{"id":"https://openalex.org/W2019325857","doi":"https://doi.org/10.1137/050646378","title":"A Vector Labeling Method for Solving Discrete Zero Point and Complementarity Problems","display_name":"A Vector Labeling Method for Solving Discrete Zero Point and Complementarity Problems","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2019325857","doi":"https://doi.org/10.1137/050646378","mag":"2019325857"},"language":"en","primary_location":{"id":"doi:10.1137/050646378","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050646378","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","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/A5111370594","display_name":"Gerard van der Laan","orcid":null},"institutions":[{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Gerard van der Laan","raw_affiliation_strings":["Vrije Universiteit Amsterdam ,"],"affiliations":[{"raw_affiliation_string":"Vrije Universiteit Amsterdam ,","institution_ids":["https://openalex.org/I865915315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111422428","display_name":"Dolf Talman","orcid":null},"institutions":[{"id":"https://openalex.org/I193700539","display_name":"Tilburg University","ror":"https://ror.org/04b8v1s79","country_code":"NL","type":"education","lineage":["https://openalex.org/I193700539"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Dolf Talman","raw_affiliation_strings":["(Tilburg University)"],"affiliations":[{"raw_affiliation_string":"(Tilburg University)","institution_ids":["https://openalex.org/I193700539"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087515779","display_name":"Zaifu Yang","orcid":"https://orcid.org/0000-0002-3265-7109"},"institutions":[{"id":"https://openalex.org/I180203408","display_name":"Yokohama National University","ror":"https://ror.org/03zyp6p76","country_code":"JP","type":"education","lineage":["https://openalex.org/I180203408"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Zaifu Yang","raw_affiliation_strings":["Yokohama National University,,,,,"],"affiliations":[{"raw_affiliation_string":"Yokohama National University,,,,,","institution_ids":["https://openalex.org/I180203408"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5111370594"],"corresponding_institution_ids":["https://openalex.org/I865915315"],"apc_list":null,"apc_paid":null,"fwci":5.003,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.95474138,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"1","first_page":"290","last_page":"308"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.97079998254776,"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":0.97079998254776,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9362000226974487,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9358999729156494,"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/mathematics","display_name":"Mathematics","score":0.8049354553222656},{"id":"https://openalex.org/keywords/nonlinear-complementarity-problem","display_name":"Nonlinear complementarity problem","score":0.7667515277862549},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.6325909495353699},{"id":"https://openalex.org/keywords/complementarity-theory","display_name":"Complementarity theory","score":0.6035991907119751},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5259062051773071},{"id":"https://openalex.org/keywords/antipodal-point","display_name":"Antipodal point","score":0.5221448540687561},{"id":"https://openalex.org/keywords/lexicographical-order","display_name":"Lexicographical order","score":0.513801634311676},{"id":"https://openalex.org/keywords/mixed-complementarity-problem","display_name":"Mixed complementarity problem","score":0.43103495240211487},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.42795905470848083},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.420693963766098},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4203590750694275},{"id":"https://openalex.org/keywords/integer-lattice","display_name":"Integer lattice","score":0.4196156859397888},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.401007741689682},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3338191509246826},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11922332644462585}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8049354553222656},{"id":"https://openalex.org/C2778646529","wikidata":"https://www.wikidata.org/wiki/Q16948724","display_name":"Nonlinear complementarity problem","level":4,"score":0.7667515277862549},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.6325909495353699},{"id":"https://openalex.org/C85404239","wikidata":"https://www.wikidata.org/wiki/Q5156417","display_name":"Complementarity theory","level":3,"score":0.6035991907119751},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5259062051773071},{"id":"https://openalex.org/C70943382","wikidata":"https://www.wikidata.org/wiki/Q505356","display_name":"Antipodal