{"id":"https://openalex.org/W2764267352","doi":"https://doi.org/10.1007/s10957-017-1176-2","title":"A Projected Subgradient Algorithm for Bilevel Equilibrium Problems and Applications","display_name":"A Projected Subgradient Algorithm for Bilevel Equilibrium Problems and Applications","publication_year":2017,"publication_date":"2017-10-10","ids":{"openalex":"https://openalex.org/W2764267352","doi":"https://doi.org/10.1007/s10957-017-1176-2","mag":"2764267352"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-017-1176-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-017-1176-2","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/A5078527522","display_name":"L. Q. Thuy","orcid":null},"institutions":[{"id":"https://openalex.org/I94518387","display_name":"Hanoi University of Science and Technology","ror":"https://ror.org/04nyv3z04","country_code":"VN","type":"education","lineage":["https://openalex.org/I94518387"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Le Quang Thuy","raw_affiliation_strings":["School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam"],"affiliations":[{"raw_affiliation_string":"School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam","institution_ids":["https://openalex.org/I94518387"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081487349","display_name":"Trinh Ngoc Hai","orcid":"https://orcid.org/0000-0002-0221-4649"},"institutions":[{"id":"https://openalex.org/I94518387","display_name":"Hanoi University of Science and Technology","ror":"https://ror.org/04nyv3z04","country_code":"VN","type":"education","lineage":["https://openalex.org/I94518387"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Trinh Ngoc Hai","raw_affiliation_strings":["School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam"],"affiliations":[{"raw_affiliation_string":"School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam","institution_ids":["https://openalex.org/I94518387"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078527522"],"corresponding_institution_ids":["https://openalex.org/I94518387"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":3.3165,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.93339874,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"175","issue":"2","first_page":"411","last_page":"431"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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":0.9998000264167786,"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/T12137","display_name":"Economic theories and models","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9854000210762024,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/subgradient-method","display_name":"Subgradient method","score":0.979091227054596},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5942909717559814},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5764320492744446},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5605679154396057},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5455588102340698},{"id":"https://openalex.org/keywords/cournot-competition","display_name":"Cournot competition","score":0.5286089777946472},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5138676166534424},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.509725034236908},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.4749082326889038},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45071399211883545},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.45009902119636536},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.44705408811569214},{"id":"https://openalex.org/keywords/dykstras-projection-algorithm","display_name":"Dykstra's projection algorithm","score":0.4407731890678406},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36484408378601074},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33173277974128723},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.13313958048820496}],"concepts":[{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.979091227054596},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5942909717559814},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5764320492744446},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5605679154396057},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5455588102340698},{"id":"https://openalex.org/C16520705","wikidata":"https://www.wikidata.org/wiki/Q601799","display_name":"Cournot competition","level":2,"score":0.5286089777946472},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5138676166534424},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.509725034236908},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.4749082326889038},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45071399211883545},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.45009902119636536},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.44705408811569214},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.4407731890678406},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36484408378601074},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33173277974128723},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.13313958048820496},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/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/s10957-017-1176-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-017-1176-2","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:175:y:2017:i:2:d:10.1007_s10957-017-1176-2","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-017-1176-2","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W154593720","https://openalex.org/W1519983590","https://openalex.org/W1546168022","https://openalex.org/W1547768397","https://openalex.org/W1585386565","https://openalex.org/W1588628884","https://openalex.org/W1594563152","https://openalex.org/W1970492798","https://openalex.org/W1975181084","https://openalex.org/W1979918647","https://openalex.org/W1981680120","https://openalex.org/W1983958212","https://openalex.org/W1989775297","https://openalex.org/W1996731061","https://openalex.org/W2003556443","https://openalex.org/W2009891988","https://openalex.org/W2014028360","https://openalex.org/W2031437264","https://openalex.org/W2040322280","https://openalex.org/W2045184230","https://openalex.org/W2045554006","https://openalex.org/W2054118322","https://openalex.org/W2061750102","https://openalex.org/W2062616144","https://openalex.org/W2065121429","https://openalex.org/W2067313264","https://openalex.org/W2067387193","https://openalex.org/W2072418419","https://openalex.org/W2073953242","https://openalex.org/W2077607486","https://openalex.org/W2085346899","https://openalex.org/W2091512449","https://openalex.org/W2109955195","https://openalex.org/W2151211707","https://openalex.org/W2159632552","https://openalex.org/W2213278820","https://openalex.org/W2254218369","https://openalex.org/W2435472869","https://openalex.org/W2443846959","https://openalex.org/W2464495997","https://openalex.org/W2532880535","https://openalex.org/W2747940975","https://openalex.org/W3099045797","https://openalex.org/W3103376690","https://openalex.org/W4236995599","https://openalex.org/W6604582033"],"related_works":["https://openalex.org/W2371658159","https://openalex.org/W2026392561","https://openalex.org/W2073460900","https://openalex.org/W3003123544","https://openalex.org/W1988854313","https://openalex.org/W2484692446","https://openalex.org/W4287588948","https://openalex.org/W2088149551","https://openalex.org/W2109154566","https://openalex.org/W3109616988"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
