{"id":"https://openalex.org/W1972014778","doi":"https://doi.org/10.1137/140969476","title":"Inexact Newton Methods and Dennis--Mor\u00e9 Theorems for Nonsmooth Generalized Equations","display_name":"Inexact Newton Methods and Dennis--Mor\u00e9 Theorems for Nonsmooth Generalized Equations","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1972014778","doi":"https://doi.org/10.1137/140969476","mag":"1972014778"},"language":"en","primary_location":{"id":"doi:10.1137/140969476","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140969476","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089016981","display_name":"Radek Cibulka","orcid":"https://orcid.org/0000-0002-3626-4652"},"institutions":[{"id":"https://openalex.org/I92715842","display_name":"University of West Bohemia","ror":"https://ror.org/040t43x18","country_code":"CZ","type":"education","lineage":["https://openalex.org/I92715842"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"R. Cibulka","raw_affiliation_strings":["#N#University of West Bohemia#N#"],"affiliations":[{"raw_affiliation_string":"#N#University of West Bohemia#N#","institution_ids":["https://openalex.org/I92715842"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083269925","display_name":"Asen L. Dontchev","orcid":"https://orcid.org/0000-0003-3160-7828"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Dontchev","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5036387118","display_name":"Michel Geoffroy","orcid":"https://orcid.org/0000-0003-0253-3209"},"institutions":[{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]},{"id":"https://openalex.org/I4210102957","display_name":"D\u00e9partement Math\u00e9matiques et Informatique Appliqu\u00e9es","ror":"https://ror.org/011emb038","country_code":"FR","type":"government","lineage":["https://openalex.org/I4210088668","https://openalex.org/I4210102957"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"M. H. Geoffroy","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques Informatique et Applications"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques Informatique et Applications","institution_ids":["https://openalex.org/I4210102957","https://openalex.org/I4210155549"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089016981"],"corresponding_institution_ids":["https://openalex.org/I92715842"],"apc_list":null,"apc_paid":null,"fwci":4.0485,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.93799058,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"53","issue":"2","first_page":"1003","last_page":"1019"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9991999864578247,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.996399998664856,"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":0.8774906396865845},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.690211296081543},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.5342841148376465},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.5194387435913086},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5053853988647461},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4749429523944855},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4463035762310028},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3942570090293884},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35606545209884644},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3495984673500061},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34299200773239136},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12994182109832764}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8774906396865845},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.690211296081543},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.5342841148376465},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.5194387435913086},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5053853988647461},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4749429523944855},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4463035762310028},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3942570090293884},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35606545209884644},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3495984673500061},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34299200773239136},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12994182109832764},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/140969476","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140969476","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:HAL:hal-01147931v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01147931","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 2015, 53 (2), pp.1003-1019","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W388179047","https://openalex.org/W581038412","https://openalex.org/W591794949","https://openalex.org/W612879516","https://openalex.org/W1525781748","https://openalex.org/W1551360398","https://openalex.org/W1567995217","https://openalex.org/W1982110324","https://openalex.org/W1992688650","https://openalex.org/W2016599513","https://openalex.org/W2030322501","https://openalex.org/W2042154949","https://openalex.org/W2053643774","https://openalex.org/W2053924315","https://openalex.org/W2059354404","https://openalex.org/W2068388303","https://openalex.org/W2107501462","https://openalex.org/W2112820497","https://openalex.org/W2116210979","https://openalex.org/W2134040273","https://openalex.org/W2750449797"],"related_works":["https://openalex.org/W3040723915","https://openalex.org/W1896162644","https://openalex.org/W2127159799","https://openalex.org/W1901133132","https://openalex.org/W4287724094","https://openalex.org/W2068966571","https://openalex.org/W2188650732","https://openalex.org/W2016630321","https://openalex.org/W2385824356","https://openalex.org/W2532207692"],"abstract_inverted_index":{"In":[0,160],"this":[1],"paper":[2,166],"we":[3,150,167,177],"study":[4],"local":[5],"convergence":[6,156,181],"of":[7,11,67,72,115,117,127,130,141,147,157,164,171,182],"inexact":[8,183],"Newton":[9],"methods":[10,186],"the":[12,31,42,65,110,113,118,121,131,135,139,158,161,165,172],"form":[13],"$":[14],"{\\big(}f(x_k)+":[15],"A_k(x_{k+1}-x_k)+F(x_{k+1}){\\big)}\\cap":[16],"R_k(x_k)":[17],"\\neq":[18],"\\emptyset":[19],"\\":[20,21,23,24],"{with}":[22],"A_k":[25],"\\in":[26],"{\\cal":[27],"H}(x_k)$":[28],"for":[29,190],"solving":[30],"generalized":[32,69,83],"equation":[33],"$f(x)":[34],"+F(x)":[35],"\\ni":[36],"0$":[37],"in":[38,75,86],"Banach":[39,87],"spaces,":[40],"where":[41],"function":[43,119],"$f$":[44,73],"is":[45,53,137],"continuous":[46],"but":[47],"not":[48],"necessarily":[49],"smooth":[50],"and":[51,134,187],"$F$":[52],"a":[54,68],"set-valued":[55,70,98],"mapping":[56,61,132],"with":[57,93],"closed":[58],"graph.":[59],"The":[60,97],"$\\cal":[62],"H$":[63],"plays":[64],"role":[66],"derivative":[71],"which":[74],"finite":[76],"dimensions":[77],"may":[78,90],"be":[79,91],"represented":[80],"by":[81],"Clarke's":[82],"Jacobian,":[84],"while":[85],"spaces":[88],"it":[89],"identified":[92],"Ioffe's":[94],"strict":[95],"prederivative.":[96],"mappings":[99,142],"$R_k$":[100],"represent":[101],"inexactness.":[102],"We":[103],"utilize":[104],"conditions":[105,149],"divided":[106],"into":[107],"three":[108],"groups:":[109],"first":[111],"concerns":[112],"kind":[114],"nonsmoothness":[116],"$f$,":[120],"second":[122,162],"involves":[123],"metric":[124],"regularity":[125],"properties":[126],"an":[128],"approximation":[129],"$f+F$,":[133],"third":[136],"about":[138],"sequence":[140],"$R_k$.":[143],"Under":[144],"various":[145],"combinations":[146],"these":[148],"show":[151],"linear,":[152],"superlinear,":[153],"or":[154],"quadratic":[155],"method.":[159],"part":[163],"give":[168],"two":[169],"generalizations":[170],"Dennis--Mor\u00e9":[173,188],"theorem.":[174],"As":[175],"corollaries,":[176],"obtain":[178],"results":[179],"regarding":[180],"semismooth":[184,191],"quasi-Newton-type":[185],"theorems":[189],"equations.":[192]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}