{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T07:14:53Z","timestamp":1783667693938,"version":"3.55.0"},"reference-count":46,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100019531","name":"Science Fund for Distinguished Young Scholars of Chongqing Municipality","doi-asserted-by":"publisher","award":["2024NSCQ-JQX0103"],"award-info":[{"award-number":["2024NSCQ-JQX0103"]}],"id":[{"id":"10.13039\/501100019531","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["SWU-XDJH202312"],"award-info":[{"award-number":["SWU-XDJH202312"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62173278"],"award-info":[{"award-number":["62173278"]}],"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":["62403394"],"award-info":[{"award-number":["62403394"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2027,1]]},"DOI":"10.1016\/j.cam.2026.117835","type":"journal-article","created":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T23:44:23Z","timestamp":1779925463000},"page":"117835","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Asynchronous distributed generalized nash equilibrium computation for aggregative games with coupling constraint"],"prefix":"10.1016","volume":"489","author":[{"given":"Liang","family":"Ran","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huaqing","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zheng","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qingguo","family":"L\u00fc","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jun","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lifeng","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.cam.2026.117835_bib0001","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2023.115610","article-title":"Existence and continuity theorems of core of multi-leader-follower games with set payoffs","volume":"439","author":"Chen","year":"2024","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.cam.2026.117835_bib0002","article-title":"Influence in social networks with stubborn agents: from competition to bargaining","volume":"444","author":"Kareeva","year":"2023","journal-title":"Appl. Math. Comput."},{"key":"10.1016\/j.cam.2026.117835_bib0003","doi-asserted-by":"crossref","DOI":"10.1016\/j.neucom.2025.129465","article-title":"Distributed Nash equilibriumseeking for constrained games over jointly strongly connected switching networks under dynamic event-triggered mechanism","volume":"624","author":"Dai","year":"2025","journal-title":"Neurocomputing"},{"issue":"1","key":"10.1016\/j.cam.2026.117835_bib0004","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0377-2217(91)90325-P","article-title":"Generalized Nash games and quasi-variational inequalities","volume":"54","author":"Harker","year":"1991","journal-title":"Eur. J. Oper. Res."},{"issue":"3","key":"10.1016\/j.cam.2026.117835_bib0005","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1109\/TAC.2018.2833140","article-title":"A passivity-based approach to Nash equilibrium seeking over networks","volume":"64","author":"Gadjov","year":"2019","journal-title":"IEEE Trans. Autom. Control"},{"issue":"3","key":"10.1016\/j.cam.2026.117835_bib0006","doi-asserted-by":"crossref","first-page":"1805","DOI":"10.1109\/TSMC.2023.3329809","article-title":"A necessary and sufficient condition beyond monotonicity for convergence of the gradient play in continuous games","volume":"54","author":"Tan","year":"2024","journal-title":"IEEE Trans. Syst. Man Cybern.: Syst."},{"key":"10.1016\/j.cam.2026.117835_bib0007","article-title":"A linearly convergent distributed Nash equilibrium seeking algorithm for aggregative games","author":"Huang","year":"2022","journal-title":"IEEE Trans. Autom. Control"},{"issue":"2","key":"10.1016\/j.cam.2026.117835_bib0008","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1109\/LCSYS.2020.3002734","article-title":"Fully distributed Nash equilibrium seeking over time-varying communication networks with linear convergence rate","volume":"5","author":"Bianchi","year":"2021","journal-title":"IEEE Control Syst. Lett."