{"id":"https://openalex.org/W3188605476","doi":"https://doi.org/10.1007/s10589-021-00306-2","title":"Newton-type methods near critical solutions of piecewise smooth nonlinear equations","display_name":"Newton-type methods near critical solutions of piecewise smooth nonlinear equations","publication_year":2021,"publication_date":"2021-08-06","ids":{"openalex":"https://openalex.org/W3188605476","doi":"https://doi.org/10.1007/s10589-021-00306-2","mag":"3188605476"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-021-00306-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-021-00306-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-021-00306-2.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10589-021-00306-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063581189","display_name":"Andreas Fischer","orcid":"https://orcid.org/0000-0001-7703-1655"},"institutions":[{"id":"https://openalex.org/I78650965","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30","country_code":"DE","type":"education","lineage":["https://openalex.org/I78650965"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"A. Fischer","raw_affiliation_strings":["Faculty of Mathematics, Technische Universit\u00e4t Dresden, 01062, Dresden, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Technische Universit\u00e4t Dresden, 01062, Dresden, Germany","institution_ids":["https://openalex.org/I78650965"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085617315","display_name":"A. F. Izmailov","orcid":"https://orcid.org/0000-0001-9851-0524"},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A. F. Izmailov","raw_affiliation_strings":["VMK Faculty, OR Department, Lomonosov Moscow State University (MSU), Uchebniy Korpus 2, Leninskiye Gory, Moscow, Russia, 119991"],"affiliations":[{"raw_affiliation_string":"VMK Faculty, OR Department, Lomonosov Moscow State University (MSU), Uchebniy Korpus 2, Leninskiye Gory, Moscow, Russia, 119991","institution_ids":["https://openalex.org/I19880235"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001614197","display_name":"Mario Jelitte","orcid":"https://orcid.org/0000-0002-8982-2136"},"institutions":[{"id":"https://openalex.org/I78650965","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30","country_code":"DE","type":"education","lineage":["https://openalex.org/I78650965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"M. Jelitte","raw_affiliation_strings":["Faculty of Mathematics, Technische Universit\u00e4t Dresden, 01062, Dresden, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Technische Universit\u00e4t Dresden, 01062, Dresden, Germany","institution_ids":["https://openalex.org/I78650965"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5063581189"],"corresponding_institution_ids":["https://openalex.org/I78650965"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":2.1838,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.86062095,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"80","issue":"2","first_page":"587","last_page":"615"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9998999834060669,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9998999834060669,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987999796867371,"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":0.9883999824523926,"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":0.8398777842521667},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6726073026657104},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5745329856872559},{"id":"https://openalex.org/keywords/nonlinear-complementarity-problem","display_name":"Nonlinear complementarity problem","score":0.5165466666221619},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5114282965660095},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5077734589576721},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.48526880145072937},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.47343042492866516},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.4541744887828827},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.4368768334388733},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42628031969070435},{"id":"https://openalex.org/keywords/mixed-complementarity-problem","display_name":"Mixed complementarity problem","score":0.16191929578781128},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08666008710861206}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8398777842521667},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6726073026657104},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5745329856872559},{"id":"https://openalex.org/C2778646529","wikidata":"https://www.wikidata.org/wiki/Q16948724","display_name":"Nonlinear complementarity problem","level":4,"score":0.5165466666221619},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5114282965660095},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5077734589576721},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48526880145072937},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.47343042492866516},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.4541744887828827},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.4368768334388733},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42628031969070435},{"id":"https://openalex.org/C77196050","wikidata":"https://www.wikidata.org/wiki/Q6883962","display_name":"Mixed complementarity problem","level":3,"score":0.16191929578781128},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08666008710861206},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","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},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10589-021-00306-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-021-00306-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-021-00306-2.