point","level":2,"score":0.5221448540687561},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.513801634311676},{"id":"https://openalex.org/C77196050","wikidata":"https://www.wikidata.org/wiki/Q6883962","display_name":"Mixed complementarity problem","level":3,"score":0.43103495240211487},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.42795905470848083},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.420693963766098},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4203590750694275},{"id":"https://openalex.org/C142885752","wikidata":"https://www.wikidata.org/wiki/Q1252145","display_name":"Integer lattice","level":3,"score":0.4196156859397888},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.401007741689682},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3338191509246826},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11922332644462585},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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},{"id":"https://openalex.org/C56863137","wikidata":"https://www.wikidata.org/wiki/Q743139","display_name":"Half-integer","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/050646378","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050646378","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:research.vu.nl:publications/49b7434b-1245-4419-89ed-5beb2a3879c2","is_oa":false,"landing_page_url":"https://hdl.handle.net/1871.1/49b7434b-1245-4419-89ed-5beb2a3879c2","pdf_url":null,"source":{"id":"https://openalex.org/S4306400546","display_name":"Digital Academic REpository of VU University Amsterdam (Vrije Universiteit Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"van der Laan, G, Talman, A J J & Yang, Z 2007, 'A vector labeling method for solving discrete zero point and complementarity problems', SIAM Journal on Optimization, vol. 18, pp. 290-308. https://doi.org/10.1137/050646378","raw_type":"article"},{"id":"pmh:vu:oai:research.vu.nl:publications/49b7434b-1245-4419-89ed-5beb2a3879c2","is_oa":false,"landing_page_url":"https://research.vu.nl/en/publications/49b7434b-1245-4419-89ed-5beb2a3879c2","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Optimization, 18, 290 - 308. Society for Industrial and Applied Mathematics Publications","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W170333011","https://openalex.org/W1983932475","https://openalex.org/W1990792759","https://openalex.org/W1994967371","https://openalex.org/W2000151369","https://openalex.org/W2013303693","https://openalex.org/W2016401302","https://openalex.org/W2035436991","https://openalex.org/W2036062917","https://openalex.org/W2039270674","https://openalex.org/W2060186712","https://openalex.org/W2061316930","https://openalex.org/W2064119669","https://openalex.org/W2070994188","https://openalex.org/W2085612614","https://openalex.org/W2096324943","https://openalex.org/W2097386942","https://openalex.org/W2136541377","https://openalex.org/W2142363911","https://openalex.org/W2152122625","https://openalex.org/W2153961011","https://openalex.org/W2325955172","https://openalex.org/W3123022539","https://openalex.org/W3124527955"],"related_works":["https://openalex.org/W2085004531","https://openalex.org/W4294529879","https://openalex.org/W2384374169","https://openalex.org/W2376754743","https://openalex.org/W2351774575","https://openalex.org/W1553741403","https://openalex.org/W2358347443","https://openalex.org/W2157124849","https://openalex.org/W2903124446","https://openalex.org/W2347608783"],"abstract_inverted_index":{"In":[0,111],"this":[1],"paper":[2],"we":[3],"establish":[4],"the":[5,16,22,34,37,79,114,127,130,136],"existence":[6,120],"of":[7,12,36,92],"a":[8,13,45,50,88,93,96,103,106,118],"discrete":[9,89,107,131],"zero":[10,90],"point":[11,91],"function":[14,94],"from":[15],"n\u2010dimensional":[17,23],"integer":[18],"lattice":[19],"$\\mathbb{Z}^n$":[20],"to":[21,33,68,77,86,101,105,140],"Euclidean":[24],"space":[25],"$\\mathbb{R}^n$":[26],"under":[27,95],"very":[28],"general":[29,97],"conditions":[30],"with":[31,53],"respect":[32],"behavior":[35],"function.":[38],"The":[39,62],"proof":[40],"is":[41,146],"constructive":[42,119],"and":[43,56,100],"uses":[44],"combinatorial":[46],"argument":[47],"based":[48],"on":[49],"simplicial":[51],"algorithm":[52,63,80,116,128],"vector":[54],"labeling":[55],"lexicographic":[57],"linear":[58],"programming":[59],"pivot":[60],"steps.":[61],"provides":[64,117],"an":[65,70],"efficient":[66],"method":[67,139],"find":[69,87,102],"exact":[71],"solution.":[72],"We":[73,123],"also":[74,147],"discuss":[75],"how":[76],"adapt":[78],"for":[81,129],"two":[82],"related":[83],"problems,":[84],"namely,":[85],"antipodal":[98],"condition":[99],"solution":[104],"nonlinear":[108,132,141],"complementarity":[109,133],"problem.":[110],"both":[112],"cases":[113],"modified":[115],"proof,":[121],"too.":[122],"further":[124],"show":[125],"that":[126],"problem":[134],"generalizes":[135],"well\u2010known":[137],"Lemke\u2019s":[138],"environments.":[142],"An":[143],"economic":[144],"application":[145],"presented.":[148]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}