{"id":"https://openalex.org/W1986490170","doi":"https://doi.org/10.1137/1035044","title":"Lagrange Multipliers and Optimality","display_name":"Lagrange Multipliers and Optimality","publication_year":1993,"publication_date":"1993-06-01","ids":{"openalex":"https://openalex.org/W1986490170","doi":"https://doi.org/10.1137/1035044","mag":"1986490170"},"language":"en","primary_location":{"id":"doi:10.1137/1035044","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1035044","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","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/A5046903273","display_name":"R. T. Rockafellar","orcid":"https://orcid.org/0000-0003-1703-5069"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"R. Tyrrell Rockafellar","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5046903273"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.7337,"has_fulltext":false,"cited_by_count":581,"citation_normalized_percentile":{"value":0.96109737,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"35","issue":"2","first_page":"183","last_page":"238"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9987999796867371,"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":0.9987999796867371,"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":0.9986000061035156,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9825000166893005,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.8578580617904663},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6783002614974976},{"id":"https://openalex.org/keywords/constraint-algorithm","display_name":"Constraint algorithm","score":0.6095595359802246},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5426069498062134},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4798664450645447},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.4698352515697479},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4689806401729584},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.4360736608505249},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09122607111930847}],"concepts":[{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.8578580617904663},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6783002614974976},{"id":"https://openalex.org/C15980293","wikidata":"https://www.wikidata.org/wiki/Q5164368","display_name":"Constraint algorithm","level":3,"score":0.6095595359802246},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5426069498062134},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4798664450645447},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.4698352515697479},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4689806401729584},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.4360736608505249},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09122607111930847},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/1035044","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1035044","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.161.7209","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.161.7209","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.washington.edu/~rtr/papers/rtr-LagrangeMultipliers.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.217.477","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.217.477","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.wisc.edu/~ferris/cs730/sirev35_183.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5699999928474426,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":67,"referenced_works":["https://openalex.org/W87140126","https://openalex.org/W100063776","https://openalex.org/W116303816","https://openalex.org/W136356331","https://openalex.org/W178640279","https://openalex.org/W187211397","https://openalex.org/W197936677","https://openalex.org/W965990085","https://openalex.org/W1484024929","https://openalex.org/W1493638084","https://openalex.org/W1551360398","https://openalex.org/W1577338488","https://openalex.org/W1608145022","https://openalex.org/W1669104078","https://openalex.org/W1896033818","https://openalex.org/W1966918398","https://openalex.org/W1968363522","https://openalex.org/W1970856396","https://openalex.org/W1974307865","https://openalex.org/W1976086748","https://openalex.org/W1982554859","https://openalex.org/W1987064381","https://openalex.org/W1996903464","https://openalex.org/W1998260066","https://openalex.org/W2000120257","https://openalex.org/W2000985550","https://openalex.org/W2008832947","https://openalex.org/W2013023588","https://openalex.org/W2016859302","https://openalex.org/W2024264959","https://openalex.org/W2025455887","https://openalex.org/W2030609769","https://openalex.org/W2037091587","https://openalex.org/W2039796103","https://openalex.org/W2042153418","https://openalex.org/W2053549375","https://openalex.org/W2053661713","https://openalex.org/W2057624533","https://openalex.org/W2065012151","https://openalex.org/W2075567596","https://openalex.org/W2110927303","https://openalex.org/W2111948593","https://openalex.org/W2117500014","https://openalex.org/W2124654085","https://openalex.org/W2135779729","https://openalex.org/W2136953603","https://openalex.org/W2139160710","https://openalex.org/W2143279738","https://openalex.org/W2144846366","https://openalex.org/W2151395035","https://openalex.org/W2155370486","https://openalex.org/W2157570139","https://openalex.org/W2158223004","https://openalex.org/W2159641394","https://openalex.org/W2223181934","https://openalex.org/W2237815984","https://openalex.org/W2329275945","https://openalex.org/W2516137114","https://openalex.org/W2595644070","https://openalex.org/W2624878328","https://openalex.org/W4235948503","https://openalex.org/W4243833218","https://openalex.org/W4245616712","https://openalex.org/W4247947599","https://openalex.org/W4249667877","https://openalex.org/W4285719527","https://openalex.org/W4293820388"],"related_works":["https://openalex.org/W2024837890","https://openalex.org/W1979241556","https://openalex.org/W2074745806","https://openalex.org/W2021667451","https://openalex.org/W2352028553","https://openalex.org/W1967449934","https://openalex.org/W1970808271","https://openalex.org/W2045861968","https://openalex.org/W2017306930","https://openalex.org/W2781111882"],"abstract_inverted_index":{"Lagrange":[0,117,157],"multipliers":[1,118],"used":[2],"to":[3,18,76,96,110,141,175],"be":[4,142],"viewed":[5],"as":[6,24,94,101,123,170],"auxiliary":[7],"variables":[8],"introduced":[9],"in":[10,16,152],"a":[11,25,56,97,126,133,163],"problem":[12,111],"of":[13,27,48,63,70,79,91,104,132,156,166],"constrained":[14],"minimization":[15],"order":[17],"write":[19],"first-order":[20],"optimality":[21],"conditions":[22,41],"formally":[23],"system":[26],"equations.":[28],"Modern":[29],"applications,":[30],"with":[31,108],"their":[32],"emphasis":[33],"on":[34],"numerical":[35],"methods":[36],"and":[37,51,73,173],"more":[38],"complicated":[39],"side":[40],"than":[42],"equations,":[43],"have":[44,113],"demanded":[45],"deeper":[46],"understanding":[47],"the":[49,67,77,82,88,105,130,153,161],"concept":[50],"how":[52],"it":[53],"fits":[54],"into":[55],"larger":[57],"theoretical":[58],"picture.":[59],"A":[60],"major":[61],"line":[62],"research":[64],"has":[65,86],"been":[66,87,115],"nonsmooth":[68,134,168],"geometry":[69],"one-sided":[71],"tangent":[72],"normal":[74],"vectors":[75,93],"set":[78],"points":[80],"satisfying":[81],"given":[83],"constraints.":[84],"Another":[85],"game-theoretic":[89],"role":[90],"multiplier":[92],"solutions":[95],"dual":[98],"problem.":[99],"Interpretations":[100],"generalized":[102],"derivatives":[103],"optimal":[106],"value":[107],"respect":[109],"parameters":[112],"also":[114],"explored.":[116],"are":[119],"now":[120],"being":[121],"seen":[122],"arising":[124],"from":[125],"general":[127],"rule":[128],"for":[129],"subdifferentiation":[131],"objective":[135],"function":[136],"which":[137],"allows":[138],"black-and-white":[139],"constraints":[140],"replaced":[143],"by":[144,172],"penalty":[145],"expressions.":[146],"This":[147],"paper":[148],"traces":[149],"such":[150],"themes":[151],"current":[154],"theory":[155],"multipliers,":[158],"providing":[159],"along":[160],"way":[162],"free-standing":[164],"exposition":[165],"basic":[167],"analysis":[169],"motivated":[171],"applied":[174],"this":[176],"subject.":[177]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":36},{"year":2024,"cited_by_count":30},{"year":2023,"cited_by_count":22},{"year":2022,"cited_by_count":33},{"year":2021,"cited_by_count":39},{"year":2020,"cited_by_count":24},{"year":2019,"cited_by_count":24},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":27},{"year":2016,"cited_by_count":18},{"year":2015,"cited_by_count":17},{"year":2014,"cited_by_count":26},{"year":2013,"cited_by_count":27},{"year":2012,"cited_by_count":21}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
