{"id":"https://openalex.org/W4382400382","doi":"https://doi.org/10.1007/s10957-023-02253-w","title":"Convergence Rates of the Stochastic Alternating Algorithm for Bi-Objective Optimization","display_name":"Convergence Rates of the Stochastic Alternating Algorithm for Bi-Objective Optimization","publication_year":2023,"publication_date":"2023-06-28","ids":{"openalex":"https://openalex.org/W4382400382","doi":"https://doi.org/10.1007/s10957-023-02253-w"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-023-02253-w","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1007/s10957-023-02253-w","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":true,"oa_status":"green","oa_url":"https://hdl.handle.net/10316/112294","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037334792","display_name":"Suyun Liu","orcid":"https://orcid.org/0000-0002-9226-7436"},"institutions":[{"id":"https://openalex.org/I186143895","display_name":"Lehigh University","ror":"https://ror.org/012afjb06","country_code":"US","type":"education","lineage":["https://openalex.org/I186143895"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Suyun Liu","raw_affiliation_strings":["Department of Industrial and Systems Engineering, Lehigh University, 200 West Packer Avenue, Bethlehem, PA, 18015-1582, USA","Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, USA"],"raw_orcid":"https://orcid.org/0000-0002-9226-7436","affiliations":[{"raw_affiliation_string":"Department of Industrial and Systems Engineering, Lehigh University, 200 West Packer Avenue, Bethlehem, PA, 18015-1582, USA","institution_ids":["https://openalex.org/I186143895"]},{"raw_affiliation_string":"Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, USA","institution_ids":["https://openalex.org/I186143895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045737795","display_name":"L. N. Vicente","orcid":"https://orcid.org/0000-0003-1097-6384"},"institutions":[{"id":"https://openalex.org/I186143895","display_name":"Lehigh University","ror":"https://ror.org/012afjb06","country_code":"US","type":"education","lineage":["https://openalex.org/I186143895"]},{"id":"https://openalex.org/I76903346","display_name":"University of Coimbra","ror":"https://ror.org/04z8k9a98","country_code":"PT","type":"education","lineage":["https://openalex.org/I76903346"]}],"countries":["PT","US"],"is_corresponding":false,"raw_author_name":"Luis Nunes Vicente","raw_affiliation_strings":["Centre for Mathematics of the University of Coimbra (CMUC), Coimbra, Portugal","Department of Industrial and Systems Engineering, Lehigh University, 200 West Packer Avenue, Bethlehem, PA, 18015-1582, USA","Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Mathematics of the University of Coimbra (CMUC), Coimbra, Portugal","institution_ids":["https://openalex.org/I76903346"]},{"raw_affiliation_string":"Department of Industrial and Systems Engineering, Lehigh University, 200 West Packer Avenue, Bethlehem, PA, 18015-1582, USA","institution_ids":["https://openalex.org/I186143895"]},{"raw_affiliation_string":"Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, USA","institution_ids":["https://openalex.org/I186143895"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037334792"],"corresponding_institution_ids":["https://openalex.org/I186143895"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.1309,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54987242,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"198","issue":"1","first_page":"165","last_page":"186"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9993000030517578,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8271167278289795},{"id":"https://openalex.org/keywords/subgradient-method","display_name":"Subgradient method","score":0.7667745351791382},{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.7365704774856567},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.6413100361824036},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5872405767440796},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5631529688835144},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.5603981018066406},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4824253022670746},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.47516223788261414},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.473509818315506},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.46580085158348083},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41008061170578003},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38398751616477966},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36244720220565796},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3281887173652649},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.31829291582107544},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10830971598625183}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8271167278289795},{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.7667745351791382},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.7365704774856567},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6413100361824036},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5872405767440796},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5631529688835144},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5603981018066406},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4824253022670746},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.47516223788261414},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.473509818315506},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.46580085158348083},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41008061170578003},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38398751616477966},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36244720220565796},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3281887173652649},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.31829291582107544},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10830971598625183},{"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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10957-023-02253-w","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1007/s10957-023-02253-w","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:198:y:2023:i:1:d:10.1007_s10957-023-02253-w","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-023-02253-w","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"},{"id":"pmh:oai:estudogeral.uc.pt:10316/112294","is_oa":true,"landing_page_url":"https://hdl.handle.net/10316/112294","pdf_url":null,"source":{"id":"https://openalex.org/S4306402070","display_name":"Estudo Geral (Universidad de Coimbra)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I76903346","host_organization_name":"University of Coimbra","host_organization_lineage":["https://openalex.org/I76903346"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:estudogeral.uc.pt:10316/112294","is_oa":true,"landing_page_url":"https://hdl.handle.net/10316/112294","pdf_url":null,"source":{"id":"https://openalex.org/S4306402070","display_name":"Estudo Geral (Universidad de Coimbra)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I76903346","host_organization_name":"University of Coimbra","host_organization_lineage":["https://openalex.org/I76903346"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W407273095","https://openalex.org/W1964442167","https://openalex.org/W1965515155","https://openalex.org/W1992208280","https://openalex.org/W1998081129","https://openalex.org/W2004586020","https://openalex.org/W2007294066","https://openalex.org/W2029932115","https://openalex.org/W2030435702","https://openalex.org/W2031232041","https://openalex.org/W2032571239","https://openalex.org/W2034136603","https://openalex.org/W2048061283","https://openalex.org/W2052471135","https://openalex.org/W2060727197","https://openalex.org/W2064114515","https://openalex.org/W2080752182","https://openalex.org/W2081313036","https://openalex.org/W2100717205","https://openalex.org/W2122235509","https://openalex.org/W2122414217","https://openalex.org/W2136320557","https://openalex.org/W2164998236","https://openalex.org/W2561080469","https://openalex.org/W2752084069","https://openalex.org/W2763081248","https://openalex.org/W2805307000","https://openalex.org/W2893010165","https://openalex.org/W2899313272","https://openalex.org/W2963433607","https://openalex.org/W3002138439","https://openalex.org/W3174533737","https://openalex.org/W4210890186","https://openalex.org/W4292864963","https://openalex.org/W4320149409","https://openalex.org/W6600446328"],"related_works":["https://openalex.org/W2128927076","https://openalex.org/W2771264586","https://openalex.org/W2963531627","https://openalex.org/W4302862688","https://openalex.org/W3165796876","https://openalex.org/W2000431671","https://openalex.org/W2467217527","https://openalex.org/W2957878543","https://openalex.org/W4221144548","https://openalex.org/W4382400382"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}