{"id":"https://openalex.org/W2136320557","doi":"https://doi.org/10.1007/s10957-013-0307-7","title":"A Subgradient Method for Multiobjective Optimization on Riemannian Manifolds","display_name":"A Subgradient Method for Multiobjective Optimization on Riemannian Manifolds","publication_year":2013,"publication_date":"2013-04-18","ids":{"openalex":"https://openalex.org/W2136320557","doi":"https://doi.org/10.1007/s10957-013-0307-7","mag":"2136320557"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-013-0307-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-013-0307-7","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/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":true,"raw_author_name":"G. C. Bento","raw_affiliation_strings":["Universidade Federal de Goi\u00e1s, Goi\u00e2nia, Brazil","Universidade Federal de GOI\u00c1S"],"affiliations":[{"raw_affiliation_string":"Universidade Federal de Goi\u00e1s, Goi\u00e2nia, Brazil","institution_ids":["https://openalex.org/I68106152"]},{"raw_affiliation_string":"Universidade Federal de GOI\u00c1S","institution_ids":["https://openalex.org/I68106152"]}]},{"author_position":"last","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\u00a0Neto","raw_affiliation_strings":["Universidade Federal Piau\u00ed, Teresina, Brazil","Universidade Federal Piau\u00ed"],"affiliations":[{"raw_affiliation_string":"Universidade Federal Piau\u00ed, Teresina, Brazil","institution_ids":["https://openalex.org/I3121799822"]},{"raw_affiliation_string":"Universidade Federal Piau\u00ed","institution_ids":["https://openalex.org/I3121799822"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112448116"],"corresponding_institution_ids":["https://openalex.org/I68106152"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":4.1094,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.94242106,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"159","issue":"1","first_page":"125","last_page":"137"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9983000159263611,"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/T11115","display_name":"Topology Optimization in Engineering","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"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/subgradient-method","display_name":"Subgradient method","score":0.9739174842834473},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7648732662200928},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6855934858322144},{"id":"https://openalex.org/keywords/sectional-curvature","display_name":"Sectional curvature","score":0.5138647556304932},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.5059263110160828},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.49410465359687805},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.47736072540283203},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.4273514449596405},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4106863737106323},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4101179838180542},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3896860182285309},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38042712211608887},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18728938698768616},{"id":"https://openalex.org/keywords/scalar-curvature","display_name":"Scalar curvature","score":0.1437942385673523},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06514552235603333}],"concepts":[{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.9739174842834473},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7648732662200928},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6855934858322144},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.5138647556304932},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.5059263110160828},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.49410465359687805},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.47736072540283203},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.4273514449596405},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4106863737106323},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4101179838180542},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3896860182285309},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38042712211608887},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18728938698768616},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.1437942385673523},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06514552235603333},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-013-0307-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-013-0307-7","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:159:y:2013:i:1:d:10.1007_s10957-013-0307-7","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-013-0307-7","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":[],"awards":[],"funders":[{"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":52,"referenced_works":["https://openalex.org/W33560209","https://openalex.org/W113278869","https://openalex.org/W1550635507","https://openalex.org/W1829751671","https://openalex.org/W1922505179","https://openalex.org/W1978282155","https://openalex.org/W1978930363","https://openalex.org/W1980574663","https://openalex.org/W1982203135","https://openalex.org/W1983057379","https://openalex.org/W1989651752","https://openalex.org/W1997143365","https://openalex.org/W2004586020","https://openalex.org/W2019338124","https://openalex.org/W2022931449","https://openalex.org/W2026724886","https://openalex.org/W2028466230","https://openalex.org/W2029840249","https://openalex.org/W2032571239","https://openalex.org/W2049830000","https://openalex.org/W2052471135","https://openalex.org/W2057187244","https://openalex.org/W2061057786","https://openalex.org/W2061455579","https://openalex.org/W2061657011","https://openalex.org/W2066214692","https://openalex.org/W2067952903","https://openalex.org/W2071569531","https://openalex.org/W2076428552","https://openalex.org/W2077321023","https://openalex.org/W2080752182","https://openalex.org/W2082584863","https://openalex.org/W2082933984","https://openalex.org/W2085379846","https://openalex.org/W2088638547","https://openalex.org/W2092736015","https://openalex.org/W2100717205","https://openalex.org/W2118806049","https://openalex.org/W2130469840","https://openalex.org/W2141519660","https://openalex.org/W2144322083","https://openalex.org/W2169708078","https://openalex.org/W2184567536","https://openalex.org/W3038420293","https://openalex.org/W3040283615","https://openalex.org/W3129186208","https://openalex.org/W4206033904","https://openalex.org/W4211092921","https://openalex.org/W4235476591","https://openalex.org/W4246883249","https://openalex.org/W4249125060","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1550635507","https://openalex.org/W2093838058","https://openalex.org/W1799346622","https://openalex.org/W1614003815","https://openalex.org/W4287550824","https://openalex.org/W3173986299","https://openalex.org/W2952785509","https://openalex.org/W3213693153","https://openalex.org/W2952421354","https://openalex.org/W4301113699"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}