},{"issue":"5","key":"10.1016\/j.cam.2026.117835_bib0009","doi-asserted-by":"crossref","first-page":"2451","DOI":"10.1109\/TAC.2021.3075183","article-title":"Differentially private distributed Nash equilibrium seeking for aggregative games","volume":"67","author":"Ye","year":"2022","journal-title":"IEEE Trans. Autom. Control"},{"issue":"6","key":"10.1016\/j.cam.2026.117835_bib0010","doi-asserted-by":"crossref","first-page":"2362","DOI":"10.1109\/TCYB.2018.2828118","article-title":"Distributed algorithms for searching generalized Nash equilibrium of noncooperative games","volume":"49","author":"Lu","year":"2019","journal-title":"IEEE Trans. Cybern."},{"issue":"11","key":"10.1016\/j.cam.2026.117835_bib0011","doi-asserted-by":"crossref","first-page":"5467","DOI":"10.1109\/TAC.2020.3047369","article-title":"A distributed forward-backward algorithm for stochastic generalized Nash equilibrium seeking","volume":"66","author":"Franci","year":"2021","journal-title":"IEEE Trans. Autom. Control"},{"issue":"1","key":"10.1016\/j.cam.2026.117835_bib0012","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1109\/TCNS.2018.2813928","article-title":"Distributed generalized nash equilibria computation of monotone games via double-layer preconditioned proximal-point algorithms","volume":"6","author":"Yi","year":"2019","journal-title":"IEEE Trans. Control Netw. Syst."},{"issue":"9","key":"10.1016\/j.cam.2026.117835_bib0013","doi-asserted-by":"crossref","first-page":"4811","DOI":"10.1109\/TAC.2017.2688452","article-title":"Distributed Nash equilibrium seeking by a consensus based approach","volume":"62","author":"Ye","year":"2017","journal-title":"IEEE Trans. Autom. Control"},{"issue":"4","key":"10.1016\/j.cam.2026.117835_bib0014","doi-asserted-by":"crossref","first-page":"1584","DOI":"10.1109\/TAC.2019.2922953","article-title":"Distributed GNE seeking under partial-decision information over networks via a doubly-augmented operator splitting approach","volume":"65","author":"Pavel","year":"2020","journal-title":"IEEE Trans. Autom. Control"},{"issue":"2","key":"10.1016\/j.cam.2026.117835_bib0015","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1109\/LCSYS.2017.2718842","article-title":"Semi-decentralized Nash equilibrium seeking in aggregative games with separable coupling constraints and non-differentiable cost functions","volume":"1","author":"Belgioioso","year":"2017","journal-title":"IEEE Control Syst. Lett."},{"issue":"5","key":"10.1016\/j.cam.2026.117835_bib0016","doi-asserted-by":"crossref","DOI":"10.1109\/TAC.2020.3005922","article-title":"Distributed generalized Nash equilibrium seeking in aggregative games on time-varying networks","volume":"66","author":"Belgioioso","year":"2021","journal-title":"IEEE Trans. Autom. Control"},{"issue":"7","key":"10.1016\/j.cam.2026.117835_bib0017","doi-asserted-by":"crossref","first-page":"3259","DOI":"10.1109\/TAC.2020.3015354","article-title":"Single-timescale distributed GNE seeking for aggregative games over networks via forward-backward operator splitting","volume":"66","author":"Gadjov","year":"2021","journal-title":"IEEE Trans. Autom. Control"},{"issue":"2","key":"10.1016\/j.cam.2026.117835_bib0018","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1109\/TCNS.2019.2944300","article-title":"A distributed algorithm for almost-nash equilibria of average aggregative games with coupling constraints","volume":"7","author":"Parise","year":"2020","journal-title":"IEEE Trans. Control Netw. Syst."},{"key":"10.1016\/j.cam.2026.117835_bib0019","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/j.automatica.2017.07.064","article-title":"Distributed Nash equilibrium seeking for aggregative games with coupled constraints","volume":"85","author":"Liang","year":"2017","journal-title":"Automatica"},{"issue":"5","key":"10.1016\/j.cam.2026.117835_bib0020","doi-asserted-by":"crossref","first-page":"A2851","DOI":"10.1137\/15M1024950","article-title":"ARock: An algorithmic framework for asynchronous parallel coordinate updates","volume":"38","author":"Peng","year":"2016","journal-title":"SIAM J. Sci. Comput."},{"issue":"6","key":"10.1016\/j.cam.2026.117835_bib0021","doi-asserted-by":"crossref","first-page":"1337","DOI":"10.1109\/TAC.2010.2079650","article-title":"Asynchronous broadcast-based convex optimization over a network","volume":"56","author":"Nedi\u0107","year":"2011","journal-title":"IEEE Trans. Autom. Control"},{"issue":"2","key":"10.1016\/j.cam.2026.117835_bib0022","first-page":"293","article-title":"Decentralized consensus optimization with asynchrony and delays","volume":"4","author":"Wu","year":"2018","journal-title":"IEEE Trans. Signal Inf. Process. Netw."