{"id":"https://openalex.org/W4236268295","doi":"https://doi.org/10.1007/978-0-387-74759-0_189","title":"Fractional Programming","display_name":"Fractional Programming","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W4236268295","doi":"https://doi.org/10.1007/978-0-387-74759-0_189"},"language":"en","primary_location":{"id":"doi:10.1007/978-0-387-74759-0_189","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-387-74759-0_189","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/1765/1610","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109373457","display_name":"Hans Frenk","orcid":null},"institutions":[{"id":"https://openalex.org/I913958620","display_name":"Erasmus University Rotterdam","ror":"https://ror.org/057w15z03","country_code":"NL","type":"education","lineage":["https://openalex.org/I913958620"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Hans Frenk","raw_affiliation_strings":["Econometric Institute, Erasmus University, Rotterdam, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Econometric Institute, Erasmus University, Rotterdam, The Netherlands","institution_ids":["https://openalex.org/I913958620"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057911947","display_name":"Siegfried Schaible","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Siegfried Schaible","raw_affiliation_strings":["A.G. Anderson Graduate School of Management, University California, Riverside, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"A.G. Anderson Graduate School of Management, University California, Riverside, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1080","last_page":"1091"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9936000108718872,"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":0.9855999946594238,"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/maximization","display_name":"Maximization","score":0.8678798675537109},{"id":"https://openalex.org/keywords/fractional-programming","display_name":"Fractional programming","score":0.8084619641304016},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6721711158752441},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5172596573829651},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5024559497833252},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.45673489570617676},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.42647111415863037},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.4252590537071228},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.4103962481021881},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3727591335773468},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.1453382670879364},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11288774013519287},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07509997487068176}],"concepts":[{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.8678798675537109},{"id":"https://openalex.org/C169069869","wikidata":"https://www.wikidata.org/wiki/Q5477546","display_name":"Fractional programming","level":4,"score":0.8084619641304016},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6721711158752441},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5172596573829651},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5024559497833252},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.45673489570617676},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.42647111415863037},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.4252590537071228},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.4103962481021881},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3727591335773468},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.1453382670879364},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11288774013519287},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07509997487068176},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-0-387-74759-0_189","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-387-74759-0_189","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"},{"id":"pmh:eur:oai:repub.eur.nl:1610","is_oa":true,"landing_page_url":"http://hdl.handle.net/1765/1610","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/workingpaper"}],"best_oa_location":{"id":"pmh:eur:oai:repub.eur.nl:1610","is_oa":true,"landing_page_url":"http://hdl.handle.net/1765/1610","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/workingpaper"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W27236945","https://openalex.org/W128572285","https://openalex.org/W192247443","https://openalex.org/W972713002","https://openalex.org/W1014849805","https://openalex.org/W1516586564","https://openalex.org/W1560235933","https://openalex.org/W1560727108","https://openalex.org/W1967956032","https://openalex.org/W1972204922","https://openalex.org/W1980908866","https://openalex.org/W1987420866","https://openalex.org/W1996591064","https://openalex.org/W1999218360","https://openalex.org/W2002939850","https://openalex.org/W2004046781","https://openalex.org/W2007081327","https://openalex.org/W2009117714","https://openalex.org/W2012183861","https://openalex.org/W2015249958","https://openalex.org/W2015973352","https://openalex.org/W2021157320","https://openalex.org/W2027029507","https://openalex.org/W2029650406","https://openalex.org/W2040606011","https://openalex.org/W2041854759","https://openalex.org/W2055751565","https://openalex.org/W2061735438","https://openalex.org/W2075978622","https://openalex.org/W2076452041","https://openalex.org/W2078203553","https://openalex.org/W2083333815","https://openalex.org/W2085478109","https://openalex.org/W2091047511","https://openalex.org/W2096652910","https://openalex.org/W2128005148","https://openalex.org/W2153437713","https://openalex.org/W2156155161","https://openalex.org/W2156577211","https://openalex.org/W2166660920","https://openalex.org/W2217406716","https://openalex.org/W2612631257","https://openalex.org/W4210963865","https://openalex.org/W4238194826","https://openalex.org/W4239992743","https://openalex.org/W4242335201","https://openalex.org/W4248623816","https://openalex.org/W4253679144","https://openalex.org/W4254629716"],"related_works":["https://openalex.org/W2802888879","https://openalex.org/W2900864464","https://openalex.org/W103185312","https://openalex.org/W972713002","https://openalex.org/W2475480881","https://openalex.org/W1999162784","https://openalex.org/W2121723556","https://openalex.org/W2288977275","https://openalex.org/W54727051","https://openalex.org/W2361430738"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}
