{"id":"https://openalex.org/W2769907661","doi":"https://doi.org/10.1007/978-0-387-74759-0_176","title":"Farkas Lemma: Generalizations","display_name":"Farkas Lemma: Generalizations","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2769907661","doi":"https://doi.org/10.1007/978-0-387-74759-0_176","mag":"2769907661"},"language":"en","primary_location":{"id":"doi:10.1007/978-0-387-74759-0_176","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-387-74759-0_176","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/A5026027785","display_name":"V. Jeyakumar","orcid":"https://orcid.org/0000-0003-0267-7800"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"V. Jeyakumar","raw_affiliation_strings":["School of Math., University New South Wales, Sydney, Australia"],"affiliations":[{"raw_affiliation_string":"School of Math., University New South Wales, Sydney, Australia","institution_ids":["https://openalex.org/I31746571"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026027785"],"corresponding_institution_ids":["https://openalex.org/I31746571"],"apc_list":null,"apc_paid":null,"fwci":5.0199,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.95513779,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"998","last_page":"1001"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9987000226974487,"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":0.9799000024795532,"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/lemma","display_name":"Lemma (botany)","score":0.7570885419845581},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5214940309524536},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36450469493865967},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.036686480045318604}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.7570885419845581},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5214940309524536},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36450469493865967},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.036686480045318604},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-0-387-74759-0_176","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-387-74759-0_176","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":26,"referenced_works":["https://openalex.org/W90601795","https://openalex.org/W179438227","https://openalex.org/W1974461145","https://openalex.org/W1985040464","https://openalex.org/W1990600811","https://openalex.org/W1996191470","https://openalex.org/W2006133663","https://openalex.org/W2008096467","https://openalex.org/W2009285839","https://openalex.org/W2030255992","https://openalex.org/W2037005512","https://openalex.org/W2049020833","https://openalex.org/W2059800021","https://openalex.org/W2065726477","https://openalex.org/W2069235686","https://openalex.org/W2075763272","https://openalex.org/W2081027419","https://openalex.org/W2087446297","https://openalex.org/W2098557421","https://openalex.org/W2109523503","https://openalex.org/W2146187364","https://openalex.org/W3152358675","https://openalex.org/W4206300570","https://openalex.org/W4245281898","https://openalex.org/W4251167060","https://openalex.org/W4396738453"],"related_works":["https://openalex.org/W2029026024","https://openalex.org/W2112445562","https://openalex.org/W1810718089","https://openalex.org/W2972930899","https://openalex.org/W2092794327","https://openalex.org/W2329424818","https://openalex.org/W2010920722","https://openalex.org/W2509175274","https://openalex.org/W2017840005","https://openalex.org/W2032611290"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