},{"issue":"12","key":"10.1016\/j.cam.2026.117835_bib0023","doi-asserted-by":"crossref","first-page":"5723","DOI":"10.1109\/TNNLS.2020.3027381","article-title":"Distributed Nesterov gradient and heavy-ball double accelerated asynchronous optimization","volume":"32","author":"Li","year":"2021","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"12","key":"10.1016\/j.cam.2026.117835_bib0024","doi-asserted-by":"crossref","first-page":"5264","DOI":"10.1109\/TAC.2020.2977940","article-title":"Achieving linear convergence in distributed asynchronous multiagent optimization","volume":"65","author":"Tian","year":"2020","journal-title":"IEEE Trans. Autom. Control"},{"issue":"6","key":"10.1016\/j.cam.2026.117835_bib0025","doi-asserted-by":"crossref","first-page":"2514","DOI":"10.1109\/TCYB.2019.2908091","article-title":"Asynchronous distributed algorithms for seeking generalized Nash equilibria under full and partial-decision information","volume":"50","author":"Yi","year":"2020","journal-title":"IEEE Trans. Cybern."},{"issue":"3","key":"10.1016\/j.cam.2026.117835_bib0026","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1287\/opre.2016.1501","article-title":"Distributed algorithms for aggregative games on graphs","volume":"64","author":"Koshal","year":"2016","journal-title":"Oper. Res."},{"issue":"1","key":"10.1016\/j.cam.2026.117835_bib0027","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1287\/moor.2018.0986","article-title":"On synchronous, asynchronous, and randomized best-response schemes for stochastic Nash games","volume":"45","author":"Lei","year":"2020","journal-title":"Math. Oper. Res."},{"key":"10.1016\/j.cam.2026.117835_bib0028","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2021.110054","article-title":"Asynchronous networked aggregative games","volume":"136","author":"Zhu","year":"2022","journal-title":"Automatica"},{"issue":"5","key":"10.1016\/j.cam.2026.117835_bib0029","doi-asserted-by":"crossref","first-page":"2095","DOI":"10.1109\/TAC.2016.2607023","article-title":"Asynchronous distributed optimization via randomized dual proximal gradient","volume":"62","author":"Notarnicola","year":"2017","journal-title":"IEEE Trans. Autom. Control"},{"issue":"1","key":"10.1016\/j.cam.2026.117835_bib0030","doi-asserted-by":"crossref","first-page":"642","DOI":"10.1109\/TAC.2024.3439652","article-title":"Convergence analysis of distributed generalized Nash equilibria seeking algorithm with asynchrony and delays","volume":"70","author":"Li","year":"2025","journal-title":"IEEE Trans. Autom. Control"},{"key":"10.1016\/j.cam.2026.117835_bib0031","series-title":"Convex Analysis and Monotone Operator Theory in Hilbert Spaces","author":"Bauschke","year":"2011"},{"issue":"4","key":"10.1016\/j.cam.2026.117835_bib0032","doi-asserted-by":"crossref","first-page":"2034","DOI":"10.1137\/16M1068256","article-title":"Augmented lagrangian methods for the solution of generalized Nash equilibrium problems","volume":"26","author":"Kanzow","year":"2016","journal-title":"SIAM J. Optim."},{"issue":"12","key":"10.1016\/j.cam.2026.117835_bib0033","first-page":"3439","article-title":"Convergence theorems for equilibrium problem, variational inequality problem and countably infinite relatively quasi-nonexpansive mappings","volume":"216","author":"Zegeye","year":"2010","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"10.1016\/j.cam.2026.117835_bib0034","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/s10479-009-0653-x","article-title":"Generalized Nash equilibrium problems","volume":"175","author":"Facchinei","year":"2010","journal-title":"Ann. Oper. Res."},{"issue":"3","key":"10.1016\/j.cam.2026.117835_bib0035","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1109\/MSP.2010.936021","article-title":"Convex optimization, game theory, and variational inequality theory","volume":"27","author":"Scutari","year":"2010","journal-title":"IEEE Signal Process. Mag."