{"id":"https://openalex.org/W2139502933","doi":"https://doi.org/10.1090/s0273-0979-1979-14595-6","title":"Nonconvex minimization problems","display_name":"Nonconvex minimization problems","publication_year":1979,"publication_date":"1979-01-01","ids":{"openalex":"https://openalex.org/W2139502933","doi":"https://doi.org/10.1090/s0273-0979-1979-14595-6","mag":"2139502933"},"language":"en","primary_location":{"id":"doi:10.1090/s0273-0979-1979-14595-6","doi":"https://doi.org/10.1090/s0273-0979-1979-14595-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0273-0979-1979-14595-6","pdf_url":"https://www.ams.org/bull/1979-01-03/S0273-0979-1979-14595-6/S0273-0979-1979-14595-6.pdf","source":{"id":"https://openalex.org/S71584477","display_name":"Bulletin of the American Mathematical Society","issn_l":"0002-9904","issn":["0002-9904","0273-0979","1088-9485","1936-881X"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-2","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bulletin of the American Mathematical Society","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.ams.org/bull/1979-01-03/S0273-0979-1979-14595-6/S0273-0979-1979-14595-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081322539","display_name":"Ivar Ekeland","orcid":"https://orcid.org/0000-0003-3429-6316","observed_orcids":["https://orcid.org/0000-0003-3429-6316"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ivar Ekeland","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5081322539"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":14.4936,"has_fulltext":true,"cited_by_count":1019,"citation_normalized_percentile":{"value":0.99806277,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"1","issue":"3","first_page":"443","last_page":"474"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9829000234603882,"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":0.9829000234603882,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.011800000444054604,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.003000000026077032,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/nonconvex-minimization","display_name":"nonconvex minimization","score":0.968999981880188},{"id":"https://openalex.org/keywords/variational-principle","display_name":"variational principle","score":0.9240000247955322},{"id":"https://openalex.org/keywords/bishop-phelps-theorem","display_name":"Bishop-Phelps theorem","score":0.8989999890327454},{"id":"https://openalex.org/keywords/banach-spaces","display_name":"Banach spaces","score":0.6430000066757202},{"id":"https://openalex.org/keywords/fixed-point-theorems","display_name":"fixed point theorems","score":0.8149999976158142},{"id":"https://openalex.org/keywords/nonlinear-semigroups","display_name":"nonlinear semigroups","score":0.9990000128746033},{"id":"https://openalex.org/keywords/mathematical-programming","display_name":"mathematical programming","score":0.7850000262260437},{"id":"https://openalex.org/keywords/control-theory","display_name":"control theory","score":0.9039999842643738},{"id":"https://openalex.org/keywords/global-analysis","display_name":"global analysis","score":0.7540000081062317},{"id":"https://openalex.org/keywords/convex-cones","display_name":"convex cones","score":0.4729999899864197},{"id":"https://openalex.org/keywords/partial-ordering","display_name":"partial ordering","score":0.6460000276565552},{"id":"https://openalex.org/keywords/transfinite-induction","display_name":"transfinite induction","score":0.6499999761581421}],"concepts":[{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.6416199803352356},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46896636486053467},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4548419713973999},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37520018219947815},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32183560729026794}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0273-0979-1979-14595-6","doi":"https://doi.org/10.1090/s0273-0979-1979-14595-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0273-0979-1979-14595-6","pdf_url":"https://www.ams.org/bull/1979-01-03/S0273-0979-1979-14595-6/S0273-0979-1979-14595-6.pdf","source":{"id":"https://openalex.org/S71584477","display_name":"Bulletin of the American Mathematical Society","issn_l":"0002-9904","issn":["0002-9904","0273-0979","1088-9485","1936-881X"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-2","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bulletin of the American Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.bams/1183544327","doi":null,"is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bams/1183544327","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"}],"best_oa_location":{"id":"doi:10.1090/s0273-0979-1979-14595-6","doi":"https://doi.org/10.1090/s0273-0979-1979-14595-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0273-0979-1979-14595-6","pdf_url":"https://www.ams.org/bull/1979-01-03/S0273-0979-1979-14595-6/S0273-0979-1979-14595-6.pdf","source":{"id":"https://openalex.org/S71584477","display_name":"Bulletin of the American Mathematical Society","issn_l":"0002-9904","issn":["0002-9904","0273-0979","1088-9485","1936-881X"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-2","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bulletin of the American Mathematical Society","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2139502933.pdf","grobid_xml":"https://content.openalex.org/works/W2139502933.