{"id":"https://openalex.org/W4385420801","doi":"https://doi.org/10.1007/s10589-023-00513-z","title":"A modified inexact Levenberg\u2013Marquardt method with the descent property for solving nonlinear equations","display_name":"A modified inexact Levenberg\u2013Marquardt method with the descent property for solving nonlinear equations","publication_year":2023,"publication_date":"2023-07-31","ids":{"openalex":"https://openalex.org/W4385420801","doi":"https://doi.org/10.1007/s10589-023-00513-z"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-023-00513-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-023-00513-z","pdf_url":null,"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046308447","display_name":"Jianghua Yin","orcid":"https://orcid.org/0000-0002-0990-4327"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jianghua Yin","raw_affiliation_strings":["College of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning, 530006, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning, 530006, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066627199","display_name":"Jinbao Jian","orcid":"https://orcid.org/0000-0001-8048-7397"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jinbao Jian","raw_affiliation_strings":["College of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning, 530006, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning, 530006, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102938855","display_name":"Guodong Ma","orcid":"https://orcid.org/0000-0002-3575-2988"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guodong Ma","raw_affiliation_strings":["College of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning, 530006, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning, 530006, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066627199"],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":14.1681,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.99699549,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"87","issue":"1","first_page":"289","last_page":"322"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9968000054359436,"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/mathematics","display_name":"Mathematics","score":0.7690819501876831},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.7286142706871033},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.721708357334137},{"id":"https://openalex.org/keywords/levenberg\u2013marquardt-algorithm","display_name":"Levenberg\u2013Marquardt algorithm","score":0.6961072087287903},{"id":"https://openalex.org/keywords/underdetermined-system","display_name":"Underdetermined system","score":0.65058434009552},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.6354957222938538},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6240170001983643},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5401830077171326},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.5283216834068298},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47386646270751953},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45630306005477905},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.436631441116333},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.42980608344078064},{"id":"https://openalex.org/keywords/trust-region","display_name":"Trust region","score":0.4217141568660736},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4183829128742218},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3024429678916931},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.2026466727256775},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18386706709861755},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13214468955993652},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.10668638348579407}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7690819501876831},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.7286142706871033},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.721708357334137},{"id":"https://openalex.org/C87578567","wikidata":"https://www.wikidata.org/wiki/Q1426494","display_name":"Levenberg\u2013Marquardt algorithm","level":3,"score":0.6961072087287903},{"id":"https://openalex.org/C179690561","wikidata":"https://www.wikidata.org/wiki/Q4316110","display_name":"Underdetermined system","level":2,"score":0.65058434009552},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.6354957222938538},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6240170001983643},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5401830077171326},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.5283216834068298},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47386646270751953},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45630306005477905},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.436631441116333},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.42980608344078064},{"id":"https://openalex.org/C89109886","wikidata":"https://www.wikidata.org/wiki/Q1535924","display_name":"Trust region","level":3,"score":0.4217141568660736},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4183829128742218},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3024429678916931},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2026466727256775},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18386706709861755},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13214468955993652},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.10668638348579407},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10589-023-00513-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-023-00513-z","pdf_url":null,"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":null,"license_id":null,"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:87:y:2024:i:1:d:10.1007_s10589-023-00513-z","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10589-023-00513-z","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2163614853","display_name":null,"funder_award_id":"12171106","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6863316139","display_name":null,"funder_award_id":"2023GXNSFBA026029","funder_id":"https://openalex.org/F4320322768","funder_display_name":"Natural Science Foundation of Guangxi Province"},{"id":"https://openalex.org/G738249777","display_name":null,"funder_award_id":"12261008","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"},{"id":"https://openalex.org/F4320322768","display_name":"Natural Science Foundation of Guangxi Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W106246290","https://openalex.org/W612879516","https://openalex.org/W1971559451","https://openalex.org/W1996701679","https://openalex.org/W2018794399","https://openalex.org/W2022428742","https://openalex.org/W2023446959","https://openalex.org/W2045538552","https://openalex.org/W2055326668","https://openalex.org/W2056603712","https://openalex.org/W2057418187","https://openalex.org/W2070335103","https://openalex.org/W2073198536","https://openalex.org/W2080611873","https://openalex.org/W2087070363","https://openalex.org/W2099003992","https://openalex.org/W2109591264","https://openalex.org/W2149454052","https://openalex.org/W2153635508","https://openalex.org/W2160846482","https://openalex.org/W2186467072","https://openalex.org/W2256578114","https://openalex.org/W2314752190","https://openalex.org/W2336212496","https://openalex.org/W2344098705","https://openalex.org/W2346412421","https://openalex.org/W2398068802","https://openalex.org/W2405649773","https://openalex.org/W2529842698","https://openalex.org/W2660052857","https://openalex.org/W2773424228","https://openalex.org/W2792739722","https://openalex.org/W2810281214","https://openalex.org/W2810507125","https://openalex.org/W2946967476","https://openalex.org/W2953387096","https://openalex.org/W2977713834","https://openalex.org/W2991289507","https://openalex.org/W3000315134","https://openalex.org/W3012581155","https://openalex.org/W3024054958","https://openalex.org/W3105742279","https://openalex.org/W4292363360","https://openalex.org/W4301014524","https://openalex.org/W4307819962"],"related_works":["https://openalex.org/W4295532945","https://openalex.org/W2160846482","https://openalex.org/W3197573213","https://openalex.org/W2991289507","https://openalex.org/W833941023","https://openalex.org/W4286986829","https://openalex.org/W2200018736","https://openalex.org/W2515666504","https://openalex.org/W3047313702","https://openalex.org/W4385420801"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":9},{"year":2025,"cited_by_count":17},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-03T22:45:19.894376","created_date":"2025-10-10T00:00:00"}