Distributed heavy-ball algorithm of Nash equilibrium seeking for aggregative games

References

• Andreasson, M., Dimarogonas, D., Sandberg, H., & Johansson, K. (2014). Distributed control of networked dynamical systems: state feedback, integral action and consensus. IEEE Transactions on Automatic Control, 59(7), 1750–1760. https://doi.org/10.1109/TAC.2014.2309281
   Web of Science ®Google Scholar
• Basar, T. (1987). Relaxation techniques and asynchronous algorithms for online computation of noncooperative equilibria. Activity Analysis of Production and Allocation, 11, 531–549. https://doi.org/10.1016/s0165-1889(87)80006-4
   Google Scholar
• Boyd, S., Parikh, N., Chu, E., Peleato, B., & Eckstein, J. (2011). Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning, 3(1), 1–122. https://doi.org/10.1561/2200000016
   Google Scholar
• Brown, G. W. (1951). Iterative solution of games by fictitious play. Activity Analysis of Production and Allocation, 13(1), 374–376.
   Google Scholar
• Daskalakis, C., Goldberg, P. W., & Papadimitriou, C. H. (2009). The complexity of computing a Nash equilibrium. SIAM Journal on Computing, 39(1), 195–259. https://doi.org/10.1137/070699652
   Web of Science ®Google Scholar
• Deng, Z., & Liang, S. (2019). Distributed algorithms for aggregative games of multiple heterogeneous Euler-Lagrange systems. Automatica, 99, 246–252. https://doi.org/10.1016/j.automatica.2018.10.041
   Web of Science ®Google Scholar
• Deng, Z., & Nian, X. (2019). Distributed generalized Nash equilibrium seeking algorithm design for aggregative games over weight-balanced digraphs. IEEE Transactions on Neural Networks and Learning Systems, 30(3), 695–706. https://doi.org/10.1109/TNNLS.2018.2850763
   PubMed Web of Science ®Google Scholar
• Facchinei, F., Fischer, A., & Picciallia, V. (2007). On generalized nash games and variational inequalities. Operations Research Letters, 35(2), 159–164. https://doi.org/10.1016/j.orl.2006.03.004
   Web of Science ®Google Scholar
• Facchinei, F., & Kanzow, C. (2010). Generalized Nash equilibrium problems. Annals of Operations Research, 175(1), 177–211. https://doi.org/10.1007/s10479-009-0653-x
   Web of Science ®Google Scholar
• Facchinei, F., & Pang, J. (2003). Finite-dimensional variational inequalities and complementarity problem. Springer.
   Google Scholar
• Fan, X., Alpcan, T., Arcak, M., Wen, T. J., & Basar, T. (2006). A passivity approach to game-theoretic CDMA power control. Automatica, 42(11), 1837–1847. https://doi.org/10.1016/j.automatica.2006.05.022
   Web of Science ®Google Scholar
• Frihauf, P., Krstic, M., & Basar, T. (2012). Nash equilibrium seeking in noncooperative games. IEEE Transactions on Automatic Control, 57(5), 1192–1207. https://doi.org/10.1109/TAC.2011.2173412
   Web of Science ®Google Scholar
• Gadjov, D., & Pavel, L. (2019). A passivity-based approach to Nash equilibrium seeking over networks. IEEE Transactions on Automatic Control, 64(3), 1077–1092. https://doi.org/10.1109/TAC.2018.2833140
   Web of Science ®Google Scholar
• Gairinga, M., Luckinga, T., Mavronicolasb, M., Moniena, B., & Spirakisc, P. (2005). Structure and complexity of extreme Nash equilibria. Theoretical Computer Science, 343(1), 122–157. https://doi.org/10.1016/j.tcs.2005.05.011
   Web of Science ®Google Scholar
• Gharesifard, B., Basar, T., & Dominguez-Garcia, A. D. (2016). Price-based coordinated aggregation of networked distributed energy resources. IEEE Transactions on Automatic Control, 61(10), 2936–2946. https://doi.org/10.1109/TAC.2015.2504964
   Web of Science ®Google Scholar
• Gharesifard, B., & Cortes, J. (2012). Distributed convergence to Nash equilibria in two-network zero-sum games. Automatica, 49(6), 1638–1692. https://doi.org/10.1016/j.automatica.2013.02.062
   Web of Science ®Google Scholar
• Grammatico, S. (2017). Dynamic control of agents playing aggregative games with coupling constraints. IEEE Transactions on Automatic Control, 62(9), 4537–4548. https://doi.org/10.1109/TAC.2017.2672902
   Web of Science ®Google Scholar
• Hobbs, B. F., & Pang, J. (2007). Nash cournot equilibria in electric power markets with piecewise linear demand functions and joint constraints. Operations Research, 55(1), 113–127. https://doi.org/10.1287/opre.1060.0342
   Web of Science ®Google Scholar
• Jadbabaie, A., Jie, L., & Morse, A. (2003). Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control, 48(6), 988–1001. https://doi.org/10.1109/TAC.2003.812781
   Web of Science ®Google Scholar
• Kannan, A., & Shanbhag, U. V. (2014). Distributed computation of equilibria in monotone Nash games via iterative regularization techniques. SIAM Journal on Optimization, 22(4), 1177–1205. https://doi.org/10.1137/110825352
