{"id":"https://openalex.org/W2001352154","doi":"https://doi.org/10.1080/02331931003596725","title":"Optimality results for a specific bilevel optimization problem","display_name":"Optimality results for a specific bilevel optimization problem","publication_year":2011,"publication_date":"2011-06-03","ids":{"openalex":"https://openalex.org/W2001352154","doi":"https://doi.org/10.1080/02331931003596725","mag":"2001352154"},"language":"en","primary_location":{"id":"doi:10.1080/02331931003596725","doi":"https://doi.org/10.1080/02331931003596725","is_oa":false,"landing_page_url":"https://doi.org/10.1080/02331931003596725","pdf_url":null,"source":{"id":"https://openalex.org/S158016561","display_name":"Optimization","issn_l":"0233-1934","issn":["0233-1934","1026-7662","1029-4945"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-c","cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization","raw_type":"journal-article"},"volume":null,"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/A5042389109","display_name":"Stephan Dempe","orcid":"https://orcid.org/0000-0001-6344-5152","observed_orcids":["https://orcid.org/0000-0001-6344-5152"]},"institutions":[{"id":"https://openalex.org/I61893789","display_name":"TU Bergakademie Freiberg","ror":"https://ror.org/031vc2293","country_code":"DE","type":"education","lineage":["https://openalex.org/I61893789"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"S. Dempe","raw_affiliation_strings":["Mathematik and Informatik, TU Bergakademie Freiberg, Freiberg, Germany","Mathematik and Informatik, TU Bergakademie Freiberg , Freiberg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematik and Informatik, TU Bergakademie Freiberg, Freiberg, Germany","institution_ids":["https://openalex.org/I61893789"]},{"raw_affiliation_string":"Mathematik and Informatik, TU Bergakademie Freiberg , Freiberg, Germany","institution_ids":["https://openalex.org/I61893789"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048932469","display_name":"Nazih Abderrazzak Gadhi","orcid":"https://orcid.org/0000-0001-6752-2709","observed_orcids":["https://orcid.org/0000-0001-6752-2709"]},"institutions":[{"id":"https://openalex.org/I81605866","display_name":"Sidi Mohamed Ben Abdellah University","ror":"https://ror.org/04efg9a07","country_code":"MA","type":"education","lineage":["https://openalex.org/I81605866"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"N. Gadhi","raw_affiliation_strings":["Department of Mathematics, Dhar El Mehrez, Sidi Mohamed Ben Abdellah University, Fes, Morocco","Department of Mathematics, Dhar El Mehrez Sidi Mohamed Ben Abdellah University, Fes, Morocco;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Dhar El Mehrez, Sidi Mohamed Ben Abdellah University, Fes, Morocco","institution_ids":["https://openalex.org/I81605866"]},{"raw_affiliation_string":"Department of Mathematics, Dhar El Mehrez Sidi Mohamed Ben Abdellah University, Fes, Morocco;","institution_ids":["https://openalex.org/I81605866"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042389109"],"corresponding_institution_ids":["https://openalex.org/I61893789"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.09645265,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":94},"biblio":{"volume":"60","issue":"7","first_page":"813","last_page":"822"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9994999766349792,"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":0.9994999766349792,"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":0.0,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.0,"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/bi-level-optimization","display_name":"bi-level optimization","score":0.9929999709129333},{"id":"https://openalex.org/keywords/necessary-optimality-conditions","display_name":"necessary optimality conditions","score":0.9729999899864197},{"id":"https://openalex.org/keywords/variational-analysis","display_name":"variational analysis","score":0.7850000262260437},{"id":"https://openalex.org/keywords/nonsmooth-optimization","display_name":"nonsmooth optimization","score":0.7820000052452087},{"id":"https://openalex.org/keywords/mangasarian-fromovitz-constraint-qualification","display_name":"Mangasarian-Fromovitz constraint