{"id":"https://openalex.org/W2075803640","doi":"https://doi.org/10.1137/100784114","title":"A Continuous Dynamical Newton-Like Approach to Solving Monotone Inclusions","display_name":"A Continuous Dynamical Newton-Like Approach to Solving Monotone Inclusions","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2075803640","doi":"https://doi.org/10.1137/100784114","mag":"2075803640"},"language":"en","primary_location":{"id":"doi:10.1137/100784114","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100784114","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00803137","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108474463","display_name":"H\u00e9dy Attouch","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"H. Attouch","raw_affiliation_strings":["attouch@math.univ-montp2.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"attouch@math.univ-montp2.fr#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053683082","display_name":"B. F. Svaiter","orcid":"https://orcid.org/0000-0003-3656-9883"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B. F. Svaiter","raw_affiliation_strings":["benar@impa.br#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"benar@impa.br#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.2414,"has_fulltext":false,"cited_by_count":90,"citation_normalized_percentile":{"value":0.94472914,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"49","issue":"2","first_page":"574","last_page":"598"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9997000098228455,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9997000098228455,"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":0.9980999827384949,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9681000113487244,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/monotone-polygon","display_name":"Monotone polygon","score":0.7953673601150513},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7767094373703003},{"id":"https://openalex.org/keywords/differential-inclusion","display_name":"Differential inclusion","score":0.7672905921936035},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7648767232894897},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5761803388595581},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.56287682056427},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5198460221290588},{"id":"https://openalex.org/keywords/strongly-monotone","display_name":"Strongly monotone","score":0.5109173655509949},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5019199848175049},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49612483382225037},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.45739492774009705},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.333866685628891},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32984310388565063},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.17327561974525452}],"concepts":[{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7953673601150513},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7767094373703003},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.7672905921936035},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7648767232894897},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5761803388595581},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.56287682056427},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5198460221290588},{"id":"https://openalex.org/C12715386","wikidata":"https://www.wikidata.org/wiki/Q7624691","display_name":"Strongly monotone","level":3,"score":0.5109173655509949},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5019199848175049},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49612483382225037},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.45739492774009705},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.333866685628891},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32984310388565063},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.17327561974525452},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/100784114","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100784114","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.414.2558","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.414.2558","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.optimization-online.org/DB_FILE/2010/12/2854.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.739.4918","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.739.4918","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.inria.fr/docs/00/80/31/37/PDF/SICON-2011-Attouch-Svaiter.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00803137v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00803137","pdf_url":null,"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 2011, 49 (3), pp.574-598. &#x27E8;10.1137/100784114&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00803137v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00803137","pdf_url":null,"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 2011, 49 (3), pp.574-598. &#x27E8;10.1137/100784114&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.6700000166893005,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G2928036526","display_name":"Optimisation, Strat\u00e9gies, Selection : Dynamiques, Approximations, et Applications","funder_award_id":"ANR-08-BLAN-0294","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W41160994","https://openalex.org/W43435585","https://openalex.org/W46627373","https://openalex.org/W84725740","https://openalex.org/W1580983414","https://openalex.org/W1582617215","https://openalex.org/W1974968775","https://openalex.org/W1997427529","https://openalex.org/W1999083556","https://openalex.org/W2038497950","https://openalex.org/W2042261731","https://openalex.org/W2046596783","https://openalex.org/W2047515743","https://openalex.org/W2053487511","https://openalex.org/W2066214692","https://openalex.org/W2074334982","https://openalex.org/W2087003257","https://openalex.org/W2091760073","https://openalex.org/W2092736015","https://openalex.org/W2099679613","https://openalex.org/W2487292604","https://openalex.org/W2582171088","https://openalex.org/W3029645440","https://openalex.org/W3211220023","https://openalex.org/W4238957126","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2048389107","https://openalex.org/W2150021166","https://openalex.org/W4386619781","https://openalex.org/W2129546971","https://openalex.org/W2042906150","https://openalex.org/W1490989651","https://openalex.org/W2024324231","https://openalex.org/W3134869168","https://openalex.org/W4239916020","https://openalex.org/W2752416643"],"abstract_inverted_index":{"We":[0],"introduce":[1],"nonautonomous":[2],"continuous":[3],"dynamical":[4],"systems":[5],"which":[6,54],"are":[7,55],"linked":[8],"to":[9,57,72],"the":[10,30,58],"Newton":[11],"and":[12],"Levenberg\u2013Marquardt":[13],"methods.":[14],"They":[15],"aim":[16],"at":[17],"solving":[18,88],"inclusions":[19],"governed":[20],"by":[21],"maximal":[22,34],"monotone":[23,35,89],"operators":[24,36],"in":[25,50],"Hilbert":[26],"spaces.":[27],"Relying":[28],"on":[29],"Minty":[31],"representation":[32],"of":[33,76],"as":[37,48],"lipschitzian":[38],"manifolds,":[39],"we":[40,65],"show":[41],"that":[42,67],"these":[43,77],"dynamics":[44,78],"can":[45],"be":[46],"formulated":[47],"first-order":[49],"time":[51],"differential":[52],"systems,":[53],"relevant":[56],"Cauchy\u2013Lipschitz":[59],"theorem.":[60],"By":[61],"using":[62],"Lyapunov":[63],"methods,":[64],"prove":[66],"their":[68],"trajectories":[69],"converge":[70],"weakly":[71],"equilibria.":[73],"Time":[74],"discretization":[75],"gives":[79],"algorithms":[80],"providing":[81],"new":[82],"insight":[83],"into":[84],"Newton's":[85],"method":[86],"for":[87],"inclusions.":[90]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-20T22:02:38.213706","created_date":"2025-10-10T00:00:00"}
