{"id":"https://openalex.org/W3193903541","doi":"https://doi.org/10.1109/tac.2023.3338981","title":"Equivalence of Linear Complementarity Problems: Theory and Application to Nonsmooth Bifurcations","display_name":"Equivalence of Linear Complementarity Problems: Theory and Application to Nonsmooth Bifurcations","publication_year":2023,"publication_date":"2023-12-04","ids":{"openalex":"https://openalex.org/W3193903541","doi":"https://doi.org/10.1109/tac.2023.3338981","mag":"3193903541"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2023.3338981","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2023.3338981","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2108.06917","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059848223","display_name":"F\u00e9lix Miranda-Villatoro","orcid":"https://orcid.org/0000-0002-2582-9857"},"institutions":[{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210149092","display_name":"Laboratoire Jean Kuntzmann","ror":"https://ror.org/04ett5b41","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210149092","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"F\u00e9lix A. Miranda-Villatoro","raw_affiliation_strings":["Institute National de Recherche en Informatique et Automatique (INRIA), Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Kuntzmann (LJK), Grenoble INP, University Grenoble-Alpes, Grenoble, France"],"raw_orcid":"https://orcid.org/0000-0002-2582-9857","affiliations":[{"raw_affiliation_string":"Institute National de Recherche en Informatique et Automatique (INRIA), Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Kuntzmann (LJK), Grenoble INP, University Grenoble-Alpes, Grenoble, France","institution_ids":["https://openalex.org/I4210149092","https://openalex.org/I1294671590","https://openalex.org/I106785703","https://openalex.org/I1326498283","https://openalex.org/I899635006"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025524300","display_name":"Fernando Casta\u00f1os","orcid":"https://orcid.org/0000-0002-0389-7955"},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Centro de Investigaci\u00f3n y de Estudios Avanzados del Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Fernando Casta\u00f1os","raw_affiliation_strings":["Departamento de Control Autom&#x00E1;tico, CINVESTAV-IPN, Mexico City, Mexico"],"raw_orcid":"https://orcid.org/0000-0002-0389-7955","affiliations":[{"raw_affiliation_string":"Departamento de Control Autom&#x00E1;tico, CINVESTAV-IPN, Mexico City, Mexico","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049699562","display_name":"Alessio Franci","orcid":"https://orcid.org/0000-0002-3911-625X"},"institutions":[{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]},{"id":"https://openalex.org/I4210142098","display_name":"Walloon Excellence in Lifesciences and Biotechnology","ror":"https://ror.org/04qbvw321","country_code":"BE","type":"nonprofit","lineage":["https://openalex.org/I4210142098"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Alessio Franci","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Liege, Liege, Belgium","WEL Research Institute, Wavre, Belgium"],"raw_orcid":"https://orcid.org/0000-0002-3911-625X","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Liege, Liege, Belgium","institution_ids":["https://openalex.org/I157674565"]},{"raw_affiliation_string":"WEL Research Institute, Wavre, Belgium","institution_ids":["https://openalex.org/I4210142098"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.155,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.39248648,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"69","issue":"7","first_page":"4570","last_page":"4582"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9914000034332275,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9901999831199646,"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/mathematics","display_name":"Mathematics","score":0.6986078023910522},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.6586058139801025},{"id":"https://openalex.org/keywords/complementarity-theory","display_name":"Complementarity theory","score":0.609878420829773},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6098244190216064},{"id":"https://openalex.org/keywords/mixed-complementarity-problem","display_name":"Mixed complementarity problem","score":0.5982165932655334},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.5407275557518005},{"id":"https://openalex.org/keywords/linear-complementarity-problem","display_name":"Linear complementarity problem","score":0.5052552819252014},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.48357266187667847},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.47081857919692993},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4626484811306},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45850592851638794},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.45358991622924805},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.43915677070617676},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4168332815170288},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4008180797100067},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3271208107471466},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23960691690444946},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21682953834533691},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21220889687538147}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6986078023910522},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.6586058139801025},{"id":"https://openalex.org/C85404239","wikidata":"https://www.wikidata.org/wiki/Q5156417","display_name":"Complementarity theory","level":3,"score":0.609878420829773},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6098244190216064},{"id":"https://openalex.org/C77196050","wikidata":"https://www.wikidata.org/wiki/Q6883962","display_name":"Mixed complementarity