{"id":"https://openalex.org/W4301742200","doi":"https://doi.org/10.1007/978-0-387-74759-0_37","title":"Bilevel Linear Programming: Complexity, Equivalence to Minmax, Concave Programs","display_name":"Bilevel Linear Programming: Complexity, Equivalence to Minmax, Concave Programs","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W4301742200","doi":"https://doi.org/10.1007/978-0-387-74759-0_37"},"language":"en","primary_location":{"id":"doi:10.1007/978-0-387-74759-0_37","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-387-74759-0_37","pdf_url":null,"source":{"id":"https://openalex.org/S4306509378","display_name":"Encyclopedia of Optimization","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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Encyclopedia of Optimization","raw_type":"book-chapter"},"type":"book-chapter","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/A5020565600","display_name":"Jonathan F. Bard","orcid":"https://orcid.org/0000-0001-8569-0909"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jonathan F. Bard","raw_affiliation_strings":["University Texas, Austin, USA"],"affiliations":[{"raw_affiliation_string":"University Texas, Austin, USA","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5020565600"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.73785282,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"225","last_page":"228"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9984999895095825,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9980999827384949,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9962000250816345,"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/minimax","display_name":"Minimax","score":0.7812381982803345},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.68577641248703},{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.6430697441101074},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5278947949409485},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4537031352519989},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.434231698513031},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40622809529304504},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.22973260283470154},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.06441468000411987}],"concepts":[{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.7812381982803345},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.68577641248703},{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.6430697441101074},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5278947949409485},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4537031352519989},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.434231698513031},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40622809529304504},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.22973260283470154},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.06441468000411987}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-0-387-74759-0_37","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-387-74759-0_37","pdf_url":null,"source":{"id":"https://openalex.org/S4306509378","display_name":"Encyclopedia of Optimization","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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Encyclopedia of Optimization","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W134337900","https://openalex.org/W1601972095","https://openalex.org/W2011039300","https://openalex.org/W2015317001","https://openalex.org/W2023858465","https://openalex.org/W2042943043","https://openalex.org/W2078101422","https://openalex.org/W2079104779","https://openalex.org/W2095818975","https://openalex.org/W4210890186"],"related_works":["https://openalex.org/W2382771378","https://openalex.org/W2134347795","https://openalex.org/W1964676846","https://openalex.org/W2347710506","https://openalex.org/W2955289704","https://openalex.org/W2509610490","https://openalex.org/W4291289303","https://openalex.org/W2338800359","https://openalex.org/W2769655742","https://openalex.org/W2296225057"],"abstract_inverted_index":null,"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
