{"id":"https://openalex.org/W2471407736","doi":"https://doi.org/10.1007/s10107-016-1047-x","title":"Critical solutions of nonlinear equations: stability issues","display_name":"Critical solutions of nonlinear equations: stability issues","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2471407736","doi":"https://doi.org/10.1007/s10107-016-1047-x","mag":"2471407736"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-016-1047-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-016-1047-x","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/A5085617315","display_name":"A. F. Izmailov","orcid":"https://orcid.org/0000-0001-9851-0524"},"institutions":[{"id":"https://openalex.org/I126527374","display_name":"Peoples' Friendship University of Russia","ror":"https://ror.org/02dn9h927","country_code":"RU","type":"education","lineage":["https://openalex.org/I126527374"]},{"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":["OR Department, VMK Faculty, Lomonosov Moscow State University (MSU), Uchebniy Korpus 2, Leninskiye Gory, Moscow, Russia, 119991","RUDN University, Miklukho-Maklaya Str. 6, Moscow, Russia, 117198"],"affiliations":[{"raw_affiliation_string":"OR Department, VMK Faculty, Lomonosov Moscow State University (MSU), Uchebniy Korpus 2, Leninskiye Gory, Moscow, Russia, 119991","institution_ids":["https://openalex.org/I19880235"]},{"raw_affiliation_string":"RUDN University, Miklukho-Maklaya Str. 6, Moscow, Russia, 117198","institution_ids":["https://openalex.org/I126527374"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016997771","display_name":"Alexey Kurennoy","orcid":"https://orcid.org/0000-0001-8216-9659"},"institutions":[{"id":"https://openalex.org/I108321963","display_name":"Tambov State University","ror":"https://ror.org/05fzc8c45","country_code":"RU","type":"education","lineage":["https://openalex.org/I108321963"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A. S. Kurennoy","raw_affiliation_strings":["Department of Mathematics, Physics and Computer Sciences, Derzhavin Tambov State University, TSU, Internationalnaya 33, Tambov, Russia, 392000"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Physics and Computer Sciences, Derzhavin Tambov State University, TSU, Internationalnaya 33, Tambov, Russia, 392000","institution_ids":["https://openalex.org/I108321963"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110039123","display_name":"M. V. Solodov","orcid":null},"institutions":[{"id":"https://openalex.org/I4210128604","display_name":"Instituto de Pesquisas Jardim Bot\u00e2nico do Rio de Janeiro","ror":"https://ror.org/033xtdz52","country_code":"BR","type":"archive","lineage":["https://openalex.org/I4210128604"]},{"id":"https://openalex.org/I141883831","display_name":"Instituto Nacional de Matem\u00e1tica Pura e Aplicada","ror":"https://ror.org/028caqe42","country_code":"BR","type":"facility","lineage":["https://openalex.org/I141883831","https://openalex.org/I4210151455"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"M. V. Solodov","raw_affiliation_strings":["IMPA \u2013 Instituto de Matem\u00e1tica Pura e Aplicada, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ, 22460-320, Brazil"],"affiliations":[{"raw_affiliation_string":"IMPA \u2013 Instituto de Matem\u00e1tica Pura e Aplicada, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ, 22460-320, Brazil","institution_ids":["https://openalex.org/I141883831","https://openalex.org/I4210128604"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5110039123"],"corresponding_institution_ids":["https://openalex.org/I141883831","https://openalex.org/I4210128604"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.406,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.79894287,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"168","issue":"1-2","first_page":"475","last_page":"507"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9986000061035156,"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":0.9986000061035156,"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":0.996999979019165,"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/T12672","display_name":"Phagocytosis and Immune Regulation","score":0.9847999811172485,"subfield":{"id":"https://openalex.org/subfields/2403","display_name":"Immunology"},"field":{"id":"https://openalex.org/fields/24","display_name":"Immunology and Microbiology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8398982882499695},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.8049567937850952},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6058070063591003},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5265653133392334},{"id":"https://openalex.org/keywords/constraint-algorithm","display_name":"Constraint algorithm","score":0.50794917345047},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4884604513645172},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4604343771934509},{"id":"https://openalex.org/keywords/criticality","display_name":"Criticality","score":0.42108678817749023},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3814013600349426},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3387548327445984},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08427435159683228}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8398982882499695},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.8049567937850952},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6058070063591003},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5265653133392334},{"id":"https://openalex.org/C15980293","wikidata":"https://www.wikidata.org/wiki/Q5164368","display_name":"Constraint algorithm","level":3,"score":0.50794917345047},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4884604513645172},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4604343771934509},{"id":"https://openalex.org/C125611927","wikidata":"https://www.wikidata.org/wiki/Q17008131","display_name":"Criticality","level":2,"score":0.42108678817749023},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3814013600349426},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3387548327445984},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08427435159683228},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C185544564","wikidata":"https://www.wikidata.org/wiki/Q81197","display_name":"Nuclear physics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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":1,"locations":[{"id":"doi:10.1007/s10107-016-1047-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-016-1047-x","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","display_name":"Climate action","score":0.5199999809265137}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W388179047","https://openalex.org/W1235853611","https://openalex.org/W1484024929","https://openalex.org/W1551360398","https://openalex.org/W1601741115","https://openalex.org/W1964445256","https://openalex.org/W1965923636","https://openalex.org/W1977794212","https://openalex.org/W2006146953","https://openalex.org/W2006963158","https://openalex.org/W2018824951","https://openalex.org/W2020968449","https://openalex.org/W2045664455","https://openalex.org/W2067758385","https://openalex.org/W2068254260","https://openalex.org/W2078921378","https://openalex.org/W2101730742","https://openalex.org/W2132977116","https://openalex.org/W2140495926","https://openalex.org/W2146829838","https://openalex.org/W2154034819","https://openalex.org/W2166972541","https://openalex.org/W2285572974","https://openalex.org/W2496276084","https://openalex.org/W2499159698","https://openalex.org/W2595644070","https://openalex.org/W2735095508","https://openalex.org/W2735097869","https://openalex.org/W2735531988","https://openalex.org/W2774032669","https://openalex.org/W2962678300","https://openalex.org/W4231531256","https://openalex.org/W4237326927","https://openalex.org/W4249513058","https://openalex.org/W4253052269"],"related_works":["https://openalex.org/W2024837890","https://openalex.org/W2074745806","https://openalex.org/W1979241556","https://openalex.org/W2021667451","https://openalex.org/W2352028553","https://openalex.org/W1967449934","https://openalex.org/W1970808271","https://openalex.org/W2045861968","https://openalex.org/W2017306930","https://openalex.org/W2781111882"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}