{"id":"https://openalex.org/W2796881136","doi":"https://doi.org/10.1137/16m107534x","title":"The Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization with Application to the Compromise Problem","display_name":"The Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization with Application to the Compromise Problem","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2796881136","doi":"https://doi.org/10.1137/16m107534x","mag":"2796881136"},"language":"en","primary_location":{"id":"doi:10.1137/16m107534x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m107534x","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://amu.hal.science/hal-01985333","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112448116","display_name":"G. C. Bento","orcid":null},"institutions":[{"id":"https://openalex.org/I68106152","display_name":"Universidade Federal de Goi\u00e1s","ror":"https://ror.org/0039d5757","country_code":"BR","type":"education","lineage":["https://openalex.org/I68106152"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"G. C. Bento","raw_affiliation_strings":["UFG - Universidade Federal de Goi\u00e1s [Goi\u00e2nia] (Goi\u00e2nia, Goi\u00e1s - Brazil)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UFG - Universidade Federal de Goi\u00e1s [Goi\u00e2nia] (Goi\u00e2nia, Goi\u00e1s - Brazil)","institution_ids":["https://openalex.org/I68106152"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065320247","display_name":"J. X. Cruz Neto","orcid":"https://orcid.org/0000-0001-7489-6303"},"institutions":[{"id":"https://openalex.org/I3121799822","display_name":"Universidade Federal do Piau\u00ed","ror":"https://ror.org/00kwnx126","country_code":"BR","type":"education","lineage":["https://openalex.org/I3121799822"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"J. X. Cruz Neto","raw_affiliation_strings":["UFPI - Universidade Federal do Piau\u00ed (Teresina - Brazil)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UFPI - Universidade Federal do Piau\u00ed (Teresina - Brazil)","institution_ids":["https://openalex.org/I3121799822"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054042176","display_name":"Genaro L\u00f3pez-Acedo","orcid":"https://orcid.org/0000-0002-8303-7858"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"G. L\u00f3pez","raw_affiliation_strings":["Universidad de Sevilla = University of Seville (C/ S. Fernando, 4, C.P. 41004-Sevilla\r\n - Spain)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad de Sevilla = University of Seville (C/ S. Fernando, 4, C.P. 41004-Sevilla\r\n - Spain)","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064946162","display_name":"Antoine Soubeyran","orcid":"https://orcid.org/0000-0002-7277-4465"},"institutions":[{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"A. Soubeyran","raw_affiliation_strings":["AMSE - Aix-Marseille Sciences Economiques (5-9 Boulevard Bourdet\r\nCS 50498\r\n13205 Marseille Cedex 1 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AMSE - Aix-Marseille Sciences Economiques (5-9 Boulevard Bourdet\r\nCS 50498\r\n13205 Marseille Cedex 1 - France)","institution_ids":["https://openalex.org/I21491767"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009257887","display_name":"Jo\u00e3o Carlos O. Souza","orcid":"https://orcid.org/0000-0003-4053-8211"},"institutions":[{"id":"https://openalex.org/I122140584","display_name":"Universidade Federal do Rio de Janeiro","ror":"https://ror.org/03490as77","country_code":"BR","type":"education","lineage":["https://openalex.org/I122140584"]},{"id":"https://openalex.org/I3121799822","display_name":"Universidade Federal do Piau\u00ed","ror":"https://ror.org/00kwnx126","country_code":"BR","type":"education","lineage":["https://openalex.org/I3121799822"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"J. C. O. Souza","raw_affiliation_strings":["UFRJ - Universidade Federal do Rio de Janeiro [Brasil] = Federal University of Rio de Janeiro [Brazil] = Universit\u00e9 f\u00e9d\u00e9rale de Rio de Janeiro [Br\u00e9sil] (Av. Pedro Calmon, 550 - Cidade Universit\u00e1ria, Rio de Janeiro - RJ, 21941-901 - Brazil)","UFPI - Universidade Federal do Piau\u00ed (Teresina - Brazil)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UFRJ - Universidade Federal do Rio de Janeiro [Brasil] = Federal University of Rio de Janeiro [Brazil] = Universit\u00e9 f\u00e9d\u00e9rale de Rio de Janeiro [Br\u00e9sil] (Av. Pedro Calmon, 550 - Cidade Universit\u00e1ria, Rio de Janeiro - RJ, 21941-901 - Brazil)","institution_ids":["https://openalex.org/I122140584"]},{"raw_affiliation_string":"UFPI - Universidade Federal do Piau\u00ed (Teresina - Brazil)","institution_ids":["https://openalex.org/I3121799822"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0026,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.92230351,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"28","issue":"2","first_page":"1104","last_page":"1120"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9995999932289124,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983999729156494,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.998199999332428,"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":0.825218677520752},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.734724223613739},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7207403779029846},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.6545407176017761},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.6330513954162598},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.6086599230766296},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5993697047233582},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.49501198530197144},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.490477055311203},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.45851728320121765},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34824156761169434},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07720130681991577}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.825218677520752},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.734724223613739},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7207403779029846},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6545407176017761},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.6330513954162598},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.6086599230766296},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5993697047233582},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.49501198530197144},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.490477055311203},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.45851728320121765},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34824156761169434},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07720130681991577},{"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},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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":4,"locations":[{"id":"doi:10.1137/16m107534x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m107534x","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:dnet:idus________::0591f1293e2826cc2593d0091cb81bb0","is_oa":false,"landing_page_url":"https://idus.us.es/handle//11441/78385","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-01985333v1","is_oa":true,"landing_page_url":"https://amu.hal.science/hal-01985333","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 Journal on Optimization, 2018, 28 (2), pp.1104-1120. &#x27E8;10.1137/16M107534X&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:RePEc:hal:journl:hal-01985333","is_oa":false,"landing_page_url":"https://amu.hal.science/hal-01985333/document","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":"preprint"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01985333v1","is_oa":true,"landing_page_url":"https://amu.hal.science/hal-01985333","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 Journal on Optimization, 2018, 28 (2), pp.1104-1120. &#x27E8;10.1137/16M107534X&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G116629194","display_name":null,"funder_award_id":"88881","funder_id":"https://openalex.org/F4320321091","funder_display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior"},{"id":"https://openalex.org/G1644452137","display_name":null,"funder_award_id":"2014-4","funder_id":"https://openalex.org/F4320321091","funder_display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior"},{"id":"https://openalex.org/G1665590671","display_name":null,"funder_award_id":"05/2012","funder_id":"https://openalex.org/F4320323204","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Goi\u00e1s"},{"id":"https://openalex.org/G3786563689","display_name":null,"funder_award_id":"458479/2014-4","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G3835743233","display_name":"Transition Toward a Greener Economy: Environmental Policies and Societal Adaptation","funder_award_id":"ANR-16-CE03-0005","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4695665132","display_name":null,"funder_award_id":"201210267000909 - 