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:coopap:v:80:y:2021:i:2:d:10.1007_s10589-021-00306-2","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10589-021-00306-2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:econstor.eu:10419/287045","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/287045","pdf_url":null,"source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"","raw_type":"doc-type:article"}],"best_oa_location":{"id":"doi:10.1007/s10589-021-00306-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-021-00306-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-021-00306-2.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1017097271","display_name":null,"funder_award_id":"97775","funder_id":"https://openalex.org/F4320320882","funder_display_name":"Volkswagen Foundation"},{"id":"https://openalex.org/G1524342187","display_name":null,"funder_award_id":"20-01-","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"},{"id":"https://openalex.org/G2078120496","display_name":null,"funder_award_id":"409756759","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3119453547","display_name":null,"funder_award_id":"19-51-12003 NNIO_a","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"},{"id":"https://openalex.org/G4304115851","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320320882","funder_display_name":"Volkswagen Foundation"},{"id":"https://openalex.org/G5106512922","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5154552578","display_name":null,"funder_award_id":"20-01-00106","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320320882","display_name":"Volkswagen Foundation","ror":"https://ror.org/03bsmfz84"},{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"},{"id":"https://openalex.org/F4320321613","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3188605476.pdf","grobid_xml":"https://content.openalex.org/works/W3188605476.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W106246290","https://openalex.org/W388179047","https://openalex.org/W1490084264","https://openalex.org/W1543439990","https://openalex.org/W1981316213","https://openalex.org/W1983585148","https://openalex.org/W2000151369","https://openalex.org/W2017478419","https://openalex.org/W2033272253","https://openalex.org/W2079693963","https://openalex.org/W2087070363","https://openalex.org/W2088528580","https://openalex.org/W2094997497","https://openalex.org/W2121625938","https://openalex.org/W2153993279","https://openalex.org/W2158249142","https://openalex.org/W2209824757","https://openalex.org/W2256578114","https://openalex.org/W2471407736","https://openalex.org/W2529842698","https://openalex.org/W2592547154","https://openalex.org/W2766958658","https://openalex.org/W2802734711","https://openalex.org/W2896002309","https://openalex.org/W3016203065","https://openalex.org/W3029645440","https://openalex.org/W3088858683","https://openalex.org/W4205236922","https://openalex.org/W4301014524","https://openalex.org/W4301791716"],"related_works":["https://openalex.org/W2960434112","https://openalex.org/W3049714198","https://openalex.org/W2036805113","https://openalex.org/W2017886776","https://openalex.org/W2035738801","https://openalex.org/W3003212247","https://openalex.org/W2322780295","https://openalex.org/W2562964647","https://openalex.org/W4311074794","https://openalex.org/W2137801386"],"abstract_inverted_index":{"Abstract":[0],"It":[1],"is":[2,84,119],"well-recognized":[3],"that":[4,46],"in":[5,11,95],"the":[6,22,32,39,74,77,107,114,124],"presence":[7],"of":[8,15,24,34,63,79,109,113,126,137,144,156],"singular":[9],"(and":[10],"particular":[12],"nonisolated)":[13],"solutions":[14,26,48,83],"unconstrained":[16],"or":[17],"constrained":[18],"smooth":[19,149],"nonlinear":[20,157],"equations,":[21,150],"existence":[23],"critical":[25],"has":[27,43],"a":[28,68,90,98,132],"crucial":[29],"impact":[30],"on":[31],"behavior":[33],"various":[35],"Newton-type":[36],"methods.":[37],"On":[38,73],"one":[40],"hand,":[41,76],"it":[42],"been":[44],"demonstrated":[45],"such":[47,82],"turn":[49],"out":[50],"to":[51,81,147,153],"be":[52],"attractors":[53],"for":[54,60,89,100,106,123,135],"sequences":[55],"generated":[56],"by":[57],"these":[58,127,145],"methods,":[59],"wide":[61],"domains":[62],"starting":[64],"points,":[65],"and":[66,87,105],"with":[67,131,151],"linear":[69],"convergence":[70,80],"rate":[71],"estimate.":[72],"other":[75],"pattern":[78],"quite":[85],"special,":[86],"allows":[88],"sharp":[91],"characterization":[92],"which":[93],"serves,":[94],"particular,":[96],"as":[97],"basis":[99],"some":[101],"known":[102],"acceleration":[103],"techniques,":[104],"proof":[108],"an":[110,120],"asymptotic":[111],"acceptance":[112],"unit":[115],"stepsize.":[116],"The":[117],"latter":[118],"essential":[121],"property":[122],"success":[125],"techniques":[128],"when":[129],"combined":[130],"linesearch":[133],"strategy":[134],"globalization":[136],"convergence.":[138],"This":[139],"paper":[140],"aims":[141],"at":[142],"extensions":[143],"results":[146],"piecewise":[148],"applications":[152],"corresponding":[154],"reformulations":[155],"complementarity":[158],"problems.":[159]},"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
