{"id":"https://openalex.org/W2041348403","doi":"https://doi.org/10.1111/j.1475-3995.2009.00743.x","title":"Lagrangean decompositions for the unconstrained binary quadratic programming problem","display_name":"Lagrangean decompositions for the unconstrained binary quadratic programming problem","publication_year":2009,"publication_date":"2009-12-04","ids":{"openalex":"https://openalex.org/W2041348403","doi":"https://doi.org/10.1111/j.1475-3995.2009.00743.x","mag":"2041348403"},"language":"en","primary_location":{"id":"doi:10.1111/j.1475-3995.2009.00743.x","is_oa":false,"landing_page_url":"https://doi.org/10.1111/j.1475-3995.2009.00743.x","pdf_url":null,"source":{"id":"https://openalex.org/S267729","display_name":"International Transactions in Operational Research","issn_l":"0969-6016","issn":["0969-6016","1475-3995"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Transactions in Operational Research","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/A5012650166","display_name":"Geraldo Regis Mauri","orcid":"https://orcid.org/0000-0002-8393-7741"},"institutions":[{"id":"https://openalex.org/I51235708","display_name":"Universidade Federal do Esp\u00edrito Santo","ror":"https://ror.org/05sxf4h28","country_code":"BR","type":"education","lineage":["https://openalex.org/I51235708"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Geraldo Regis Mauri","raw_affiliation_strings":["Center for Agrarian Sciences, Federal University of Espi\u0301rito Santo \u2013 UFES, PO Box 16, 29.500-000, Alegre - ES, BrazilE-mail: [email protected]","Center for Agrarian Sciences, Federal University of Esp\u00edrito Santo \u2013 UFES, PO Box 16, 29.500\u2010000, Alegre \u2010 ES, Brazil\u2028"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Agrarian Sciences, Federal University of Espi\u0301rito Santo \u2013 UFES, PO Box 16, 29.500-000, Alegre - ES, BrazilE-mail: [email protected]","institution_ids":["https://openalex.org/I51235708"]},{"raw_affiliation_string":"Center for Agrarian Sciences, Federal University of Esp\u00edrito Santo \u2013 UFES, PO Box 16, 29.500\u2010000, Alegre \u2010 ES, Brazil\u2028","institution_ids":["https://openalex.org/I51235708"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068445974","display_name":"Luiz Ant\u00f4nio Nogueira Lorena","orcid":"https://orcid.org/0000-0003-2043-1441"},"institutions":[{"id":"https://openalex.org/I80849659","display_name":"Instituto Nacional de Pesquisas Espaciais","ror":"https://ror.org/04xbn6x09","country_code":"BR","type":"facility","lineage":["https://openalex.org/I4210151455","https://openalex.org/I80849659"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Luiz Antonio Nogueira Lorena","raw_affiliation_strings":["E-mail: Laboratory for Computing and Applied Mathematics, National Institute for Space Research \u2013 INPE, PO Box 515, 12.227-010, Sa\u0303o Jose\u0301 dos Campos - SP, Brazil. [email protected]","E-mail: Laboratory for Computing and Applied Mathematics, National Institute for Space Research \u2013 INPE, PO Box 515, 12.227-010, S\u00e3o Jos\u00e9 dos Campos - SP, Brazil. lorena@lac.inpe.br"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"E-mail: Laboratory for Computing and Applied Mathematics, National Institute for Space Research \u2013 INPE, PO Box 515, 12.227-010, Sa\u0303o Jose\u0301 dos Campos - SP, Brazil. [email protected]","institution_ids":["https://openalex.org/I80849659"]},{"raw_affiliation_string":"E-mail: Laboratory for Computing and Applied Mathematics, National Institute for Space Research \u2013 INPE, PO Box 515, 12.227-010, S\u00e3o Jos\u00e9 dos Campos - SP, Brazil. lorena@lac.inpe.br","institution_ids":["https://openalex.org/I80849659"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012650166","https://openalex.org/A5068445974"],"corresponding_institution_ids":["https://openalex.org/I51235708","https://openalex.org/I80849659"],"apc_list":{"value":3660,"currency":"USD","value_usd":3660},"apc_paid":null,"fwci":0.4099,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.63465608,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"18","issue":"2","first_page":"257","last_page":"270"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994000196456909,"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/T12176","display_name":"Optimization and Packing Problems","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9980000257492065,"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/subgradient-method","display_name":"Subgradient method","score":0.8266990780830383},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.7571501731872559},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6420226693153381},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.6083316206932068},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5811269283294678},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5777192115783691},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.47807741165161133},{"id":"https://openalex.org/keywords/quadratic-unconstrained-binary-optimization","display_name":"Quadratic unconstrained binary