qualification","score":0.8820000290870667},{"id":"https://openalex.org/keywords/lower-level-problem","display_name":"lower level problem","score":0.6840000152587891}],"concepts":[{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.783481240272522},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7333559989929199},{"id":"https://openalex.org/C2778712213","wikidata":"https://www.wikidata.org/wiki/Q20740046","display_name":"Calmness","level":2,"score":0.7215853333473206},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6381314992904663},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5644021034240723},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5110477209091187},{"id":"https://openalex.org/C523394659","wikidata":"https://www.wikidata.org/wiki/Q17086892","display_name":"Variational analysis","level":2,"score":0.46974045038223267},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.43712836503982544},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3958035707473755},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.31152260303497314},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2029096782207489},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08904415369033813},{"id":"https://openalex.org/C118552586","wikidata":"https://www.wikidata.org/wiki/Q7867","display_name":"Psychiatry","level":1,"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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/02331931003596725","doi":"https://doi.org/10.1080/02331931003596725","is_oa":false,"landing_page_url":"https://doi.org/10.1080/02331931003596725","pdf_url":null,"source":{"id":"https://openalex.org/S158016561","display_name":"Optimization","issn_l":"0233-1934","issn":["0233-1934","1026-7662","1029-4945"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-c","cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1563534836","https://openalex.org/W1582299569","https://openalex.org/W1601960826","https://openalex.org/W1983644172","https://openalex.org/W2007679787","https://openalex.org/W2015317001","https://openalex.org/W2035317043","https://openalex.org/W2063909906","https://openalex.org/W2076094660","https://openalex.org/W2082990205","https://openalex.org/W2150459262","https://openalex.org/W2153562582","https://openalex.org/W3157341860"],"related_works":["https://openalex.org/W2997066415","https://openalex.org/W4391210806","https://openalex.org/W2796088210","https://openalex.org/W2102686659","https://openalex.org/W2801758777","https://openalex.org/W2890257643","https://openalex.org/W1495503294","https://openalex.org/W2161149697","https://openalex.org/W2126813526","https://openalex.org/W2131023196"],"abstract_inverted_index":{"We":[0],"develop":[1],"necessary":[2],"optimality":[3,56,131],"conditions":[4,38,57],"using":[5],"techniques":[6],"from":[7],"variational":[8],"analysis":[9],"for":[10,39,58],"a":[11,71],"bilevel":[12,40,59],"optimization":[13],"problem":[14,19,69],"without":[15],"assuming":[16],"the":[17,22,28,68,79],"lower-level":[18],"satisfying":[20],"neither":[21],"Mangasarian":[23],"Fromovitz":[24],"constraint":[25],"qualification":[26],"nor":[27],"partial":[29],"calmness":[30],"condition":[31],"[D.L.":[32],"Ye":[33,49],"and":[34,50,74,87,109,129],"D.L.":[35],"Zhu,":[36,52],"Optimality":[37],"programming":[41,60],"problems,":[42,61],"Optimization":[43,62],"33":[44],"(1995),":[45],"pp.":[46,65],"9\u201327;":[47],"J.J.":[48,51],"A":[53],"note":[54],"on":[55],"39":[63],"(1997),":[64],"361\u2013366].":[66],"Reducing":[67],"into":[70],"one-level":[72],"nonlinear":[73],"nonsmooth":[75],"programme,":[76],"we":[77],"use":[78],"approximate":[80],"extremal":[81],"principle":[82],"[B.S.":[83],"Mordukhovich,":[84,106],"Variational":[85,107],"Analysis":[86,108],"Generalized":[88,110],"Differentiation:":[89,111],"I.":[90],"Basic":[91],"Theory,":[92],"Grundlehren":[93,114],"Series,":[94,115],"Fundamental":[95,116],"Principles":[96,117],"of":[97,118],"Mathematical":[98,119],"Sciences,":[99,120],"Vol.":[100,121],"330,":[101],"Springer,":[102,123],"Berlin,":[103,124],"2006;":[104],"B.S.":[105],"II.":[112],"Applications,":[113],"331,":[122],"2006]":[125],"to":[126],"get":[127],"fuzzy":[128],"exact":[130],"conditions.":[132]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}
