{"id":"https://openalex.org/W4299895957","doi":"https://doi.org/10.1007/978-0-387-74759-0_47","title":"Bilevel Programming: Optimality Conditions and Duality","display_name":"Bilevel Programming: Optimality Conditions and Duality","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W4299895957","doi":"https://doi.org/10.1007/978-0-387-74759-0_47"},"language":"en","primary_location":{"id":"doi:10.1007/978-0-387-74759-0_47","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-387-74759-0_47","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":"reference-entry","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/A5046096217","display_name":"S. Zlobec","orcid":null},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Sanjo Zlobec","raw_affiliation_strings":["Department Math. Statist., McGill University, Montreal, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department Math. Statist., McGill University, Montreal, Canada","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5046096217"],"corresponding_institution_ids":["https://openalex.org/I5023651"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"274","last_page":"279"},"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9962000250816345,"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"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.85224449634552},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.7422263622283936},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.48381108045578003},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4229903519153595},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3976695239543915},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.39023980498313904},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16813170909881592},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.13272133469581604}],"concepts":[{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.85224449634552},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.7422263622283936},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.48381108045578003},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4229903519153595},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3976695239543915},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.39023980498313904},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16813170909881592},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.13272133469581604}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-0-387-74759-0_47","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-387-74759-0_47","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W63858031","https://openalex.org/W120321778","https://openalex.org/W158987826","https://openalex.org/W187928793","https://openalex.org/W568537268","https://openalex.org/W1490629706","https://openalex.org/W1513869646","https://openalex.org/W1523483560","https://openalex.org/W1590137327","https://openalex.org/W1969100915","https://openalex.org/W1969368779","https://openalex.org/W1982335532","https://openalex.org/W1983644172","https://openalex.org/W1985961576","https://openalex.org/W1990676004","https://openalex.org/W1997364884","https://openalex.org/W1999339345","https://openalex.org/W2001759562","https://openalex.org/W2005629858","https://openalex.org/W2008816206","https://openalex.org/W2014457744","https://openalex.org/W2015308984","https://openalex.org/W2024247801","https://openalex.org/W2029031872","https://openalex.org/W2033573391","https://openalex.org/W2035317043","https://openalex.org/W2058386292","https://openalex.org/W2058958838","https://openalex.org/W2068554647","https://openalex.org/W2068965009","https://openalex.org/W2072026898","https://openalex.org/W2079173630","https://openalex.org/W2095196162","https://openalex.org/W2095818975","https://openalex.org/W2118880851","https://openalex.org/W2150459262","https://openalex.org/W2167013561","https://openalex.org/W2173106774","https://openalex.org/W2342128024","https://openalex.org/W2494622204"],"related_works":["https://openalex.org/W147717802","https://openalex.org/W3157915181","https://openalex.org/W3044651776","https://openalex.org/W2952112154","https://openalex.org/W2980244552","https://openalex.org/W2137432509","https://openalex.org/W2748939420","https://openalex.org/W3156469768","https://openalex.org/W2107490282","https://openalex.org/W1970596092"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2025-10-10T00:00:00"}