{"id":"https://openalex.org/W2189373477","doi":"https://doi.org/10.1137/140974687","title":"Levenberg--Marquardt Methods Based on Probabilistic Gradient Models and Inexact Subproblem Solution, with Application to Data Assimilation","display_name":"Levenberg--Marquardt Methods Based on Probabilistic Gradient Models and Inexact Subproblem Solution, with Application to Data Assimilation","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2189373477","doi":"https://doi.org/10.1137/140974687","mag":"2189373477"},"language":"en","primary_location":{"id":"doi:10.1137/140974687","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140974687","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000183128","display_name":"El Houcine Bergou","orcid":"https://orcid.org/0000-0001-8685-6974"},"institutions":[{"id":"https://openalex.org/I4210106946","display_name":"Centre Europ\u00e9en de Recherche et de Formation Avanc\u00e9e en Calcul Scientifique","ror":"https://ror.org/02dzbc556","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210106946"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"E. Bergou","raw_affiliation_strings":["CERFACS - Centre Europ\u00e9en de Recherche et de Formation Avanc\u00e9e en Calcul Scientifique (42 Avenue Gaspard Coriolis 31057 TOULOUSE CEDEX 1  - France)"],"affiliations":[{"raw_affiliation_string":"CERFACS - Centre Europ\u00e9en de Recherche et de Formation Avanc\u00e9e en Calcul Scientifique (42 Avenue Gaspard Coriolis 31057 TOULOUSE CEDEX 1  - France)","institution_ids":["https://openalex.org/I4210106946"]}]},{"author_position":"middle","author":{"id":null,"display_name":"S. Gratton","orcid":null},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I205747304","display_name":"Institut National Polytechnique de Toulouse","ror":"https://ror.org/033p9g875","country_code":"FR","type":"education","lineage":["https://openalex.org/I205747304","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I3131550300","display_name":"Universit\u00e9 Toulouse-I-Capitole","ror":"https://ror.org/0443n9e75","country_code":"FR","type":"education","lineage":["https://openalex.org/I3131550300"]},{"id":"https://openalex.org/I4210119061","display_name":"Institut de Recherche en Informatique de Toulouse","ror":"https://ror.org/01rx4qw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I205747304","https://openalex.org/I205747304","https://openalex.org/I4210119061","https://openalex.org/I4387153255","https://openalex.org/I4405258862","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I4210152422","display_name":"Universit\u00e9 Toulouse - Jean Jaur\u00e8s","ror":"https://ror.org/04ezk3x31","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210152422","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"S. Gratton","raw_affiliation_strings":["Toulouse INP - Institut National Polytechnique (Toulouse) (France)","IRIT-APO - Algorithmes Parall\u00e8les et Optimisation (Institut de recherche en informatique de Toulouse - IRIT\r\n2 rue Charles Camichel \r\n31071 Toulouse Cedex 7 \r\n - France)"],"affiliations":[{"raw_affiliation_string":"Toulouse INP - Institut National Polytechnique (Toulouse) (France)","institution_ids":["https://openalex.org/I205747304"]},{"raw_affiliation_string":"IRIT-APO - Algorithmes Parall\u00e8les et Optimisation (Institut de recherche en informatique de Toulouse - IRIT\r\n2 rue Charles Camichel \r\n31071 Toulouse Cedex 7 \r\n - France)","institution_ids":["https://openalex.org/I4210152422","https://openalex.org/I134560555","https://openalex.org/I4210119061","https://openalex.org/I3131550300","https://openalex.org/I4210160189"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045737795","display_name":"L. N. Vicente","orcid":"https://orcid.org/0000-0003-1097-6384"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L. N. Vicente","raw_affiliation_strings":["CMUC - Center for Mathematics [Coimbra] (Department of Mathematics - Apartado 3008, EC Santa Cruz, 3001-501 Coimbra - Portugal)"],"affiliations":[{"raw_affiliation_string":"CMUC - Center for Mathematics [Coimbra] (Department of Mathematics - Apartado 3008, EC Santa Cruz, 3001-501 Coimbra - Portugal)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000183128"],"corresponding_institution_ids":["https://openalex.org/I4210106946"],"apc_list":null,"apc_paid":null,"fwci":1.2459,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.78043095,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"4","issue":"1","first_page":"924","last_page":"951"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11588","display_name":"Atmospheric and Environmental Gas Dynamics","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10029","display_name":"Climate variability and models","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"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":0.8462895154953003},{"id":"https://openalex.org/keywords/data-assimilation","display_name":"Data assimilation","score":0.673137903213501},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5167598128318787},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5083226561546326},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.508068323135376},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.49176838994026184},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4870493710041046},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4695839285850525},{"id":"https://openalex.org/keywords/non-linear-least-squares","display_name":"Non-linear least squares","score":0.46703407168388367},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4654484689235687},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.43768197298049927},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43609619140625},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.4167901575565338},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.4137056767940521},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4106558859348297},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3305131793022156},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.16101351380348206},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11577993631362915},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.07924777269363403},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07107269763946533}],"concepts":[{"id":"https://openalex.org/C87578567","wikidata":"https://www.wikidata.org/wiki/Q1426494","display_name":"Levenberg\u2013Marquardt algorithm","level":3,"score":0.8462895154953003},{"id":"https://openalex.org/C24552861","wikidata":"https://www.wikidata.org/wiki/Q2670177","display_name":"Data