{"id":"https://openalex.org/W2336212496","doi":"https://doi.org/10.1080/10556788.2016.1171863","title":"Improved convergence results for a modified Levenberg\u2013Marquardt method for nonlinear equations and applications in MPCC","display_name":"Improved convergence results for a modified Levenberg\u2013Marquardt method for nonlinear equations and applications in MPCC","publication_year":2016,"publication_date":"2016-04-14","ids":{"openalex":"https://openalex.org/W2336212496","doi":"https://doi.org/10.1080/10556788.2016.1171863","mag":"2336212496"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2016.1171863","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2016.1171863","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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/A5077210988","display_name":"Xide Zhu","orcid":"https://orcid.org/0000-0002-4132-0575"},"institutions":[{"id":"https://openalex.org/I180203408","display_name":"Yokohama National University","ror":"https://ror.org/03zyp6p76","country_code":"JP","type":"education","lineage":["https://openalex.org/I180203408"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Xide Zhu","raw_affiliation_strings":["Faculty of Business Administration, Yokohama National University, 79-4 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan"],"affiliations":[{"raw_affiliation_string":"Faculty of Business Administration, Yokohama National University, 79-4 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan","institution_ids":["https://openalex.org/I180203408"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101224182","display_name":"Gui-Hua Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Gui-Hua Lin","raw_affiliation_strings":["School of Management, Shanghai University, Shanghai 200444, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Management, Shanghai University, Shanghai 200444, People's Republic of China","institution_ids":["https://openalex.org/I113940042"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101224182"],"corresponding_institution_ids":["https://openalex.org/I113940042"],"apc_list":null,"apc_paid":null,"fwci":2.7633,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.88772846,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"31","issue":"4","first_page":"791","last_page":"804"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","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/T10963","display_name":"Advanced Optimization Algorithms Research","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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9940000176429749,"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"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9936000108718872,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/levenberg\u2013marquardt-algorithm","display_name":"Levenberg\u2013Marquardt algorithm","score":0.9439390897750854},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7676973342895508},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6714246869087219},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5087929368019104},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46313241124153137},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.4466191530227661},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4277498722076416},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4136374592781067},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.23393100500106812},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10451111197471619},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.050363630056381226}],"concepts":[{"id":"https://openalex.org/C87578567","wikidata":"https://www.wikidata.org/wiki/Q1426494","display_name":"Levenberg\u2013Marquardt algorithm","level":3,"score":0.9439390897750854},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7676973342895508},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6714246869087219},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5087929368019104},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46313241124153137},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.4466191530227661},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4277498722076416},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4136374592781067},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.23393100500106812},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10451111197471619},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.050363630056381226},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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":1,"locations":[{"id":"doi:10.1080/10556788.2016.1171863","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2016.1171863","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1736552040","display_name":null,"funder_award_id":"11431004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1983644172","https://openalex.org/W2023446959","https://openalex.org/W2037678919","https://openalex.org/W2057418187","https://openalex.org/W2087070363","https://openalex.org/W2121625938","https://openalex.org/W2138849538","https://openalex.org/W2171126500","https://openalex.org/W2256578114","https://openalex.org/W4205236922"],"related_works":["https://openalex.org/W1978671516","https://openalex.org/W2895947699","https://openalex.org/W2374738832","https://openalex.org/W3196668723","https://openalex.org/W2794551249","https://openalex.org/W2074154109","https://openalex.org/W4392064155","https://openalex.org/W4249788058","https://openalex.org/W2349898028","https://openalex.org/W2110047879"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,32,48],"first":[4],"consider":[5],"a":[6,22],"modified":[7,52],"Levenberg\u2013Marquardt":[8,53],"method":[9,18,54],"for":[10],"solving":[11],"nonlinear":[12,26,44],"equations":[13,27,45],"and":[14],"show":[15,63],"that":[16,47,64],"the":[17,25,34,51,65],"converges":[19],"superlinearly":[20],"to":[21,55],"solution":[23],"of":[24,37],"under":[28],"suitable":[29],"conditions.":[30],"Then,":[31],"reformulate":[33],"C-/M-/S-stationarity":[35],"conditions":[36],"mathematical":[38],"program":[39],"with":[40],"complementarity":[41],"constraints":[42],"as":[43],"so":[46],"may":[49],"employ":[50],"solve":[56],"these":[57],"stationarity":[58],"systems.":[59],"Preliminary":[60],"numerical":[61],"experiments":[62],"new":[66],"approach":[67],"is":[68],"promising.":[69]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-12T07:58:50.170612","created_date":"2025-10-10T00:00:00"}