},{"key":"10.1016\/j.cam.2026.117835_bib0036","doi-asserted-by":"crossref","first-page":"2333","DOI":"10.1109\/LCSYS.2025.3615593","article-title":"On variance-reduced extragradient methods for stochastic generalized Nash equilibrium problems","volume":"9","author":"Franci","year":"2025","journal-title":"IEEE Control Syst. Lett."},{"issue":"11","key":"10.1016\/j.cam.2026.117835_bib0037","doi-asserted-by":"crossref","first-page":"8469","DOI":"10.1109\/TSMC.2025.3606747","article-title":"Stochastic generalized Nash equilibrium seeking: reflected gradient methods","volume":"55","author":"Su","year":"2025","journal-title":"IEEE Trans. Syst. Man Cybern.: Syst."},{"issue":"3","key":"10.1016\/j.cam.2026.117835_bib0038","doi-asserted-by":"crossref","first-page":"1912","DOI":"10.1137\/151003076","article-title":"Convergence rate analysis of primal-dual splitting schemes","volume":"25","author":"Davis","year":"2015","journal-title":"SIAM J. Optim."},{"key":"10.1016\/j.cam.2026.117835_bib0039","article-title":"A primal-dual forward-backward splitting algorithm for distributed convex optimization","author":"Li","year":"2021","journal-title":"IEEE Trans. Emerg. Top. Comput. Intell."},{"issue":"1","key":"10.1016\/j.cam.2026.117835_bib0040","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s10589-017-9909-6","article-title":"Asymmetric forward-backward-adjoint splitting for solving monotone inclusions involving three operators","volume":"68","author":"Latafat","year":"2017","journal-title":"Comput. Optim. Appl."},{"issue":"6","key":"10.1016\/j.cam.2026.117835_bib0041","doi-asserted-by":"crossref","first-page":"1698","DOI":"10.1007\/s10915-018-0680-3","article-title":"A new primal-dual algorithm for minimizing the sum of three functions with a linear operator","volume":"73","author":"Yan","year":"2018","journal-title":"J. Sci. Comput."},{"issue":"1","key":"10.1016\/j.cam.2026.117835_bib0042","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1137\/140961134","article-title":"Asynchronous stochastic coordinate descent: parallelism and convergence properties","volume":"25","author":"Liu","year":"2015","journal-title":"SIAM J. Optim."},{"key":"10.1016\/j.cam.2026.117835_bib0043","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/s10915-017-0628-z","article-title":"On unbounded delays in asynchronous parallel fixed-point algorithms","volume":"76","author":"Hannah","year":"2018","journal-title":"J. Sci. Comput."},{"issue":"4","key":"10.1016\/j.cam.2026.117835_bib0044","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1090\/S0002-9904-1967-11761-0","article-title":"Weak convergence of the sequence of successive approximations for nonexpansive mappings","volume":"73","author":"Opial","year":"1967","journal-title":"Bull. Am. Math. Soc."},{"issue":"3","key":"10.1016\/j.cam.2026.117835_bib0045","doi-asserted-by":"crossref","first-page":"720","DOI":"10.1109\/TCYB.2016.2524452","article-title":"Game design and analysis for price-based demand response: an aggregate game approach","volume":"47","author":"Ye","year":"2017","journal-title":"IEEE Trans. Cybern."},{"issue":"1","key":"10.1016\/j.cam.2026.117835_bib0046","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1109\/TAC.2021.3135360","article-title":"Semi-decentralized generalized Nash equilibrium seeking in monotone aggregative games","volume":"68","author":"Belgioioso","year":"2023","journal-title":"IEEE Trans. Autom. Control"}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726004772?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726004772?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T06:43:03Z","timestamp":1783665783000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042726004772"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2027,1]]},"references-count":46,"alternative-id":["S0377042726004772"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2026.117835","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2027,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Asynchronous distributed generalized nash equilibrium computation for aggregative games with coupling constraint","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2026.117835","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"117835"}}