[8],"that":[9],"abstract":[10,58],"convexity":[11,59],"provides":[12],"a":[13,17,39],"natural":[14],"language":[15],"and":[16,28,43,48],"suitable":[18],"framework":[19],"for":[20],"the":[21,45,51],"examination":[22],"zero":[24],"duality":[25,64],"gap":[26],"properties":[27],"exact":[29],"multipliers":[30],"augmented":[32,36,52],"Lagrangians.":[33],"We":[34,61],"study":[35],"Lagrangians":[37],"in":[38,55],"very":[40],"general":[41],"setting":[42],"formulate":[44],"main":[46],"definitions":[47],"facts":[49],"describing":[50],"Lagrangian":[53],"theory":[54],"terms":[56],"tools.":[60],"illustrate":[62],"our":[63],"scheme":[65],"with":[66],"an":[67],"application":[68],"stochastic":[70],"semi\u2010infinite":[71],"optimization.":[72]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}