{"id":"https://openalex.org/W2951117356","doi":"https://doi.org/10.1137/18m119759x","title":"The Standard Pessimistic Bilevel Problem","display_name":"The Standard Pessimistic Bilevel Problem","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2951117356","doi":"https://doi.org/10.1137/18m119759x","mag":"2951117356"},"language":"en","primary_location":{"id":"doi:10.1137/18m119759x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m119759x","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11573/1288069","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047792212","display_name":"Lorenzo Lampariello","orcid":"https://orcid.org/0000-0003-4177-3598"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]},{"id":"https://openalex.org/I119003972","display_name":"Roma Tre University","ror":"https://ror.org/05vf0dg29","country_code":"IT","type":"education","lineage":["https://openalex.org/I119003972"]},{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["DE","IT"],"is_corresponding":false,"raw_author_name":"Lorenzo Lampariello","raw_affiliation_strings":["Roma Tre University, Department of Business Studies, Rome, Italy","\\S Institute of Operations Research, Karlsruhe Institute of Technology (KIT), Germany","\\ddagger Sapienza University of Rome, Department of Computer, Control and Management Engineering Antonio Ruberti, Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Roma Tre University, Department of Business Studies, Rome, Italy","institution_ids":["https://openalex.org/I119003972"]},{"raw_affiliation_string":"\\S Institute of Operations Research, Karlsruhe Institute of Technology (KIT), Germany","institution_ids":["https://openalex.org/I102335020"]},{"raw_affiliation_string":"\\ddagger Sapienza University of Rome, Department of Computer, Control and Management Engineering Antonio Ruberti, Rome, Italy","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084019843","display_name":"Simone Sagratella","orcid":"https://orcid.org/0000-0001-5888-1953"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]},{"id":"https://openalex.org/I119003972","display_name":"Roma Tre University","ror":"https://ror.org/05vf0dg29","country_code":"IT","type":"education","lineage":["https://openalex.org/I119003972"]},{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["DE","IT"],"is_corresponding":false,"raw_author_name":"Simone Sagratella","raw_affiliation_strings":["Roma Tre University, Department of Business Studies, Rome, Italy","\\ddagger Sapienza University of Rome, Department of Computer, Control and Management Engineering Antonio Ruberti, Rome, Italy","\\S Institute of Operations Research, Karlsruhe Institute of Technology (KIT), Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Roma Tre University, Department of Business Studies, Rome, Italy","institution_ids":["https://openalex.org/I119003972"]},{"raw_affiliation_string":"\\ddagger Sapienza University of Rome, Department of Computer, Control and Management Engineering Antonio Ruberti, Rome, Italy","institution_ids":["https://openalex.org/I861853513"]},{"raw_affiliation_string":"\\S Institute of Operations Research, Karlsruhe Institute of Technology (KIT), Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052388878","display_name":"Oliver Stein","orcid":"https://orcid.org/0000-0001-9514-6317"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]},{"id":"https://openalex.org/I119003972","display_name":"Roma Tre University","ror":"https://ror.org/05vf0dg29","country_code":"IT","type":"education","lineage":["https://openalex.org/I119003972"]},{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["DE","IT"],"is_corresponding":false,"raw_author_name":"Oliver Stein","raw_affiliation_strings":["Roma Tre University, Department of Business Studies, Rome, Italy","\\S Institute of Operations Research, Karlsruhe Institute of Technology (KIT), Germany","\\ddagger Sapienza University of Rome, Department of Computer, Control and Management Engineering Antonio Ruberti, Rome, Italy"],"raw_orcid":"https://orcid.org/0000-0001-9514-6317","affiliations":[{"raw_affiliation_string":"Roma Tre University, Department of Business Studies, Rome, Italy","institution_ids":["https://openalex.org/I119003972"]},{"raw_affiliation_string":"\\S Institute of Operations Research, Karlsruhe Institute of Technology (KIT), Germany","institution_ids":["https://openalex.org/I102335020"]},{"raw_affiliation_string":"\\ddagger Sapienza University of Rome, Department of Computer, Control and Management Engineering Antonio Ruberti, Rome, Italy","institution_ids":["https://openalex.org/I861853513"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0215,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.87891912,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"29","issue":"2","first_page":"1634","last_page":"1656"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9990000128746033,"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":0.9990000128746033,"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/T12137","display_name":"Economic theories and models","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9847999811172485,"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/bilevel-optimization","display_name":"Bilevel optimization","score":0.9072275161743164},{"id":"https://openalex.org/keywords/infimum-and-supremum","display_name":"Infimum and supremum","score":0.842984139919281},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7017338275909424},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6421303153038025},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.5466558933258057},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.49362337589263916},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.4815700054168701},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.46386685967445374},{"id":"https://openalex.org/keywords/pessimism","display_name":"Pessimism","score":0.43126043677330017},{"id":"https://openalex.org/keywords/complementarity-theory","display_name":"Complementarity