   Web of Science ®Google Scholar
• Koshal, J., Nedic, A., & Shanbhag, U. V. (2016). Distributed algorithms for aggregative games on graphs. Operations Research, 64(3), 680–704. https://doi.org/10.1287/opre.2016.1501
   Web of Science ®Google Scholar
• Liang, S., Yi, P., & Hong, Y. (2017a). Distributed Nash equilibrium seeking for aggregative games with coupled constraints. Automatica, 85, 179–185. https://doi.org/10.1016/j.automatica.2017.07.064
   Web of Science ®Google Scholar
• Liang, S., Yi, P., & Hong, Y. (2017b). Distributed Nash equilibrium seeking of a class of aggregative games. International Conference on Control and Automation, 25, 58–63. https://doi.org/10.1109/ICCA.2017.8003035
   Google Scholar
• Liu, Z., Wu, Q., Huang, S., Wang, L., Shahidehpour, M., & Xue, Y. (2018). Optimal day-ahead charging scheduling of electric vehicles through an aggregative game model. IEEE Transactions on Smart Grid, 9(5), 5173–5184. https://doi.org/10.1109/TSG.5165411
   Web of Science ®Google Scholar
• Ma, Z., Callaway, D. S., & Hiskens, I. A. (2010). Decentralized charging control of large populations of plug-in electric vehicles. IEEE Transactions on Control Systems Technology, 21(1), 67–78. https://doi.org/10.1109/TCST.2011.2174059
   Google Scholar
• Ma, Z., Zou, S., & Liu, X. (2015). A distributed charging coordination for large-scale plug-in electric vehicles considering battery degradation cost. IEEE Transactions on Control Systems Technology, 23(5), 2044–2052. https://doi.org/10.1109/TCST.2015.2394319
   Web of Science ®Google Scholar
• Mohsenian-Rad, A., Wong, V. W. S., Jatskevich, J., Schober, R., & Leon-Garcia, A. (2010). Autonomous demand-side management based on game-theoretic energy consumption scheduling for the future smart grid. IEEE Transactions on Smart Grid, 1(3), 320–331. https://doi.org/10.1109/TSG.2010.2089069
   Web of Science ®Google Scholar
• Molzahn, D. K., Dorfler, F., Sandberg, H., Low, S. H., Chakrabarti, S., Baldick, R., & Lavaei, J. (2017). A survey of distributed optimization and control algorithms for electric power systems. IEEE Transactions on Smart Grid, 8(6), 2941–2962. https://doi.org/10.1109/TSG.2017.2720471
   Web of Science ®Google Scholar
• Nabetani, K., Tseng, P., & Fukushima, M. (2011). Parametrized variational inequality approaches to generalized nash equilibrium problems with shared constraints. Computational Optimization and Applications, 48(3), 423–452. https://doi.org/10.1007/s10589-009-9256-3
   Web of Science ®Google Scholar
• Nedic, A., & Olshevsky, A. (2015). Distributed optimization over time-varying directed graphs. IEEE Transactions on Automatic Control, 60(3), 601–615. https://doi.org/10.1109/TAC.2014.2364096
   Web of Science ®Google Scholar
• Olfati-Saber, R., & Murray, R. (2004). Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 49(9), 1520–1533. https://doi.org/10.1109/TAC.2004.834113
   Web of Science ®Google Scholar
• Persis, C. D., & Grammatico, S. (2019). Distributed averaging integral Nash equilibrium seeking on networks. Automatica, 110(4), 1–8. https://doi.org/10.1016/j.automatica.2019.108548
   Google Scholar
• Persis, C. D., & Grammatico, S. (2020). Continuous-time integral dynamics for a class of aggregative games with coupling constraints. IEEE Transactions on Automatic Control, 65(5), 2171–2176. https://doi.org/10.1109/TAC.9
   Web of Science ®Google Scholar
• Persis, C. D., & Monshizadeh, N. (2019). A feedback control algorithm to steer networks to a Cournot Nash equilibrium. IEEE Transactions on Control of Network Systems, 6(4), 1486–1497. https://doi.org/10.1109/TCNS.6509490
   Web of Science ®Google Scholar
• Ren, W., & Beard, R. (2005). Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control, 50(5), 655–661. https://doi.org/10.1109/TAC.2005.846556
   Web of Science ®Google Scholar
• Ritzberger, K. (2002). Foundations of non-cooperative game theory. Oxford University Press.
   Google Scholar
• Rosen, J. B. (1965). Existence and uniqueness of equilibrium points for concave N-person games. Econometrica, 33(3), 520–534. https://doi.org/10.2307/1911749
   Web of Science ®Google Scholar
• Salehisadaghiani, F., & Pavel, L. (2016). Distributed Nash equilibrium seeking: A gossip-based algorithm. Automatica, 72, 209–216. https://doi.org/10.1016/j.automatica.2016.06.004
   Web of Science ®Google Scholar
• Shakarami, M., Persis, C., & Monshizadeh, N. (2019). Privacy and robustness guarantees in distributed dynamics for aggregative games. arXiv:1910.13928.
