{"id":"https://openalex.org/W2239703712","doi":"https://doi.org/10.1007/s10957-015-0861-2","title":"A New Approach to the Proximal Point Method: Convergence on General Riemannian Manifolds","display_name":"A New Approach to the Proximal Point Method: Convergence on General Riemannian Manifolds","publication_year":2016,"publication_date":"2016-01-11","ids":{"openalex":"https://openalex.org/W2239703712","doi":"https://doi.org/10.1007/s10957-015-0861-2","mag":"2239703712"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-015-0861-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-015-0861-2","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory 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/A5062039563","display_name":"Glaydston de Carvalho Bento","orcid":"https://orcid.org/0000-0001-6983-4132"},"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":true,"raw_author_name":"Glaydston de Carvalho Bento","raw_affiliation_strings":["IME, Universidade Federal de Goi\u00e1s, Goi\u00e2nia, GO, 74001-970, Brazil"],"affiliations":[{"raw_affiliation_string":"IME, Universidade Federal de Goi\u00e1s, Goi\u00e2nia, GO, 74001-970, Brazil","institution_ids":["https://openalex.org/I68106152"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110064311","display_name":"Jo\u00e3o Xavier da Cruz Neto","orcid":null},"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":"Jo\u00e3o Xavier da Cruz Neto","raw_affiliation_strings":["DM, Universidade Federal do Piau\u00ed, Terezina, PI, 64049-550, Brazil"],"affiliations":[{"raw_affiliation_string":"DM, Universidade Federal do Piau\u00ed, Terezina, PI, 64049-550, Brazil","institution_ids":["https://openalex.org/I3121799822"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102272028","display_name":"Paulo Roberto Oliveira","orcid":"https://orcid.org/0009-0002-6187-4177"},"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"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Paulo Roberto Oliveira","raw_affiliation_strings":["COPPE-Sistemas, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ,  21945-970, Brazil"],"affiliations":[{"raw_affiliation_string":"COPPE-Sistemas, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ,  21945-970, Brazil","institution_ids":["https://openalex.org/I122140584"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5062039563"],"corresponding_institution_ids":["https://openalex.org/I68106152"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":4.3423,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.94366114,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"168","issue":"3","first_page":"743","last_page":"755"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9954000115394592,"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":0.9954000115394592,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9829000234603882,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.802976131439209},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.6878579258918762},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.6222914457321167},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.587992787361145},{"id":"https://openalex.org/keywords/sectional-curvature","display_name":"Sectional curvature","score":0.562330961227417},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.545253336429596},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5380197763442993},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.529403567314148},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.49142682552337646},{"id":"https://openalex.org/keywords/ricci-curvature","display_name":"Ricci curvature","score":0.4741898477077484},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.46777525544166565},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.46380212903022766},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.462547242641449},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4584078788757324},{"id":"https://openalex.org/keywords/riemannian-geometry","display_name":"Riemannian geometry","score":0.44671133160591125},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43331021070480347},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4071812331676483},{"id":"https://openalex.org/keywords/scalar-curvature","display_name":"Scalar curvature","score":0.31367677450180054},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19553601741790771},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12670528888702393},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12070474028587341}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.802976131439209},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.6878579258918762},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.6222914457321167},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.587992787361145},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.562330961227417},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.545253336429596},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5380197763442993},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.529403567314148},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.49142682552337646},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.4741898477077484},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.46777525544166565},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.46380212903022766},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.462547242641449},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4584078788757324},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.44671133160591125},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43331021070480347},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4071812331676483},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.31367677450180054},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19553601741790771},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12670528888702393},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12070474028587341},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-015-0861-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-015-0861-2","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:168:y:2016:i:3:d:10.1007_s10957-015-0861-2","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-015-0861-2","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":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.6899999976158142,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"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/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"}],"funders":[{"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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W1491029103","https://openalex.org/W1512226162","https://openalex.org/W1770194937","https://openalex.org/W1788938005","https://openalex.org/W1804110266","https://openalex.org/W1967138577","https://openalex.org/W1983057379","https://openalex.org/W1987964049","https://openalex.org/W1989651752","https://openalex.org/W1996195522","https://openalex.org/W2005669112","https://openalex.org/W2017475874","https://openalex.org/W2021361347","https://openalex.org/W2022164193","https://openalex.org/W2022541060","https://openalex.org/W2027239288","https://openalex.org/W2028466230","https://openalex.org/W2029840249","https://openalex.org/W2048742402","https://openalex.org/W2049830000","https://openalex.org/W2061455579","https://openalex.org/W2065103551","https://openalex.org/W2068357778","https://openalex.org/W2070997813","https://openalex.org/W2078853581","https://openalex.org/W2079004067","https://openalex.org/W2080002852","https://openalex.org/W2080698304","https://openalex.org/W2082933984","https://openalex.org/W2105735474","https://openalex.org/W2120731700","https://openalex.org/W2129732816","https://openalex.org/W2130071206","https://openalex.org/W2136320557","https://openalex.org/W2144322083","https://openalex.org/W2272546632","https://openalex.org/W2614092146","https://openalex.org/W2735780419","https://openalex.org/W2783729014","https://openalex.org/W3038420293","https://openalex.org/W3129186208","https://openalex.org/W4205293427","https://openalex.org/W4206033904","https://openalex.org/W4285719527","https://openalex.org/W4298032328"],"related_works":["https://openalex.org/W2421980838","https://openalex.org/W2087112780","https://openalex.org/W2254577414","https://openalex.org/W4307537658","https://openalex.org/W2005999811","https://openalex.org/W2017266758","https://openalex.org/W2097417475","https://openalex.org/W2368958746","https://openalex.org/W2393498249","https://openalex.org/W2118815436"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}