assimilation","level":2,"score":0.673137903213501},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5167598128318787},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5083226561546326},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.508068323135376},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.49176838994026184},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4870493710041046},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4695839285850525},{"id":"https://openalex.org/C45923927","wikidata":"https://www.wikidata.org/wiki/Q3319230","display_name":"Non-linear least squares","level":3,"score":0.46703407168388367},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4654484689235687},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.43768197298049927},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43609619140625},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.4167901575565338},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.4137056767940521},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4106558859348297},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3305131793022156},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.16101351380348206},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11577993631362915},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.07924777269363403},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07107269763946533},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/140974687","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140974687","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},{"id":"pmh:oai:oatao.univ-toulouse.fr:22604","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401987","display_name":"Open Archive Toulouse Archive Ouverte (University of Toulouse)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I17866349","host_organization_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","host_organization_lineage":["https://openalex.org/I17866349"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:estudogeral.sib.uc.pt:10316/45235","is_oa":true,"landing_page_url":"http://hdl.handle.net/10316/45235","pdf_url":"http://hdl.handle.net/10316/45235","source":{"id":"https://openalex.org/S4306401208","display_name":"Estudo Geral (Universidade de Coimbra)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2802025818","host_organization_name":"Hospitais da Universidade de Coimbra","host_organization_lineage":["https://openalex.org/I2802025818"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"http://purl.org/coar/resource_type/c_6501"},{"id":"pmh:oai:HAL:hal-02147989v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02147989","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification, 2016, 4 (1), pp.924-951. ⟨10.1137/140974687⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:oatao.univ-toulouse.fr:22604","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401987","display_name":"Open Archive Toulouse Archive Ouverte (University of Toulouse)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I17866349","host_organization_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","host_organization_lineage":["https://openalex.org/I17866349"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7831561873","display_name":null,"funder_award_id":"PTDC/MAT/116736/2010","funder_id":"https://openalex.org/F4320323392","funder_display_name":"Universidade de Coimbra"},{"id":"https://openalex.org/G8114687558","display_name":null,"funder_award_id":"PEst-C/MAT/UI0324/2011","funder_id":"https://openalex.org/F4320323392","funder_display_name":"Universidade de Coimbra"}],"funders":[{"id":"https://openalex.org/F4320323392","display_name":"Universidade de Coimbra","ror":"https://ror.org/04z8k9a98"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W64233612","https://openalex.org/W147998453","https://openalex.org/W181733065","https://openalex.org/W1522319528","https://openalex.org/W1874771276","https://openalex.org/W1896953440","https://openalex.org/W1966764026","https://openalex.org/W1976748077","https://openalex.org/W1984310153","https://openalex.org/W2087070363","https://openalex.org/W2087158441","https://openalex.org/W2091077439","https://openalex.org/W2098840904","https://openalex.org/W2120126266","https://openalex.org/W2139004160","https://openalex.org/W2146643351","https://openalex.org/W2164422015","https://openalex.org/W2169071224","https://openalex.org/W2256578114","https://openalex.org/W3029645440","https://openalex.org/W3099813880","https://openalex.org/W3100611908","https://openalex.org/W3133644220"],"related_works":["https://openalex.org/W2207919472","https://openalex.org/W4287100774","https://openalex.org/W3178591032","https://openalex.org/W2026943567","https://openalex.org/W4392713763","https://openalex.org/W4390841026","https://openalex.org/W1528610309","https://openalex.org/W1993594538","https://openalex.org/W2619923004","https://openalex.org/W3215115147"],"abstract_inverted_index":{"The":[0],"Levenberg--Marquardt":[1,36],"algorithm":[2,37,71],"is":[3,54,86,96,110],"one":[4],"of":[5,13,33,123],"the":[6,11,20,31,34,39,42,51,69,93,124,129],"most":[7],"popular":[8],"algorithms":[9],"for":[10],"solution":[12],"nonlinear":[14],"least":[15,44],"squares":[16,45],"problems.":[17],"Motivated":[18],"by":[19,128],"problem":[21],"structure":[22],"in":[23,28,116],"data":[24,118],"assimilation,":[25],"we":[26,66],"consider":[27],"this":[29],"paper":[30],"extension":[32],"classical":[35],"to":[38,74,113],"scenarios":[40],"where":[41,92,120],"linearized":[43],"subproblems":[46],"are":[47,126],"solved":[48],"inexactly":[49],"and/or":[50],"gradient":[52,95,125],"model":[53],"noisy":[55],"and":[56],"accurate":[57],"only":[58,103],"within":[59],"a":[60,75,99,106],"certain":[61,107],"probability.":[62,108],"Under":[63],"appropriate":[64],"assumptions,":[65],"show":[67],"that":[68],"modified":[70],"converges":[72],"globally":[73],"first":[76,87],"order":[77],"stationary":[78],"point":[79],"with":[80,98,105],"probability":[81],"one.":[82],"Our":[83],"proposed":[84],"approach":[85],"tested":[88],"on":[89],"simple":[90],"problems":[91],"exact":[94],"perturbed":[97],"Gaussian":[100],"noise":[101],"or":[102],"called":[104],"It":[109],"then":[111],"applied":[112],"an":[114],"instance":[115],"variational":[117],"assimilation":[119],"stochastic":[121],"models":[122],"computed":[127],"so-called":[130],"ensemble":[131],"methods.":[132]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}