{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T15:53:08Z","timestamp":1781797988014,"version":"3.54.5"},"reference-count":47,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"7","license":[{"start":{"date-parts":[[2023,7,1]],"date-time":"2023-07-01T00:00:00Z","timestamp":1688169600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2023,7,1]],"date-time":"2023-07-01T00:00:00Z","timestamp":1688169600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2023,7,1]],"date-time":"2023-07-01T00:00:00Z","timestamp":1688169600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2018YFA0703800"],"award-info":[{"award-number":["2018YFA0703800"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61733018"],"award-info":[{"award-number":["61733018"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61873262"],"award-info":[{"award-number":["61873262"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62173250"],"award-info":[{"award-number":["62173250"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shanghai Municipal Science and Technology Major Project","award":["2021SHZDZX0100"],"award-info":[{"award-number":["2021SHZDZX0100"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Cybern."],"published-print":{"date-parts":[[2023,7]]},"DOI":"10.1109\/tcyb.2022.3175831","type":"journal-article","created":{"date-parts":[[2022,5,30]],"date-time":"2022-05-30T22:04:30Z","timestamp":1653948270000},"page":"4375-4387","source":"Crossref","is-referenced-by-count":26,"title":["Efficient Algorithm for Approximating Nash Equilibrium of Distributed Aggregative Games"],"prefix":"10.1109","volume":"53","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4134-8455","authenticated-orcid":false,"given":"Gehui","family":"Xu","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0698-7910","authenticated-orcid":false,"given":"Guanpu","family":"Chen","sequence":"additional","affiliation":[{"name":"Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1698-7570","authenticated-orcid":false,"given":"Hongsheng","family":"Qi","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9505-8739","authenticated-orcid":false,"given":"Yiguang","family":"Hong","sequence":"additional","affiliation":[{"name":"Department of Control Science and Engineering, Shanghai Research Institute for Intelligent Autonomous Systems, Tongji University, Shanghai, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"263","reference":[{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970791"},{"key":"ref35","first-page":"709","article-title":"The efficiency of Hausdorff algorithms for approximating convex bodies by polytopes","volume":"33","author":"kamenev","year":"1993","journal-title":"Comput Math Math Phys"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492900002518"},{"key":"ref34","first-page":"892","article-title":"Numerical analysis of the efficiency of an algorithm for approximating convex bodies by polyhedra","volume":"32","author":"dzholdybaeva","year":"1992","journal-title":"Comput Math Math Phys"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1162\/evco_a_00223"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2020.2972824"},{"key":"ref14","author":"fortin","year":"2000","journal-title":"Augmented Lagrangian Methods Applications to the Numerical Solution of Boundary-Value Problems"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2016.07.003"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1214\/009053606000000335"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2016.01.001"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2020.3005922"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1016\/0041-5553(85)90170-3"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/CDC42340.2020.9303804"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1007\/s10958-008-9144-x"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA14720"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2016.2524452"},{"key":"ref17","author":"facchinei","year":"2007","journal-title":"Finite-Dimensional Variational Inequalities and Complementarity Problems"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1002\/nav.3800030110"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2002.1017625"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2021.109661"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2018.2828118"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1515\/9781400831470"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2020.109180"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1137\/040607605"},{"key":"ref23","article-title":"Distributed Nash equilibrium seeking for aggregative games via a small-gain approach","author":"liang","year":"2019","journal-title":"arXiv 1911 06458"},{"key":"ref45","author":"stewart","year":"1990","journal-title":"Matrix Perturbation Theory"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2020.109313"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2018.2850763"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-21554-9"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2019.01.008"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1515\/9781400862528.19"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1007\/BF01587076"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2020.2989755"},{"key":"ref44","author":"khalil","year":"2002","journal-title":"Nonlinear Systems"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2019.2929394"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1007\/BF02592073"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1145\/231731.231732"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2014.2309261"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1016\/0041-5553(75)90135-4"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2016.7799210"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1287\/opre.2016.1501"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2017.07.064"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2019.108548"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2015.2504964"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2021.3075183"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2019.2908091"},{"key":"ref40","author":"vavasis","year":"1991","journal-title":"Nonlinear Optimization Complexity Issues"}],"container-title":["IEEE Transactions on Cybernetics"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/6221036\/10153804\/09784880.pdf?arnumber=9784880","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,3]],"date-time":"2023-07-03T18:20:38Z","timestamp":1688408438000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9784880\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7]]},"references-count":47,"journal-issue":{"issue":"7"},"URL":"https:\/\/doi.org\/10.1109\/tcyb.2022.3175831","relation":{},"ISSN":["2168-2267","2168-2275"],"issn-type":[{"value":"2168-2267","type":"print"},{"value":"2168-2275","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7]]}}}