{"id":"https://openalex.org/W2748610528","doi":"https://doi.org/10.1007/s10589-017-9937-2","title":"Augmented Lagrangians with constrained subproblems and convergence to second-order stationary points","display_name":"Augmented Lagrangians with constrained subproblems and convergence to second-order stationary points","publication_year":2017,"publication_date":"2017-08-16","ids":{"openalex":"https://openalex.org/W2748610528","doi":"https://doi.org/10.1007/s10589-017-9937-2","mag":"2748610528"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-017-9937-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-017-9937-2","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":true,"oa_status":"green","oa_url":"http://dx.doi.org/10.1007/s10589-017-9937-2","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087290455","display_name":"Ernesto G. Birgin","orcid":"https://orcid.org/0000-0002-7466-7663"},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"E. G. Birgin","raw_affiliation_strings":["Department of Computer Science, Institute of Mathematics and Statistics, University of S\u00e3o Paulo, Rua do Mat\u00e3o, 1010, Cidade Universit\u00e1ria, S\u00e3o Paulo, SP, 05508-090, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Institute of Mathematics and Statistics, University of S\u00e3o Paulo, Rua do Mat\u00e3o, 1010, Cidade Universit\u00e1ria, S\u00e3o Paulo, SP, 05508-090, Brazil","institution_ids":["https://openalex.org/I17974374"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045269430","display_name":"Gabriel Haeser","orcid":"https://orcid.org/0000-0002-1195-3347"},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["BR","US"],"is_corresponding":false,"raw_author_name":"G. Haeser","raw_affiliation_strings":["Department of Applied Mathematics, Institute of Mathematics and Statistics, University of S\u00e3o Paulo, Rua do Mat\u00e3o, 1010, Cidade Universit\u00e1ria, S\u00e3o Paulo, SP, 05508-090, Brazil","Department of Management Science and Engineering, Stanford University, Stanford, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Institute of Mathematics and Statistics, University of S\u00e3o Paulo, Rua do Mat\u00e3o, 1010, Cidade Universit\u00e1ria, S\u00e3o Paulo, SP, 05508-090, Brazil","institution_ids":["https://openalex.org/I17974374"]},{"raw_affiliation_string":"Department of Management Science and Engineering, Stanford University, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101825307","display_name":"Alberto Ramos","orcid":"https://orcid.org/0000-0003-0656-255X"},"institutions":[{"id":"https://openalex.org/I52418104","display_name":"Universidade Federal do Paran\u00e1","ror":"https://ror.org/05syd6y78","country_code":"BR","type":"education","lineage":["https://openalex.org/I52418104"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"A. Ramos","raw_affiliation_strings":["Department of Mathematics, Federal University of Paran\u00e1, Curitiba, PR, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Federal University of Paran\u00e1, Curitiba, PR, Brazil","institution_ids":["https://openalex.org/I52418104"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087290455"],"corresponding_institution_ids":["https://openalex.org/I17974374"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":7.4396,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.98162291,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"69","issue":"1","first_page":"51","last_page":"75"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9994000196456909,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8014935851097107},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.7900173664093018},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.6955888867378235},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.6587616205215454},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6524407863616943},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.583061933517456},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5381892919540405},{"id":"https://openalex.org/keywords/limit-point","display_name":"Limit point","score":0.47558534145355225},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.43646419048309326},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42364710569381714},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.410250186920166},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10711479187011719}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8014935851097107},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.7900173664093018},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.6955888867378235},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.6587616205215454},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6524407863616943},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.583061933517456},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5381892919540405},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.47558534145355225},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.43646419048309326},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42364710569381714},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.410250186920166},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10711479187011719},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10589-017-9937-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-017-9937-2","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:002856528","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10589-017-9937-2","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"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":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:RePEc:spr:coopap:v:69:y:2018:i:1:d:10.1007_s10589-017-9937-2","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10589-017-9937-2","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":{"id":"pmh:002856528","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10589-017-9937-2","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"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":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.46000000834465027}],"awards":[{"id":"https://openalex.org/G305158216","display_name":null,"funder_award_id":"2016/01860-1","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G3459681482","display_name":null,"funder_award_id":"309517/2014-1","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G4891547815","display_name":null,"funder_award_id":"2013/05475-7","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G5525191642","display_name":null,"funder_award_id":"2016/02092-8","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G5990746028","display_name":null,"funder_award_id":"2013/07375-0","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G7017918759","display_name":null,"funder_award_id":"303264/2015-2","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G7431257979","display_name":null,"funder_award_id":"2013/03447-6","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G8410287510","display_name":null,"funder_award_id":"481992/2013-8","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":64,"referenced_works":["https://openalex.org/W646582900","https://openalex.org/W1502501036","https://openalex.org/W1506690472","https://openalex.org/W1588628884","https://openalex.org/W1601741115","https://openalex.org/W1669104078","https://openalex.org/W1969778961","https://openalex.org/W1978100686","https://openalex.org/W1978804995","https://openalex.org/W1986491462","https://openalex.org/W1987995897","https://openalex.org/W1989012930","https://openalex.org/W1991359458","https://openalex.org/W1999386511","https://openalex.org/W2003949305","https://openalex.org/W2010007910","https://openalex.org/W2022054056","https://openalex.org/W2027347504","https://openalex.org/W2037091587","https://openalex.org/W2042555539","https://openalex.org/W2042613327","https://openalex.org/W2045497213","https://openalex.org/W2045512849","https://openalex.org/W2057565823","https://openalex.org/W2057624533","https://openalex.org/W2067263573","https://openalex.org/W2069612911","https://openalex.org/W2075572180","https://openalex.org/W2079135578","https://openalex.org/W2081019385","https://openalex.org/W2086194488","https://openalex.org/W2093112915","https://openalex.org/W2094214271","https://openalex.org/W2094299970","https://openalex.org/W2096686957","https://openalex.org/W2111920137","https://openalex.org/W2111948593","https://openalex.org/W2121445773","https://openalex.org/W2125712877","https://openalex.org/W2130633138","https://openalex.org/W2144963972","https://openalex.org/W2155865164","https://openalex.org/W2218983664","https://openalex.org/W2227855362","https://openalex.org/W2327853323","https://openalex.org/W2346238354","https://openalex.org/W2346844867","https://openalex.org/W2491661152","https://openalex.org/W2502970747","https://openalex.org/W2546420264","https://openalex.org/W2547797606","https://openalex.org/W2575646877","https://openalex.org/W2587436146","https://openalex.org/W2623997598","https://openalex.org/W2630805023","https://openalex.org/W2757525832","https://openalex.org/W2796766994","https://openalex.org/W2798766386","https://openalex.org/W2963687412","https://openalex.org/W3029645440","https://openalex.org/W4242209908","https://openalex.org/W4285719527","https://openalex.org/W4300448178","https://openalex.org/W6777545565"],"related_works":["https://openalex.org/W2015060724","https://openalex.org/W3105202832","https://openalex.org/W2058578573","https://openalex.org/W2012871340","https://openalex.org/W3046535663","https://openalex.org/W3035320230","https://openalex.org/W4317581747","https://openalex.org/W4287694146","https://openalex.org/W120058203","https://openalex.org/W2076425042"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2}],"updated_date":"2026-05-16T08:24:45.110214","created_date":"2017-08-31T00:00:00"}