theory","score":0.4226230978965759},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.422112375497818},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.412430077791214},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.337831974029541},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.1193067729473114},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0843428373336792}],"concepts":[{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.9072275161743164},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.842984139919281},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7017338275909424},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6421303153038025},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.5466558933258057},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.49362337589263916},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.4815700054168701},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.46386685967445374},{"id":"https://openalex.org/C9992130","wikidata":"https://www.wikidata.org/wiki/Q484954","display_name":"Pessimism","level":2,"score":0.43126043677330017},{"id":"https://openalex.org/C85404239","wikidata":"https://www.wikidata.org/wiki/Q5156417","display_name":"Complementarity theory","level":3,"score":0.4226230978965759},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.422112375497818},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.412430077791214},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.337831974029541},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.1193067729473114},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0843428373336792},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/18m119759x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m119759x","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:iris.uniroma1.it:11573/1288069","is_oa":true,"landing_page_url":"http://hdl.handle.net/11573/1288069","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.uniroma3.it:11590/356157","is_oa":true,"landing_page_url":"http://hdl.handle.net/11590/356157","pdf_url":null,"source":{"id":"https://openalex.org/S4377196120","display_name":"Iris (Roma Tre University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119003972","host_organization_name":"Roma Tre University","host_organization_lineage":["https://openalex.org/I119003972"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:iris.uniroma1.it:11573/1288069","is_oa":true,"landing_page_url":"http://hdl.handle.net/11573/1288069","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1877448469","display_name":null,"funder_award_id":"34793","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"}],"funders":[{"id":"https://openalex.org/F4320320875","display_name":"Deutscher Akademischer Austauschdienst","ror":"https://ror.org/039djdh30"},{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W119503700","https://openalex.org/W1503428021","https://openalex.org/W1968859249","https://openalex.org/W1974549991","https://openalex.org/W1974632857","https://openalex.org/W1976478782","https://openalex.org/W1977649329","https://openalex.org/W1977794212","https://openalex.org/W1994325510","https://openalex.org/W2002357448","https://openalex.org/W2012888164","https://openalex.org/W2025377957","https://openalex.org/W2028887826","https://openalex.org/W2034550534","https://openalex.org/W2044830700","https://openalex.org/W2047071794","https://openalex.org/W2069577676","https://openalex.org/W2074376561","https://openalex.org/W2088111670","https://openalex.org/W2102686659","https://openalex.org/W2109357498","https://openalex.org/W2159420800","https://openalex.org/W2294679248","https://openalex.org/W2560830503","https://openalex.org/W2570904163","https://openalex.org/W2673442559","https://openalex.org/W2736942756","https://openalex.org/W2745660793","https://openalex.org/W2963899121","https://openalex.org/W3100460810","https://openalex.org/W4205159739","https://openalex.org/W4236123449"],"related_works":["https://openalex.org/W3109055551","https://openalex.org/W2796980109","https://openalex.org/W1107289","https://openalex.org/W2085014864","https://openalex.org/W2350200292","https://openalex.org/W2765841216","https://openalex.org/W2011175430","https://openalex.org/W190854043","https://openalex.org/W2607337407","https://openalex.org/W2599483915"],"abstract_inverted_index":{"Pessimistic":[0],"bilevel":[1,86,99,138],"optimization":[2,14],"problems,":[3,70],"as":[4,63,95,147,149],"do":[5],"optimistic":[6,69,98],"ones,":[7],"possess":[8],"a":[9,31,37,54,96,102,125,184],"structure":[10],"involving":[11],"three":[12],"interrelated":[13],"problems.":[15,59],"Moreover,":[16],"their":[17,161,172],"finite":[18,46],"infima":[19,47],"are":[20,156],"only":[21],"attained":[22],"under":[23],"strong":[24],"conditions.":[25],"We":[26,132,165],"address":[27],"these":[28],"difficulties":[29],"within":[30],"framework":[32],"of":[33,53,56,83,192],"moderate":[34],"assumptions":[35],"and":[36],"perturbation":[38,194],"approach":[39],"which":[40],"allows":[41],"us":[42],"to":[43,160],"approximate":[44],"such":[45],"arbitrarily":[48],"well":[49,148],"by":[50,119],"minimal":[51,163,174],"values":[52,191],"sequence":[55],"solvable":[57],"single-level":[58,126],"To":[60],"this":[61],"end,":[62],"has":[64],"already":[65],"been":[66],"done":[67],"for":[68,71,189],"the":[72,76,80,84,108,135,143,150,167,193],"first":[73],"time":[74],"in":[75,107,115,124,176],"literature":[77],"we":[78,92,181],"introduce":[79],"standard":[81,97,141],"version":[82],"pessimistic":[85,137],"problem.":[87],"For":[88],"its":[89,120,140],"algorithmic":[90],"treatment,":[91],"reformulate":[93],"it":[94],"program":[100,128,152],"with":[101,129,153,158],"two":[103,144],"follower":[104,145],"Nash":[105],"game":[106],"lower":[109],"level.":[110],"The":[111],"latter":[112],"lower-level":[113],"game,":[114,146],"turn,":[116],"is":[117],"replaced":[118],"Karush--Kuhn--Tucker":[121],"conditions,":[122],"resulting":[123],"mathematical":[127,151],"complementarity":[130,154],"constraints.":[131],"prove":[133],"that":[134],"perturbed":[136],"problem,":[139],"version,":[142],"constraints":[155],"equivalent":[157],"respect":[159],"global":[162],"points.":[164],"study":[166],"more":[168],"intricate":[169],"connections":[170],"between":[171],"local":[173],"points":[175],"detail.":[177],"As":[178],"an":[179],"illustration,":[180],"numerically":[182],"solve":[183],"regulator":[185],"problem":[186],"from":[187],"economics":[188],"different":[190],"parameters.":[195]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":6}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}