{"id":"https://openalex.org/W3044789008","doi":"https://doi.org/10.1007/s11075-020-00983-w","title":"Modulus-based matrix splitting methods for a class of horizontal nonlinear complementarity problems","display_name":"Modulus-based matrix splitting methods for a class of horizontal nonlinear complementarity problems","publication_year":2020,"publication_date":"2020-07-21","ids":{"openalex":"https://openalex.org/W3044789008","doi":"https://doi.org/10.1007/s11075-020-00983-w","mag":"3044789008"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-020-00983-w","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-020-00983-w","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11380/1257543","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085088392","display_name":"Francesco Mezzadri","orcid":"https://orcid.org/0000-0002-9779-7647"},"institutions":[{"id":"https://openalex.org/I122346577","display_name":"University of Modena and Reggio Emilia","ror":"https://ror.org/02d4c4y02","country_code":"IT","type":"education","lineage":["https://openalex.org/I122346577"]},{"id":"https://openalex.org/I4210161797","display_name":"Ferrari (Italy)","ror":"https://ror.org/05p859a12","country_code":"IT","type":"company","lineage":["https://openalex.org/I4210161797"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Francesco Mezzadri","raw_affiliation_strings":["Department of Engineering \u201cEnzo Ferrari\u201d, University of Modena and Reggio Emilia, via P. Vivarelli 10/1, building 26, I-41125, Modena, Italy","Department of Engineering \"Enzo Ferrari\", University of Modena and Reggio Emilia, via P. Vivarelli 10/1, building 26, I-41125, Modena, Italy"],"raw_orcid":"https://orcid.org/0000-0002-9779-7647","affiliations":[{"raw_affiliation_string":"Department of Engineering \u201cEnzo Ferrari\u201d, University of Modena and Reggio Emilia, via P. Vivarelli 10/1, building 26, I-41125, Modena, Italy","institution_ids":["https://openalex.org/I122346577"]},{"raw_affiliation_string":"Department of Engineering \"Enzo Ferrari\", University of Modena and Reggio Emilia, via P. Vivarelli 10/1, building 26, I-41125, Modena, Italy","institution_ids":["https://openalex.org/I122346577","https://openalex.org/I4210161797"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063997920","display_name":"Emanuele Galligani","orcid":"https://orcid.org/0000-0002-0253-6963"},"institutions":[{"id":"https://openalex.org/I122346577","display_name":"University of Modena and Reggio Emilia","ror":"https://ror.org/02d4c4y02","country_code":"IT","type":"education","lineage":["https://openalex.org/I122346577"]},{"id":"https://openalex.org/I4210161797","display_name":"Ferrari (Italy)","ror":"https://ror.org/05p859a12","country_code":"IT","type":"company","lineage":["https://openalex.org/I4210161797"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Emanuele Galligani","raw_affiliation_strings":["Department of Engineering \u201cEnzo Ferrari\u201d, University of Modena and Reggio Emilia, via P. Vivarelli 10/1, building 26, I-41125, Modena, Italy","Department of Engineering \"Enzo Ferrari\", University of Modena and Reggio Emilia, via P. Vivarelli 10/1, building 26, I-41125, Modena, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering \u201cEnzo Ferrari\u201d, University of Modena and Reggio Emilia, via P. Vivarelli 10/1, building 26, I-41125, Modena, Italy","institution_ids":["https://openalex.org/I122346577"]},{"raw_affiliation_string":"Department of Engineering \"Enzo Ferrari\", University of Modena and Reggio Emilia, via P. Vivarelli 10/1, building 26, I-41125, Modena, Italy","institution_ids":["https://openalex.org/I122346577","https://openalex.org/I4210161797"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5085088392"],"corresponding_institution_ids":["https://openalex.org/I122346577","https://openalex.org/I4210161797"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.932,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.89178211,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"87","issue":"2","first_page":"667","last_page":"687"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","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/T10792","display_name":"Matrix Theory and Algorithms","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":0.9945999979972839,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9926999807357788,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mixed-complementarity-problem","display_name":"Mixed complementarity problem","score":0.796092689037323},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7627895474433899},{"id":"https://openalex.org/keywords/complementarity-theory","display_name":"Complementarity theory","score":0.7455505132675171},{"id":"https://openalex.org/keywords/nonlinear-complementarity-problem","display_name":"Nonlinear complementarity problem","score":0.7170300483703613},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.6792036294937134},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6585438251495361},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5796887874603271},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5480903387069702},{"id":"https://openalex.org/keywords/linear-complementarity-problem","display_name":"Linear complementarity