{"id":"https://openalex.org/W2963952936","doi":"https://doi.org/10.1137/17m1151420","title":"Linear-Quadratic-Gaussian Mixed Mean-Field Games with Heterogeneous Input Constraints","display_name":"Linear-Quadratic-Gaussian Mixed Mean-Field Games with Heterogeneous Input Constraints","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2963952936","doi":"https://doi.org/10.1137/17m1151420","mag":"2963952936"},"language":"en","primary_location":{"id":"doi:10.1137/17m1151420","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1151420","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-01590971","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040645589","display_name":"Ying Hu","orcid":"https://orcid.org/0000-0002-1080-2600"},"institutions":[{"id":"https://openalex.org/I4210161663","display_name":"Institut de recherche math\u00e9matique de Rennes","ror":"https://ror.org/05y76vp22","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2800285241","https://openalex.org/I28221208","https://openalex.org/I3124938446","https://openalex.org/I4210117091","https://openalex.org/I4210141950","https://openalex.org/I4210146044","https://openalex.org/I4210161663","https://openalex.org/I4399657933","https://openalex.org/I56067802","https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Ying Hu","raw_affiliation_strings":["IRMAR - Institut de Recherche Math\u00e9matique de Rennes (Campus de Beaulieu, b\u00e2timents 22 et 23, \r\n263 avenue du G\u00e9n\u00e9ral Leclerc, CS 74205\r\n35042  RENNES C\u00e9dex - France)"],"affiliations":[{"raw_affiliation_string":"IRMAR - Institut de Recherche Math\u00e9matique de Rennes (Campus de Beaulieu, b\u00e2timents 22 et 23, \r\n263 avenue du G\u00e9n\u00e9ral Leclerc, CS 74205\r\n35042  RENNES C\u00e9dex - France)","institution_ids":["https://openalex.org/I4210161663"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075552347","display_name":"Jianhui Huang","orcid":"https://orcid.org/0000-0003-3315-6549"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Jianhui Huang","raw_affiliation_strings":["POLYU - The Hong Kong Polytechnic University [Hong Kong] (Hung Hom, Kowloon, Hong Kong - China)"],"affiliations":[{"raw_affiliation_string":"POLYU - The Hong Kong Polytechnic University [Hong Kong] (Hung Hom, Kowloon, Hong Kong - China)","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080251686","display_name":"Tianyang Nie","orcid":"https://orcid.org/0000-0001-9062-4762"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tianyang Nie","raw_affiliation_strings":["Shandong University (27 Shanda Nanlu, Jinan , Shandong , P.R.China 250100 - China)"],"affiliations":[{"raw_affiliation_string":"Shandong University (27 Shanda Nanlu, Jinan , Shandong , P.R.China 250100 - China)","institution_ids":["https://openalex.org/I154099455"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5040645589"],"corresponding_institution_ids":["https://openalex.org/I4210161663"],"apc_list":null,"apc_paid":null,"fwci":4.3474,"has_fulltext":false,"cited_by_count":54,"citation_normalized_percentile":{"value":0.94514185,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"56","issue":"4","first_page":"2835","last_page":"2877"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9994000196456909,"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":0.9994000196456909,"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/T12137","display_name":"Economic theories and models","score":0.9776999950408936,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.972100019454956,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/mathematics","display_name":"Mathematics","score":0.8673971891403198},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5079017281532288},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.492149293422699},{"id":"https://openalex.org/keywords/mean-field-theory","display_name":"Mean field theory","score":0.4897024929523468},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.4873681664466858},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4781982898712158},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4781152606010437},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.44110092520713806},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.42921650409698486},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.42764484882354736},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.42029380798339844},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3865431845188141},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32377421855926514},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2514110505580902},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09189477562904358},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.09121894836425781}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8673971891403198},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5079017281532288},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.492149293422699},{"id":"https://openalex.org/C202213908","wikidata":"https://www.wikidata.org/wiki/Q626011","display_name":"Mean field theory","level":2,"score":0.4897024929523468},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.4873681664466858},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4781982898712158},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4781152606010437},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.44110092520713806},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.42921650409698486},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.42764484882354736},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.42029380798339844},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3865431845188141},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32377421855926514},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2514110505580902},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09189477562904358},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09121894836425781},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/17m1151420","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1151420","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01590971v2","is_oa":true,"landing_page_url":"https://hal.science/hal-01590971","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 