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W176188505","https://openalex.org/W1502786272","https://openalex.org/W1528234719","https://openalex.org/W1540661531","https://openalex.org/W1653619892","https://openalex.org/W1967175421","https://openalex.org/W1977750299","https://openalex.org/W1981760956","https://openalex.org/W1997538328","https://openalex.org/W2000985550","https://openalex.org/W2009256553","https://openalex.org/W2025475099","https://openalex.org/W2028272594","https://openalex.org/W2039031367","https://openalex.org/W2039163213","https://openalex.org/W2039934664","https://openalex.org/W2044470832","https://openalex.org/W2045305277","https://openalex.org/W2059315821","https://openalex.org/W2062097352","https://openalex.org/W2064092523","https://openalex.org/W2066595382","https://openalex.org/W2067243588","https://openalex.org/W2069369032","https://openalex.org/W2076759666","https://openalex.org/W2079365729","https://openalex.org/W2081260926","https://openalex.org/W2085706830","https://openalex.org/W2116598569","https://openalex.org/W2143279738","https://openalex.org/W2334285086","https://openalex.org/W3206777520","https://openalex.org/W4213199372","https://openalex.org/W4239995116"],"related_works":["https://openalex.org/W91790467","https://openalex.org/W2127120924","https://openalex.org/W2016804469","https://openalex.org/W2067743604","https://openalex.org/W2025098779","https://openalex.org/W1998032108","https://openalex.org/W2040676043","https://openalex.org/W2007314881","https://openalex.org/W1969752345","https://openalex.org/W2097854669"],"abstract_inverted_index":{"I.":[0],"The":[1],"central":[2,50],"result":[3,160],"II.The":[4],"weak":[5],"statement":[6,24,35],"A.":[7,25,36],"Fixed":[8],"point":[9],"theorems":[10],"B.":[11,28,41],"Nonlinear":[12],"semigroups":[13],"C.":[14,31],"Optimization":[15],"and":[16,63,117,137,141,165,169,189,211],"control":[17,184],"D.":[18],"Existence":[19],"of":[20,38,47,53,61,71,99,181],"solutions":[21],"III.The":[22],"full":[23],"Mathematical":[26],"programming":[27],"Control":[29],"theory":[30,185],"Calculus":[32],"IV.The":[33],"local":[34],"Geometry":[37],"Banach":[39,77],"spaces":[40],"Global":[42],"analysis":[43],"V.":[44],"By":[45],"way":[46],"conclusion":[48],"I.The":[49],"result.The":[51],"grandfather":[52],"it":[54,113,190],"all":[55],"is":[56,94,191],"the":[57,69,100,120,162,166,205,226,232,236,242],"celebrated":[58],"1961":[59],"theorem":[60],"Bishop":[62],"Phelps":[64],"(see":[65,139,145],"[7],":[66],"[8])":[67],"that":[68,193],"set":[70],"continuous":[72],"linear":[73],"functionals":[74],"on":[75,84,161],"a":[76,85,105,114,122,154,178],"space":[78],"E":[79,93],"which":[80,171],"attain":[81],"their":[82],"maximum":[83],"prescribed":[86],"closed":[87],"convex":[88,107],"bounded":[89],"subset":[90],"X":[91],"c":[92],"norm-dense":[95],"in":[96,103,109,132,153],"\u00a3*.The":[97],"crux":[98],"proof":[101],"lies":[102],"introducing":[104],"certain":[106],"cone":[108],"E,":[110],"associating":[111],"with":[112],"partial":[115],"ordering,":[116],"applying":[118],"to":[119,186,199,216,231],"latter":[121],"transfinite":[123],"induction":[124],"argument":[125,128],"(Zorn's":[126],"lemma).This":[127],"was":[129],"later":[130],"used":[131],"different":[133],"settings":[134],"by":[135,142,219,241],"Brondsted":[136],"Rockafellar":[138],"[9])":[140],"F.":[143],"Browder":[144],"[11]).The":[146],"various":[147,167],"situations":[148],"can":[149],"be":[150,202,229],"adequately":[151],"summarized":[152],"diagram:This":[155],"paper":[156],"surveys":[157],"my":[158],"1972":[159],"variational":[163],"principle":[164],"advances":[168],"applications":[170],"have":[172,213],"been":[173],"registered":[174],"since.They":[175],"stretch":[176],"over":[177],"vast":[179],"field":[180],"mathematics,":[182],"from":[183],"global":[187],"analysis,":[188],"hoped":[192],"every":[194],"mathematician":[195],"will":[196,228],"find":[197],"something":[198],"enjoy.This":[200],"should":[201],"possible,":[203],"because":[204],"ideas":[206],"involved":[207],"are":[208],"quite":[209],"simple,":[210],"I":[212],"tried":[214],"not":[215],"obscure":[217],"them":[218],"too":[220],"technical":[221],"or":[222],"detailed":[223],"an":[224],"exposition;":[225],"reader":[227],"referred":[230],"original":[233],"papers":[234],"for":[235],"more":[237],"peripheral":[238],"lemmas;":[239],"received":[240],"editors":[243],"September":[244],"1,":[245],"1978.":[246]},"counts_by_year":[{"year":2026,"cited_by_count":20},{"year":2025,"cited_by_count":19},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":26},{"year":2022,"cited_by_count":20},{"year":2021,"cited_by_count":31},{"year":2020,"cited_by_count":28},{"year":2019,"cited_by_count":36},{"year":2018,"cited_by_count":31},{"year":2017,"cited_by_count":35},{"year":2016,"cited_by_count":25},{"year":2015,"cited_by_count":26},{"year":2014,"cited_by_count":33},{"year":2013,"cited_by_count":50},{"year":2012,"cited_by_count":36}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2016-06-24T00:00:00"}