optimization","score":0.4773573875427246},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4311738908290863},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42609724402427673},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3351357579231262},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14118099212646484}],"concepts":[{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.8266990780830383},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.7571501731872559},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6420226693153381},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6083316206932068},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5811269283294678},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5777192115783691},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.47807741165161133},{"id":"https://openalex.org/C177179195","wikidata":"https://www.wikidata.org/wiki/Q7268372","display_name":"Quadratic unconstrained binary optimization","level":4,"score":0.4773573875427246},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4311738908290863},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42609724402427673},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3351357579231262},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14118099212646484},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"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/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1111/j.1475-3995.2009.00743.x","is_oa":false,"landing_page_url":"https://doi.org/10.1111/j.1475-3995.2009.00743.x","pdf_url":null,"source":{"id":"https://openalex.org/S267729","display_name":"International Transactions in Operational Research","issn_l":"0969-6016","issn":["0969-6016","1475-3995"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Transactions in Operational Research","raw_type":"journal-article"},{"id":"pmh:oai:urlib.net:dpi.inpe.br/plutao/2011/06.11.14.44.17-0","is_oa":false,"landing_page_url":"http://urlib.net/J8LNKAN8RW/39RSFH3","pdf_url":null,"source":{"id":"https://openalex.org/S4377196298","display_name":"Biblioteca Digital da Mem\u00f3ria Cient\u00edfica do INPE (National Institute for Space Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I80849659","host_organization_name":"Instituto Nacional de Pesquisas Espaciais","host_organization_lineage":["https://openalex.org/I80849659"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.5899999737739563}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W197491803","https://openalex.org/W1501516191","https://openalex.org/W1992162584","https://openalex.org/W2004951603","https://openalex.org/W2007500789","https://openalex.org/W2008389133","https://openalex.org/W2020567423","https://openalex.org/W2026973340","https://openalex.org/W2035758901","https://openalex.org/W2037033044","https://openalex.org/W2050274364","https://openalex.org/W2050336256","https://openalex.org/W2054297043","https://openalex.org/W2057884923","https://openalex.org/W2058748455","https://openalex.org/W2060252799","https://openalex.org/W2065941671","https://openalex.org/W2071702553","https://openalex.org/W2082603400","https://openalex.org/W2115910554","https://openalex.org/W2122604873","https://openalex.org/W2126662731","https://openalex.org/W2135187522","https://openalex.org/W2167700392","https://openalex.org/W4211250195","https://openalex.org/W4243118528"],"related_works":["https://openalex.org/W2962988543","https://openalex.org/W2582746905","https://openalex.org/W3036464408","https://openalex.org/W2020990755","https://openalex.org/W2377851227","https://openalex.org/W4293088966","https://openalex.org/W2366868484","https://openalex.org/W2917463375","https://openalex.org/W2142369290","https://openalex.org/W2155219672"],"abstract_inverted_index":{"The":[0,36,73,98],"unconstrained":[1],"binary":[2,22,42],"quadratic":[3,15],"programming":[4],"problem":[5,11,65],"(QP)":[6],"is":[7,56,67],"a":[8,14,18,40,52,63,70,87],"classical":[9],"non-linear":[10],"of":[12,21,46,60,103],"optimizing":[13],"objective":[16],"by":[17,51,69,76,82,91],"suitable":[19],"choice":[20],"decision":[23],"variables.":[24],"This":[25,54],"paper":[26],"proposes":[27],"new":[28],"Lagrangean":[29,109],"decompositions":[30],"to":[31],"find":[32],"bounds":[33],"for":[34],"QP.":[35],"methods":[37,106,113],"presented":[38],"treat":[39],"mixed":[41],"linear":[43],"version":[44],"(LQP)":[45],"QP":[47],"with":[48,95],"constraints":[49],"represented":[50],"graph.":[53],"graph":[55],"partitioned":[57],"into":[58],"clusters":[59],"vertices":[61],"forming":[62],"dual":[64],"that":[66],"solved":[68,81],"subgradient":[71],"algorithm.":[72],"subproblems":[74],"formed":[75,90],"the":[77,101,104,116],"generated":[78],"subgraphs":[79],"are":[80],"CPLEX.":[83],"Computational":[84],"experiments":[85],"consider":[86],"data":[88],"set":[89],"several":[92],"difficult":[93],"instances":[94],"different":[96],"features.":[97],"results":[99],"show":[100],"efficiency":[102],"proposed":[105],"over":[107],"traditional":[108],"relaxations":[110],"and":[111],"other":[112],"found":[114],"in":[115],"literature.":[117]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}