problem","level":3,"score":0.5982165932655334},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.5407275557518005},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.5052552819252014},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.48357266187667847},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.47081857919692993},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4626484811306},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45850592851638794},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.45358991622924805},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.43915677070617676},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4168332815170288},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4008180797100067},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3271208107471466},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23960691690444946},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21682953834533691},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21220889687538147},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"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/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tac.2023.3338981","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2023.3338981","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2108.06917","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2108.06917","pdf_url":"https://arxiv.org/pdf/2108.06917","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"},{"id":"pmh:oai:HAL:hal-03319638v2","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-03319638","pdf_url":"https://inria.hal.science/hal-03319638v2/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"IEEE Transactions on Automatic Control, 2024, 69 (7), pp.4570-4582. &#x27E8;10.1109/TAC.2023.3338981&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:orbi.ulg.ac.be:2268/320269","is_oa":true,"landing_page_url":"https://orbi.uliege.be/handle/2268/320269","pdf_url":"https://orbi.uliege.be/bitstream/2268/320269/1/Equivalence_of_Linear_Complementarity_Problems_Theory_and_Application_to_Nonsmooth_Bifurcations.pdf","source":{"id":"https://openalex.org/S4306401300","display_name":"ORBi (University of Li\u00e8ge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I157674565","host_organization_name":"University of Li\u00e8ge","host_organization_lineage":["https://openalex.org/I157674565"],"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":"IEEE Transactions on Automatic Control, 1 - 12 (2024)","raw_type":"peer reviewed"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2108.06917","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2108.06917","pdf_url":"https://arxiv.org/pdf/2108.06917","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":73,"referenced_works":["https://openalex.org/W568178739","https://openalex.org/W584634945","https://openalex.org/W1504265359","https://openalex.org/W1543439990","https://openalex.org/W1551205560","https://openalex.org/W1551360398","https://openalex.org/W1551877617","https://openalex.org/W1606695234","https://openalex.org/W1692754621","https://openalex.org/W1965778005","https://openalex.org/W1967848725","https://openalex.org/W1973794046","https://openalex.org/W1993647205","https://openalex.org/W2000061146","https://openalex.org/W2004936497","https://openalex.org/W2004945943","https://openalex.org/W2011584763","https://openalex.org/W2024195317","https://openalex.org/W2031135002","https://openalex.org/W2036219060","https://openalex.org/W2038150727","https://openalex.org/W2042192623","https://openalex.org/W2059390486","https://openalex.org/W2062434421","https://openalex.org/W2064028560","https://openalex.org/W2082798332","https://openalex.org/W2083823140","https://openalex.org/W2084502562","https://openalex.org/W2089639583","https://openalex.org/W2089876099","https://openalex.org/W2094913794","https://openalex.org/W2098982596","https://openalex.org/W2127015451","https://openalex.org/W2128234186","https://openalex.org/W2138947309","https://openalex.org/W2149675356","https://openalex.org/W2172412686","https://openalex.org/W2293945336","https://openalex.org/W2401190273","https://openalex.org/W2407793931","https://openalex.org/W2508313130","https://openalex.org/W2597062055","https://openalex.org/W2786855474","https://openalex.org/W2790729824","https://openalex.org/W2798300375","https://openalex.org/W2914714640","https://openalex.org/W2962965869","https://openalex.org/W2963203577","https://openalex.org/W2985481128","https://openalex.org/W2989067185","https://openalex.org/W2990251667","https://openalex.org/W2995133334","https://openalex.org/W3012119224","https://openalex.org/W3084114652","https://openalex.org/W3084169441","https://openalex.org/W3154414624","https://openalex.org/W3163953477","https://openalex.org/W3190138800","https://openalex.org/W4205561218","https://openalex.org/W4206311976","https://openalex.org/W4213213245","https://openalex.org/W4214764776","https://openalex.org/W4238307931","https://openalex.org/W4248606763","https://openalex.org/W4250589301","https://openalex.org/W4255990987","https://openalex.org/W4288108722","https://openalex.org/W4292665375","https://openalex.org/W4301791716","https://openalex.org/W4385277614","https://openalex.org/W6748615252","https://openalex.org/W6782651988","https://openalex.org/W6940672572"],"related_works":["https://openalex.org/W2276648117","https://openalex.org/W2063320018","https://openalex.org/W2042813889","https://openalex.org/W2358901572","https://openalex.org/W2028943836","https://openalex.org/W4220847489","https://openalex.org/W2091810828","https://openalex.org/W2567598518","https://openalex.org/W2735070409","https://openalex.org/W2181941970"],"abstract_inverted_index":{"Linear":[0],"complementarity":[1,39,62,106],"problems":[2,40],"provide":[3],"a":[4,32,46,51],"powerful":[5],"framework":[6],"to":[7,21,67],"model":[8],"nonsmooth":[9,55,76,80],"phenomena":[10],"in":[11,27,50,60,103],"dynamical":[12],"control":[13],"systems.":[14,63],"Mimicking":[15],"the":[16,22,43,75,94],"general":[17],"strategy":[18],"that":[19,41],"led":[20],"foundation":[23],"of":[24,35,48,54,98],"bifurcation":[25],"theory":[26,47,86],"smooth":[28],"maps,":[29,56],"we":[30],"introduce":[31],"novel":[33],"notion":[34],"equivalence":[36,101],"between":[37],"linear":[38,61,105],"sets":[42],"basis":[44],"for":[45,71],"bifurcations":[49,59],"large":[52],"class":[53],"including":[57],"steady-state":[58],"Our":[64],"definition":[65],"leads":[66],"constructive":[68],"algebraic":[69],"conditions":[70],"identifying":[72],"and":[73,92,96],"classifying":[74],"singularities":[77],"associated":[78],"with":[79],"bifurcations.":[81],"We":[82],"thoroughly":[83],"illustrate":[84],"our":[85],"on":[87,93],"an":[88],"extended":[89],"applied":[90],"example":[91],"identification":[95],"classification":[97],"all":[99],"possible":[100],"classes":[102],"two-dimensional":[104],"problems.":[107]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-13T07:54:00.901334","created_date":"2025-10-10T00:00:00"}