problem","score":0.4851268231868744},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.48371341824531555},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4792056977748871},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.47888845205307007},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.43656104803085327},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4176541566848755},{"id":"https://openalex.org/keywords/modulus","display_name":"Modulus","score":0.4163905680179596},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41580435633659363},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40702494978904724},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22424185276031494},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2063126564025879},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17019259929656982},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1277180016040802}],"concepts":[{"id":"https://openalex.org/C77196050","wikidata":"https://www.wikidata.org/wiki/Q6883962","display_name":"Mixed complementarity problem","level":3,"score":0.796092689037323},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7627895474433899},{"id":"https://openalex.org/C85404239","wikidata":"https://www.wikidata.org/wiki/Q5156417","display_name":"Complementarity theory","level":3,"score":0.7455505132675171},{"id":"https://openalex.org/C2778646529","wikidata":"https://www.wikidata.org/wiki/Q16948724","display_name":"Nonlinear complementarity problem","level":4,"score":0.7170300483703613},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.6792036294937134},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6585438251495361},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5796887874603271},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5480903387069702},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.4851268231868744},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48371341824531555},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4792056977748871},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.47888845205307007},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.43656104803085327},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4176541566848755},{"id":"https://openalex.org/C193867417","wikidata":"https://www.wikidata.org/wiki/Q6889814","display_name":"Modulus","level":2,"score":0.4163905680179596},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41580435633659363},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40702494978904724},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22424185276031494},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2063126564025879},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17019259929656982},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1277180016040802},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11075-020-00983-w","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-020-00983-w","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:iris.unimore.it:11380/1257543","is_oa":true,"landing_page_url":"http://hdl.handle.net/11380/1257543","pdf_url":null,"source":{"id":"https://openalex.org/S4306400718","display_name":"IRIS UNIMORE (University of Modena and Reggio Emilia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122346577","host_organization_name":"University of Modena and Reggio Emilia","host_organization_lineage":["https://openalex.org/I122346577"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:iris.unimore.it:11380/1257543","is_oa":true,"landing_page_url":"http://hdl.handle.net/11380/1257543","pdf_url":null,"source":{"id":"https://openalex.org/S4306400718","display_name":"IRIS UNIMORE (University of Modena and Reggio Emilia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122346577","host_organization_name":"University of Modena and Reggio Emilia","host_organization_lineage":["https://openalex.org/I122346577"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W878500305","https://openalex.org/W1956819437","https://openalex.org/W1963924275","https://openalex.org/W1979337419","https://openalex.org/W1982337446","https://openalex.org/W1988196159","https://openalex.org/W1998519780","https://openalex.org/W1999067864","https://openalex.org/W2000151369","https://openalex.org/W2005707106","https://openalex.org/W2005865704","https://openalex.org/W2024146995","https://openalex.org/W2024148298","https://openalex.org/W2052028268","https://openalex.org/W2054786539","https://openalex.org/W2061152612","https://openalex.org/W2078271509","https://openalex.org/W2087837774","https://openalex.org/W2089529944","https://openalex.org/W2090963365","https://openalex.org/W2143366782","https://openalex.org/W2210690239","https://openalex.org/W2235905735","https://openalex.org/W2296233246","https://openalex.org/W2404507129","https://openalex.org/W2566482849","https://openalex.org/W2607344773","https://openalex.org/W2753851050","https://openalex.org/W2786123509","https://openalex.org/W2792680258","https://openalex.org/W2802955816","https://openalex.org/W2883446839","https://openalex.org/W2886832173","https://openalex.org/W2887313567","https://openalex.org/W2893144408","https://openalex.org/W2901673765","https://openalex.org/W2905690982","https://openalex.org/W2914365367","https://openalex.org/W2916397347","https://openalex.org/W2972096426","https://openalex.org/W2978668726","https://openalex.org/W2984612229","https://openalex.org/W2992218295","https://openalex.org/W3035235874","https://openalex.org/W3047850446","https://openalex.org/W4299512035"],"related_works":["https://openalex.org/W2091810828","https://openalex.org/W136255994","https://openalex.org/W1553741403","https://openalex.org/W2988170224","https://openalex.org/W1979597395","https://openalex.org/W2946458654","https://openalex.org/W1974381735","https://openalex.org/W2041272264","https://openalex.org/W4382794904","https://openalex.org/W2339051099"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":5}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}