{"id":"https://openalex.org/W2056927789","doi":"https://doi.org/10.1007/s10107-006-0019-y","title":"Newton\u2019s iterates can converge to non-stationary points","display_name":"Newton\u2019s iterates can converge to non-stationary points","publication_year":2006,"publication_date":"2006-09-14","ids":{"openalex":"https://openalex.org/W2056927789","doi":"https://doi.org/10.1007/s10107-006-0019-y","mag":"2056927789"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-006-0019-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-006-0019-y","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","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/A5064718420","display_name":"Walter F. Mascarenhas","orcid":"https://orcid.org/0000-0002-5943-3228"},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Walter F. Mascarenhas","raw_affiliation_strings":["Computer Science Department, University of S\u00e3o Paulo, S\u00e3o Paulo, Brazil","University of S\u00e3o Paulo, Computer Science Department, S\u00e3o Paulo, Brazil#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, University of S\u00e3o Paulo, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I17974374"]},{"raw_affiliation_string":"University of S\u00e3o Paulo, Computer Science Department, S\u00e3o Paulo, Brazil#TAB#","institution_ids":["https://openalex.org/I17974374"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5064718420"],"corresponding_institution_ids":["https://openalex.org/I17974374"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":0.8607,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.72810169,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"112","issue":"2","first_page":"327","last_page":"334"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9995999932289124,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9973000288009644,"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/iterated-function","display_name":"Iterated function","score":0.9012989401817322},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.8608202934265137},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7488799095153809},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.7147594690322876},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6124966144561768},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.6083027720451355},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5775195360183716},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.5199231505393982},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5194025039672852},{"id":"https://openalex.org/keywords/newtons-method-in-optimization","display_name":"Newton's method in optimization","score":0.5172398686408997},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5055763721466064},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.43259352445602417},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4290786683559418},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.42004796862602234},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.2719734013080597},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.2662041187286377},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21739837527275085},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1734185516834259},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.13547369837760925},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08619663119316101},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.07130229473114014}],"concepts":[{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.9012989401817322},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.8608202934265137},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7488799095153809},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.7147594690322876},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6124966144561768},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.6083027720451355},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5775195360183716},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.5199231505393982},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5194025039672852},{"id":"https://openalex.org/C179127668","wikidata":"https://www.wikidata.org/wiki/Q17086396","display_name":"Newton's method in optimization","level":4,"score":0.5172398686408997},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5055763721466064},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.43259352445602417},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4290786683559418},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.42004796862602234},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.2719734013080597},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2662041187286377},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21739837527275085},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1734185516834259},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.13547369837760925},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08619663119316101},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.07130229473114014},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10107-006-0019-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-006-0019-y","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:www.producao.usp.br:BDPI/30413","is_oa":false,"landing_page_url":"http://producao.usp.br/handle/BDPI/30413","pdf_url":null,"source":{"id":"https://openalex.org/S4306401373","display_name":"Scientific Electronic Library Online (S\u00e3o Paulo Research Foundation, Latin American and Caribbean Center on Health Sciences Information, Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2982035970","host_organization_name":"Costa Rican Department of Social Security","host_organization_lineage":["https://openalex.org/I2982035970"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7099999785423279,"id":"https://metadata.un.org/sdg/13","display_name":"Climate action"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W563711960","https://openalex.org/W1988488690","https://openalex.org/W1998749910","https://openalex.org/W2009941369","https://openalex.org/W2058194880","https://openalex.org/W2077658674","https://openalex.org/W2095671204","https://openalex.org/W3012317737","https://openalex.org/W4212997115"],"related_works":["https://openalex.org/W2996136316","https://openalex.org/W2489086843","https://openalex.org/W2972343833","https://openalex.org/W2463007134","https://openalex.org/W4388964614","https://openalex.org/W4298544744","https://openalex.org/W2963397933","https://openalex.org/W2152951271","https://openalex.org/W2983297293","https://openalex.org/W2970432723"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}