05/2012","funder_id":"https://openalex.org/F4320323204","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Goi\u00e1s"},{"id":"https://openalex.org/G5885205928","display_name":null,"funder_award_id":"2016-01","funder_id":"https://openalex.org/F4320321091","funder_display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior"},{"id":"https://openalex.org/G5905040377","display_name":null,"funder_award_id":"2014-1","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G5907931268","display_name":null,"funder_award_id":"05/2012","funder_id":"https://openalex.org/F4320321091","funder_display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior"},{"id":"https://openalex.org/G5938272058","display_name":null,"funder_award_id":"312077/2014-9","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G6036676456","display_name":null,"funder_award_id":"203360/2014-1","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G6549679978","display_name":null,"funder_award_id":"2014-4","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G6815844370","display_name":null,"funder_award_id":"88881","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G7084771859","display_name":null,"funder_award_id":"471815/2012-8","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G7882215916","display_name":null,"funder_award_id":"305462/2014-8","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G827246598","display_name":null,"funder_award_id":"88881.117595/2016-01","funder_id":"https://openalex.org/F4320321091","funder_display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior"}],"funders":[{"id":"https://openalex.org/F4320309911","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20"},{"id":"https://openalex.org/F4320310967","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320323204","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Goi\u00e1s","ror":"https://ror.org/00w8cq239"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1953936588","https://openalex.org/W1969872429","https://openalex.org/W1973407216","https://openalex.org/W1981155649","https://openalex.org/W1983485346","https://openalex.org/W1987964049","https://openalex.org/W1998081129","https://openalex.org/W1998770947","https://openalex.org/W2000985550","https://openalex.org/W2004586020","https://openalex.org/W2011414908","https://openalex.org/W2014234363","https://openalex.org/W2024008934","https://openalex.org/W2029509128","https://openalex.org/W2032571239","https://openalex.org/W2034688818","https://openalex.org/W2038497950","https://openalex.org/W2044903028","https://openalex.org/W2045368552","https://openalex.org/W2048061283","https://openalex.org/W2052471135","https://openalex.org/W2053190248","https://openalex.org/W2057357578","https://openalex.org/W2060363103","https://openalex.org/W2063375245","https://openalex.org/W2065109455","https://openalex.org/W2067252707","https://openalex.org/W2078040808","https://openalex.org/W2080752182","https://openalex.org/W2081186095","https://openalex.org/W2081313036","https://openalex.org/W2087732079","https://openalex.org/W2100717205","https://openalex.org/W2119162261","https://openalex.org/W2154167715","https://openalex.org/W2561080469"],"related_works":["https://openalex.org/W4243698225","https://openalex.org/W2090178682","https://openalex.org/W2001591765","https://openalex.org/W4241467429","https://openalex.org/W2073147994","https://openalex.org/W1588199609","https://openalex.org/W2384474142","https://openalex.org/W1550055091","https://openalex.org/W2744462909","https://openalex.org/W3083133203"],"abstract_inverted_index":{"This":[0,109],"paper":[1],"studies":[2],"the":[3,40,56,61,66,92,100,105,123],"constrained":[4],"multiobjective":[5,43,81],"optimization":[6],"problem":[7,68,126],"of":[8,13,55,65,79,97],"finding":[9],"Pareto":[10,77],"critical":[11],"points":[12,78],"vector-valued":[14],"functions.":[15],"The":[16],"proximal":[17],"point":[18],"method":[19,57,93],"considered":[20],"by":[21,71],"Bonnel,":[22],"Iusem,":[23],"and":[24,130],"Svaiter":[25],"[SIAM":[26],"J.":[27],"Optim.,":[28],"15":[29],"(2005),":[30],"pp.":[31],"953--970]":[32],"is":[33,58,69,110],"extended":[34],"to":[35,90,117,119],"locally":[36],"Lipschitz":[37],"functions":[38],"in":[39,127],"finite":[41],"dimensional":[42],"setting.":[44],"To":[45],"this":[46,86],"end,":[47],"a":[48,72,80,84,120],"new":[49],"(scalarization-free)":[50],"approach":[51],"for":[52,75,113,115],"convergence":[53],"analysis":[54],"proposed":[59],"where":[60],"first-order":[62],"optimality":[63],"condition":[64,74],"scalarized":[67],"replaced":[70],"necessary":[73],"weak":[76],"problem.":[82],"As":[83],"consequence,":[85],"has":[87],"allowed":[88],"us":[89],"consider":[91],"without":[94],"any":[95],"assumption":[96],"convexity":[98],"over":[99],"constraint":[101],"sets":[102],"that":[103],"determine":[104],"vectorial":[106],"improvement":[107],"steps.":[108],"very":[111],"important":[112],"applications;":[114],"example,":[116],"extend":[118],"dynamic":[121],"setting":[122],"famous":[124],"compromise":[125],"management":[128],"sciences":[129],"game":[131],"theory.":[132]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}
