{"id":"https://openalex.org/W2048223470","doi":"https://doi.org/10.1007/bf01585928","title":"On bilevel programming, Part I: General nonlinear cases","display_name":"On bilevel programming, Part I: General nonlinear cases","publication_year":1995,"publication_date":"1995-10-01","ids":{"openalex":"https://openalex.org/W2048223470","doi":"https://doi.org/10.1007/bf01585928","mag":"2048223470"},"language":"en","primary_location":{"id":"doi:10.1007/bf01585928","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01585928","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","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/A5061973938","display_name":"James E. Falk","orcid":null},"institutions":[{"id":"https://openalex.org/I193531525","display_name":"George Washington University","ror":"https://ror.org/00y4zzh67","country_code":"US","type":"education","lineage":["https://openalex.org/I193531525"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"James E. Falk","raw_affiliation_strings":["Department of Operations Research, School of Engineering and Applied Science, The George Washington University, 20052, Washington, DC, USA","Department of Operations Research, School of Engineering and Applied Science, The George Washington University, Washington, DC, USA 20052#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Operations Research, School of Engineering and Applied Science, The George Washington University, 20052, Washington, DC, USA","institution_ids":["https://openalex.org/I193531525"]},{"raw_affiliation_string":"Department of Operations Research, School of Engineering and Applied Science, The George Washington University, Washington, DC, USA 20052#TAB#","institution_ids":["https://openalex.org/I193531525"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062375227","display_name":"Jiming Liu","orcid":"https://orcid.org/0000-0002-8669-9064"},"institutions":[{"id":"https://openalex.org/I193531525","display_name":"George Washington University","ror":"https://ror.org/00y4zzh67","country_code":"US","type":"education","lineage":["https://openalex.org/I193531525"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jiming Liu","raw_affiliation_strings":["Department of Operations Research, School of Engineering and Applied Science, The George Washington University, 20052, Washington, DC, USA","Department of Operations Research, School of Engineering and Applied Science, The George Washington University, Washington, DC, USA 20052#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Operations Research, School of Engineering and Applied Science, The George Washington University, 20052, Washington, DC, USA","institution_ids":["https://openalex.org/I193531525"]},{"raw_affiliation_string":"Department of Operations Research, School of Engineering and Applied Science, The George Washington University, Washington, DC, USA 20052#TAB#","institution_ids":["https://openalex.org/I193531525"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061973938"],"corresponding_institution_ids":["https://openalex.org/I193531525"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":3.7579,"has_fulltext":false,"cited_by_count":98,"citation_normalized_percentile":{"value":0.93350806,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"70","issue":"1-3","first_page":"47","last_page":"72"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9782999753952026,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9643999934196472,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/subgradient-method","display_name":"Subgradient method","score":0.8960609436035156},{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.8106979131698608},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7627770900726318},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6474869847297668},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6213165521621704},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.6009714603424072},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.588515043258667},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5105165243148804},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.30427199602127075},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17752200365066528}],"concepts":[{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.8960609436035156},{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.8106979131698608},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7627770900726318},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6474869847297668},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6213165521621704},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.6009714603424072},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.588515043258667},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5105165243148804},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.30427199602127075},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17752200365066528},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","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},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf01585928","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01585928","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W84056083","https://openalex.org/W220758854","https://openalex.org/W1572204513","https://openalex.org/W1586015540","https://openalex.org/W1591758562","https://openalex.org/W1607072065","https://openalex.org/W1971405736","https://openalex.org/W1975756369","https://openalex.org/W1977904123","https://openalex.org/W1981068702","https://openalex.org/W1985270863","https://openalex.org/W1993647205","https://openalex.org/W2004568888","https://openalex.org/W2008571296","https://openalex.org/W2030667419","https://openalex.org/W2041928877","https://openalex.org/W2050151464","https://openalex.org/W2050713766","https://openalex.org/W2067547116","https://openalex.org/W2069900289","https://openalex.org/W2071800913","https://openalex.org/W2072026898","https://openalex.org/W2074376561","https://openalex.org/W2077658674","https://openalex.org/W2078101422","https://openalex.org/W2079340989","https://openalex.org/W2079688774","https://openalex.org/W2088809818","https://openalex.org/W2090411045","https://openalex.org/W2113734366","https://openalex.org/W2127587365","https://openalex.org/W2163089608","https://openalex.org/W2218983664","https://openalex.org/W2911911537","https://openalex.org/W3012317737","https://openalex.org/W3106807711","https://openalex.org/W4212912562","https://openalex.org/W4212997115","https://openalex.org/W4294808056"],"related_works":["https://openalex.org/W2892725081","https://openalex.org/W4289490618","https://openalex.org/W2890257643","https://openalex.org/W1495503294","https://openalex.org/W2161149697","https://openalex.org/W2340378315","https://openalex.org/W2131023196","https://openalex.org/W2013038594","https://openalex.org/W2069013992","https://openalex.org/W1604175135"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}