{"id":"https://openalex.org/W4415897416","doi":"https://doi.org/10.1007/s11432-025-4646-9","title":"Policy iteration method for discounted infinite horizon mean field games: the semi-Lagrangian approach","display_name":"Policy iteration method for discounted infinite horizon mean field games: the semi-Lagrangian approach","publication_year":2025,"publication_date":"2025-11-01","ids":{"openalex":"https://openalex.org/W4415897416","doi":"https://doi.org/10.1007/s11432-025-4646-9"},"language":"en","primary_location":{"id":"doi:10.1007/s11432-025-4646-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11432-025-4646-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210218743","display_name":"Science China Information Sciences","issn_l":"1674-733X","issn":["1674-733X","1869-1919"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Science China Information Sciences","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/A5101641786","display_name":"Qing Tang","orcid":"https://orcid.org/0009-0003-6152-9549"},"institutions":[{"id":"https://openalex.org/I3124059619","display_name":"China University of Geosciences","ror":"https://ror.org/04gcegc37","country_code":"CN","type":"education","lineage":["https://openalex.org/I3124059619"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qing Tang","raw_affiliation_strings":["School of Mathematics and Physics, China University of Geosciences (Wuhan), Wuhan, 430074, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, China University of Geosciences (Wuhan), Wuhan, 430074, China","institution_ids":["https://openalex.org/I3124059619"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018541911","display_name":"Fabio Camilli","orcid":"https://orcid.org/0000-0003-2976-8112"},"institutions":[{"id":"https://openalex.org/I39387349","display_name":"University of Chieti-Pescara","ror":"https://ror.org/00qjgza05","country_code":"IT","type":"education","lineage":["https://openalex.org/I39387349"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Fabio Camilli","raw_affiliation_strings":["Department of Engineering and Geology, University of Chieti-Pescara \u201cG. d\u2019Annunzio\u201d, Pescara, 65127, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering and Geology, University of Chieti-Pescara \u201cG. d\u2019Annunzio\u201d, Pescara, 65127, Italy","institution_ids":["https://openalex.org/I39387349"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027467852","display_name":"Y. Zhou","orcid":"https://orcid.org/0009-0009-6363-6923"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Yong-Shen Zhou","raw_affiliation_strings":["Department of Basic and Applied Sciences for Engineering, Sapienza University of Rome, Rome, 00161, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Basic and Applied Sciences for Engineering, Sapienza University of Rome, Rome, 00161, Italy","institution_ids":["https://openalex.org/I861853513"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101641786"],"corresponding_institution_ids":["https://openalex.org/I3124059619"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.3527049,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"68","issue":"11","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.40139999985694885,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.40139999985694885,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.1671999990940094,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.03500000014901161,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6496000289916992},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5781999826431274},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.4934000074863434},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.48969998955726624},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4726000130176544},{"id":"https://openalex.org/keywords/fixed-point-iteration","display_name":"Fixed-point iteration","score":0.3774000108242035},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.37610000371932983},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.34360000491142273}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7563999891281128},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6496000289916992},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.590399980545044},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5781999826431274},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5162000060081482},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.4934000074863434},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.48969998955726624},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4726000130176544},{"id":"https://openalex.org/C157449380","wikidata":"https://www.wikidata.org/wiki/Q1030759","display_name":"Fixed-point iteration","level":3,"score":0.3774000108242035},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.37610000371932983},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.34360000491142273},{"id":"https://openalex.org/C162443888","wikidata":"https://www.wikidata.org/wiki/Q1426504","display_name":"Power iteration","level":3,"score":0.32190001010894775},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.313400000333786},{"id":"https://openalex.org/C28761237","wikidata":"https://www.wikidata.org/wiki/Q7805321","display_name":"Time horizon","level":2,"score":0.301800012588501},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.2992999851703644},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2976999878883362},{"id":"https://openalex.org/C6177178","wikidata":"https://www.wikidata.org/wiki/Q10998070","display_name":"Discounting","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C159176650","wikidata":"https://www.wikidata.org/wiki/Q43261","display_name":"Horizon","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.2606000006198883},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.2540999948978424},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.25189998745918274}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11432-025-4646-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11432-025-4646-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210218743","display_name":"Science China Information Sciences","issn_l":"1674-733X","issn":["1674-733X","1869-1919"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Science China Information Sciences","raw_type":"journal-article"},{"id":"pmh:oai:iris.uniroma1.it:11573/1755980","is_oa":false,"landing_page_url":"https://hdl.handle.net/11573/1755980","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W61439753","https://openalex.org/W1487586009","https://openalex.org/W1915316363","https://openalex.org/W1983321045","https://openalex.org/W1985124402","https://openalex.org/W2038686546","https://openalex.org/W2067521925","https://openalex.org/W2088299544","https://openalex.org/W2095257746","https://openalex.org/W2149713433","https://openalex.org/W2149953340","https://openalex.org/W2549076960","https://openalex.org/W2755331706","https://openalex.org/W2791784110","https://openalex.org/W2962909000","https://openalex.org/W2964344784","https://openalex.org/W3157898245","https://openalex.org/W3164756548","https://openalex.org/W3178011931","https://openalex.org/W3190367256","https://openalex.org/W4210840654","https://openalex.org/W4239802052","https://openalex.org/W4304759582","https://openalex.org/W4316041475","https://openalex.org/W4390913432","https://openalex.org/W4391170322","https://openalex.org/W4391508738","https://openalex.org/W4406364983","https://openalex.org/W4407057483","https://openalex.org/W4409785891"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-11-05T00:00:00"}