2018, 56 (4), pp.2835-2877. &#x27E8;10.1137/17M1151420&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/81166","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/81166","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"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":"Journal/Magazine Article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01590971v2","is_oa":true,"landing_page_url":"https://hal.science/hal-01590971","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 2018, 56 (4), pp.2835-2877. &#x27E8;10.1137/17M1151420&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1272366887","display_name":null,"funder_award_id":"ZR2016AQ13","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G1287313309","display_name":null,"funder_award_id":"15300514P","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G3846589334","display_name":null,"funder_award_id":"ANR-15-CE05-0024","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4253236736","display_name":null,"funder_award_id":"11601285","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4830050000","display_name":null,"funder_award_id":"ANR-11-LABX-0020-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6840876211","display_name":null,"funder_award_id":"15327516P","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G7611503662","display_name":null,"funder_award_id":"2015HW023","funder_id":"https://openalex.org/F4320311026","funder_display_name":"Shandong University"},{"id":"https://openalex.org/G7642546210","display_name":null,"funder_award_id":"11571205","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8130988100","display_name":null,"funder_award_id":"ANR-16-CE40-0015-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8969244820","display_name":null,"funder_award_id":"500613P","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G8979139846","display_name":null,"funder_award_id":"61573217","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320311026","display_name":"Shandong University","ror":"https://ror.org/0207yh398"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1491976841","https://openalex.org/W1607455690","https://openalex.org/W1736238968","https://openalex.org/W1821455959","https://openalex.org/W1965098697","https://openalex.org/W1968010891","https://openalex.org/W1968067611","https://openalex.org/W1973258650","https://openalex.org/W1983321045","https://openalex.org/W1983997656","https://openalex.org/W1985050062","https://openalex.org/W1986431940","https://openalex.org/W1992169727","https://openalex.org/W1994712972","https://openalex.org/W1997481555","https://openalex.org/W2011435133","https://openalex.org/W2016864253","https://openalex.org/W2022460928","https://openalex.org/W2026814250","https://openalex.org/W2028316825","https://openalex.org/W2029794338","https://openalex.org/W2030450473","https://openalex.org/W2038518354","https://openalex.org/W2038686546","https://openalex.org/W2043380962","https://openalex.org/W2045577524","https://openalex.org/W2054595450","https://openalex.org/W2057470999","https://openalex.org/W2062240654","https://openalex.org/W2075099603","https://openalex.org/W2081458347","https://openalex.org/W2091265977","https://openalex.org/W2129951390","https://openalex.org/W2161370261","https://openalex.org/W2328013571","https://openalex.org/W2766094959","https://openalex.org/W2963769350","https://openalex.org/W2963980460","https://openalex.org/W2964128536","https://openalex.org/W3105231990","https://openalex.org/W3105898488"],"related_works":["https://openalex.org/W4210735314","https://openalex.org/W2092374696","https://openalex.org/W1705316893","https://openalex.org/W2129581964","https://openalex.org/W4315489088","https://openalex.org/W2375947969","https://openalex.org/W4320924209","https://openalex.org/W2952444919","https://openalex.org/W2036330223","https://openalex.org/W4312782710"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,9,50,54],"class":[3,55],"of":[4,20,34,39,56,69],"linear-quadratic-Gaussian":[5],"mean-field":[6,21,57],"games":[7],"having":[8],"major":[10],"agent":[11],"and":[12,42,79,86],"numerous":[13],"heterogeneous":[14],"minor":[15],"agents":[16,41],"in":[17,29,49,75],"the":[18,43,70,77,83],"presence":[19],"interactions.":[22],"The":[23,36,67],"individual":[24,40],"admissible":[25],"controls":[26],"are":[27,47],"constrained":[28],"closed":[30],"convex":[31],"subsets":[32],"$\\Gamma_{k}$":[33],"$\\Bbb{R}^{m}$.":[35],"decentralized":[37],"strategies":[38],"consistency":[44,71],"condition":[45],"system":[46,72],"represented":[48],"unified":[51],"manner":[52],"through":[53,82],"forward-backward":[58],"stochastic":[59],"differential":[60],"equations":[61],"involving":[62],"projection":[63],"operators":[64],"on":[65],"$\\Gamma_{k}$.":[66],"well-posedness":[68],"is":[73,94],"established":[74],"both":[76],"local":[78],"global":[80],"cases":[81],"contraction":[84],"mapping":[85],"discounting":[87],"methods,":[88],"respectively.":[89],"A":[90],"related":[91],"$\\varepsilon$-Nash-equilibrium":[92],"property":[93],"also":[95],"verified.":[96]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}