   Google Scholar
• Shamma, J. S., & Arslan, G. (2005). Dynamic fictitious play, dynamic gradient play, and distributed convergence to Nash equilibria. IEEE Transactions on Automatic Control, 50(3), 312–327. https://doi.org/10.1109/TAC.2005.843878
   Web of Science ®Google Scholar
• Wang, H., Li, C., Li, J., He, X., & Huang, T. (2018). A survey on distributed optimisation approaches and applications in smart grids. Journal of Control and Decision, 6(1), 41–60. https://doi.org/10.1080/23307706.2018.1549516
   Google Scholar
• Xin, R., & Khan, U. A. (2018). A linear algorithm for optimization over directed graphs with geometric convergence. IEEE Control Systems Letters, 2(3), 315–320. https://doi.org/10.1109/LCSYS.2018.2834316
   Google Scholar
• Xin, R., & Khan, U. A. (2020). Distributed heavy-ball: A generalization and acceleration of first-order methods with gradient tracking. IEEE Transactions on Automatic Control, 65(6), 2627–2633. https://doi.org/10.1109/TAC.9
   Web of Science ®Google Scholar
• Yang, B., & Johansson, M. (2010). Distributed optimization and games: A tutorial overview. IEEE Transactions on Automatic Control, 406(3), 109–148. https://doi.org/10.1007/978-0-85729-033-5_4
   Google Scholar
• Ye, M. (2021). Distributed Nash equilibrium seeking for games in systems with bounded control inputs. IEEE Transactions on Automatic Control, 66(8), 3833–3839. https://doi.org/10.1109/TAC.2020.3027795
   Web of Science ®Google Scholar
• Ye, M., & Hu, G. (2016). Game design and analysis for price-based demand response: An aggregate game approach. IEEE Transactions on Cybernetics, 47(3), 720–730. https://doi.org/10.1109/TCYB.2016.2524452
   PubMed Web of Science ®Google Scholar
• Ye, M., & Hu, G. (2017). Distributed Nash equilibrium seeking by a consensus based approach. IEEE Transactions on Automatic Control, 62(9), 4811–4818. https://doi.org/10.1109/TAC.2017.2688452
   Web of Science ®Google Scholar
• Ye, M., Hu, G., Lewis, F., & Xie, L. (2019). A unified strategy for solution seeking in graphical N-coalition noncooperative games. IEEE Transactions on Automatic Control, 64(11), 4645–4652. https://doi.org/10.1109/TAC.9
   Web of Science ®Google Scholar
• Ye, M., Hu, G., Xie, L., & Xu, S. (2021). Differentially private distributed nash equilibrium seeking for aggregative games. IEEE Transactions on Automatic Control. https://doi.org/10.1109/TAC.2021.3075183
   Google Scholar
• Yi, P., Hong, Y., & Liu, F. (2016). Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and application to economic dispatch of power systems. Automatica, 74, 259–269. https://doi.org/10.1016/j.automatica.2016.08.007
   Web of Science ®Google Scholar
• Yi, P., & Pavel, L. (2019). Distributed generalized nash equilibria computation of monotone games via double-layer preconditioned proximal-point algorithms. IEEE Transactions on Control of Network Systems, 6(1), 299–311. https://doi.org/10.1109/TCNS.2018.2813928
   Web of Science ®Google Scholar
• Yi, P., Zhang, Y., & Hong, Y. (2014). Potential game design for a class of distributed optimisation problems. Journal of Control and Decision, 1(2), 166–179. https://doi.org/10.1080/23307706.2014.899111
   Google Scholar
• Yin, H., U. V. Shanbhag, & Mehta, P. G. (2011). Nash equilibrium problems with scaled congestion costs and shared constraints. IEEE Transactions on Automatic Control, 56(7), 1702–1708. https://doi.org/10.1109/TAC.2011.2137590
   Web of Science ®Google Scholar
• Zhang, Y., Liang, S., & Ji, H. (2020). Distributed Nash equilibrium seeking for aggregative games via derivative feedback. International Journal of Control, Automation and Systems, 18, 1075–1082. https://doi.org/10.1007/s12555-019-0011-y
   Web of Science ®Google Scholar
• Zhu, M., & Frazzoli, E. (2016). Distributed robust adaptive equilibrium computation for generalized convex games. Automatica, 63, 82–91. https://doi.org/10.1016/j.automatica.2015.10.012
   Web of Science ®Google Scholar
• Zhu, Y., Yu, W., Wen, G., & Chen, G. (2021). Distributed Nash equilibrium seeking in an aggregative game on a directed graph. IEEE Transactions on Automatic Control, 66(6), 2746–2753. https://doi.org/10.1109/TAC.2020.3008113
   Web of Science ®Google Scholar