{"id":"https://openalex.org/W2155611394","doi":"https://doi.org/10.1007/s11075-012-9613-7","title":"A perturbed version of an inexact generalized Newton method for solving nonsmooth equations","display_name":"A perturbed version of an inexact generalized Newton method for solving nonsmooth equations","publication_year":2012,"publication_date":"2012-06-29","ids":{"openalex":"https://openalex.org/W2155611394","doi":"https://doi.org/10.1007/s11075-012-9613-7","mag":"2155611394"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-012-9613-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-012-9613-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-012-9613-7.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","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/s11075-012-9613-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022709642","display_name":"Marek J. \u015amieta\u0144ski","orcid":"https://orcid.org/0000-0002-6557-6436"},"institutions":[{"id":"https://openalex.org/I34250744","display_name":"University of \u0141\u00f3d\u017a","ror":"https://ror.org/05cq64r17","country_code":"PL","type":"education","lineage":["https://openalex.org/I34250744"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Marek J. \u015amieta\u0144ski","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, University of \u0141\u00f3d\u017a, Banacha 22, 90-238, \u0141\u00f3d\u017a, Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, University of \u0141\u00f3d\u017a, Banacha 22, 90-238, \u0141\u00f3d\u017a, Poland","institution_ids":["https://openalex.org/I34250744"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022709642"],"corresponding_institution_ids":["https://openalex.org/I34250744"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.18216192,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"63","issue":"1","first_page":"89","last_page":"106"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9994999766349792,"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":0.9962999820709229,"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/mathematics","display_name":"Mathematics","score":0.8455199003219604},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.6996263265609741},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6364899277687073},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5574314594268799},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5568180680274963},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.5510460138320923},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32664093375205994},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.3213244080543518},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.26314687728881836},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.25851041078567505},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.09851786494255066}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8455199003219604},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.6996263265609741},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6364899277687073},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5574314594268799},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5568180680274963},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.5510460138320923},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32664093375205994},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3213244080543518},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.26314687728881836},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25851041078567505},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09851786494255066},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/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/s11075-012-9613-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-012-9613-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-012-9613-7.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11075-012-9613-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-012-9613-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-012-9613-7.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2155611394.pdf","grobid_xml":"https://content.openalex.org/works/W2155611394.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W37633699","https://openalex.org/W68750926","https://openalex.org/W114360678","https://openalex.org/W172672465","https://openalex.org/W593515487","https://openalex.org/W621833885","https://openalex.org/W1748199557","https://openalex.org/W1968932160","https://openalex.org/W1983691524","https://openalex.org/W1987789634","https://openalex.org/W1992688650","https://openalex.org/W2004819861","https://openalex.org/W2017711521","https://openalex.org/W2030446182","https://openalex.org/W2034511718","https://openalex.org/W2041280162","https://openalex.org/W2042725681","https://openalex.org/W2048564717","https://openalex.org/W2062692049","https://openalex.org/W2067547116","https://openalex.org/W2068484625","https://openalex.org/W2070890393","https://openalex.org/W2078787010","https://openalex.org/W2082746403","https://openalex.org/W2088055586","https://openalex.org/W2090963365","https://openalex.org/W2101858062","https://openalex.org/W2107501462","https://openalex.org/W2113734366","https://openalex.org/W2116210979","https://openalex.org/W2119592490","https://openalex.org/W2135622428","https://openalex.org/W2238101614","https://openalex.org/W2494622204","https://openalex.org/W2920856728","https://openalex.org/W2963670035","https://openalex.org/W3216976781","https://openalex.org/W4246993478","https://openalex.org/W4299512035"],"related_works":["https://openalex.org/W2350788688","https://openalex.org/W2358591430","https://openalex.org/W2103912232","https://openalex.org/W2031390949","https://openalex.org/W2026900827","https://openalex.org/W3094698614","https://openalex.org/W1964267519","https://openalex.org/W3180920337","https://openalex.org/W3140142921","https://openalex.org/W4308670056"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"present":[4],"the":[5,8,13,25,31,43,59,69,79,84,96],"combination":[6],"of":[7,30,61,75,81,86,95],"inexact":[9,98],"Newton":[10,15,100],"method":[11,16,101],"and":[12,33,45],"generalized":[14,99],"for":[17,102],"solving":[18,103],"nonsmooth":[19],"equations":[20],"F(x)":[21],"=":[22],"0,":[23],"characterizing":[24],"local":[26],"convergence":[27,80],"in":[28],"terms":[29],"perturbations":[32,76],"residuals.":[34],"We":[35,67],"assume":[36],"that":[37],"both":[38],"iteration":[39],"matrices":[40],"taken":[41],"from":[42],"B-differential":[44],"vectors":[46],"F(x":[47],"(k))":[48],"are":[49,56],"perturbed":[50,97],"at":[51],"each":[52],"step.":[53],"Some":[54],"results":[55,88],"motivated":[57],"by":[58],"approach":[60],"C\u0103tina\u015f":[62],"regarding":[63],"to":[64,77],"smooth":[65],"equations.":[66],"study":[68],"conditions,":[70],"which":[71],"determine":[72],"admissible":[73],"magnitude":[74],"preserve":[78],"method.":[82],"Finally,":[83],"utility":[85],"these":[87],"is":[89],"considered":[90],"based":[91],"on":[92],"some":[93,104],"variant":[94],"general":[105],"optimization":[106],"problems.":[107]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}