{"id":"https://openalex.org/W2160559638","doi":"https://doi.org/10.1080/10556788.2015.1025401","title":"A globally and quadratically convergent primal\u2013dual augmented Lagrangian algorithm for equality constrained optimization","display_name":"A globally and quadratically convergent primal\u2013dual augmented Lagrangian algorithm for equality constrained optimization","publication_year":2015,"publication_date":"2015-05-05","ids":{"openalex":"https://openalex.org/W2160559638","doi":"https://doi.org/10.1080/10556788.2015.1025401","mag":"2160559638"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2015.1025401","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2015.1025401","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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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/A5074795044","display_name":"Paul Armand","orcid":"https://orcid.org/0000-0002-8821-5799"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I65806277","display_name":"Universit\u00e9 de Limoges","ror":"https://ror.org/02cp04407","country_code":"FR","type":"education","lineage":["https://openalex.org/I65806277"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Paul Armand","raw_affiliation_strings":["University of Limoges (France), XLIM Laboratory \u2013 UMR CNRS n\u00b07252, Limoges, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Limoges (France), XLIM Laboratory \u2013 UMR CNRS n\u00b07252, Limoges, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I65806277"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091077750","display_name":"Riadh Omheni","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I65806277","display_name":"Universit\u00e9 de Limoges","ror":"https://ror.org/02cp04407","country_code":"FR","type":"education","lineage":["https://openalex.org/I65806277"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Riadh Omheni","raw_affiliation_strings":["University of Limoges (France), XLIM Laboratory \u2013 UMR CNRS n\u00b07252, Limoges, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Limoges (France), XLIM Laboratory \u2013 UMR CNRS n\u00b07252, Limoges, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I65806277"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074795044"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I65806277"],"apc_list":null,"apc_paid":null,"fwci":5.2562,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.96124207,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"32","issue":"1","first_page":"1","last_page":"21"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":1.0,"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":1.0,"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":0.9994999766349792,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9884999990463257,"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/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.9012570977210999},{"id":"https://openalex.org/keywords/quadratic-growth","display_name":"Quadratic growth","score":0.8099778294563293},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.640004575252533},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6032091379165649},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5930733680725098},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5731815099716187},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5371426343917847},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5204982161521912},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.5007121562957764},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4881010949611664},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.48622480034828186},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.4623485803604126},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46221914887428284},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.376269668340683},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3296751379966736},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11408472061157227}],"concepts":[{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.9012570977210999},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.8099778294563293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.640004575252533},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6032091379165649},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5930733680725098},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5731815099716187},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5371426343917847},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5204982161521912},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.5007121562957764},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4881010949611664},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.48622480034828186},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.4623485803604126},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46221914887428284},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.376269668340683},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3296751379966736},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11408472061157227},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"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/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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/10556788.2015.1025401","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2015.1025401","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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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"},{"id":"pmh:oai:HAL:hal-01313701v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01313701","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Optimization Methods and Software, 2015, pp.Online. ⟨10.1080/10556788.2015.1025401⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-02415230v1","is_oa":false,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-02415230","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1055-6788","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W147998453","https://openalex.org/W175029015","https://openalex.org/W646582900","https://openalex.org/W1502501036","https://openalex.org/W1669104078","https://openalex.org/W1977108089","https://openalex.org/W1978554456","https://openalex.org/W1987995897","https://openalex.org/W1989427372","https://openalex.org/W2027507632","https://openalex.org/W2031560822","https://openalex.org/W2033477411","https://openalex.org/W2033624514","https://openalex.org/W2034835449","https://openalex.org/W2037328914","https://openalex.org/W2042613327","https://openalex.org/W2050267927","https://openalex.org/W2057767216","https://openalex.org/W2058342841","https://openalex.org/W2068484625","https://openalex.org/W2076940249","https://openalex.org/W2123871098","https://openalex.org/W2125410188","https://openalex.org/W2149454052","https://openalex.org/W2155865164","https://openalex.org/W3029645440","https://openalex.org/W3118870036","https://openalex.org/W4252894371","https://openalex.org/W4301014524"],"related_works":["https://openalex.org/W2044296933","https://openalex.org/W4322011789","https://openalex.org/W2315802443","https://openalex.org/W4281679269","https://openalex.org/W2160559638","https://openalex.org/W4233380117","https://openalex.org/W2366409812","https://openalex.org/W4281493533","https://openalex.org/W102932032","https://openalex.org/W2375228751"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,16,21,30,51,63,69],"primal\u2013dual":[3],"augmented":[4,39],"Lagrangian":[5,40],"method":[6,18,66,103],"to":[7,20,62,68],"solve":[8],"an":[9,38],"equality":[10],"constrained":[11],"minimization":[12],"problem.":[13],"This":[14],"is":[15,48,77,85,91,104],"Newton-like":[17],"applied":[19,67],"perturbation":[22],"of":[23,32,45,53,57,71],"the":[24,33,59,102],"optimality":[25,72],"system":[26],"that":[27,101],"follows":[28],"from":[29],"reformulation":[31],"initial":[34],"problem":[35],"by":[36,50],"introducing":[37],"function.":[41],"An":[42,82],"important":[43],"aspect":[44],"this":[46],"approach":[47],"that,":[49],"choice":[52],"suitable":[54],"updating":[55],"rules":[56],"parameters,":[58],"algorithm":[60],"reduces":[61],"regularized":[64],"Newton":[65],"sequence":[70],"systems.":[73],"The":[74],"global":[75],"convergence":[76,90],"proved":[78,92],"under":[79,93],"mild":[80],"assumptions.":[81,96],"asymptotic":[83],"analysis":[84],"also":[86],"presented":[87],"and":[88,107],"quadratic":[89],"standard":[94],"regularity":[95],"Some":[97],"numerical":[98],"results":[99],"show":[100],"very":[105],"efficient":[106],"robust.":[108]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}