Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 32
Number of page(s) 38
DOI https://doi.org/10.1051/cocv/2024020
Published online 16 April 2024
  1. M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale and V. Zdravkovic, Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study. Proc. Natl. Acad. Sci. U.S.A. 105 (2008) 1232–1237. [CrossRef] [PubMed] [Google Scholar]
  2. N. Bellomo and C. Dogbé, On the modeling of traffic and crowds: a survey of models, speculations, and perspectives. SIAM Rev. 53 (2011) 409–463. [CrossRef] [MathSciNet] [Google Scholar]
  3. D. Helbing, Traffic and related self-driven many-particle systems. Rev. Mod. Phys. 73 (2001) 1067–1141. [CrossRef] [Google Scholar]
  4. S. Cordier, L. Pareschi and G. Toscani, On a kinetic model for a simple market economy. J. Stat. Phys. 120 (2005) 253–277. [CrossRef] [MathSciNet] [Google Scholar]
  5. S. Ahn, H.O. Bae and S.Y. Ha, Y. Kim and H. Lim, Application of flocking mechanism to the modeling of stochastic volatility. Math. Models Methods Appl. Sci. 23 (2013) 1603–1628. [CrossRef] [MathSciNet] [Google Scholar]
  6. M. Dorigo and C. Blum, Ant colony optimization theory: a survey. Theoret. Comput. Sci. 344 (2005) 243–278. [CrossRef] [MathSciNet] [Google Scholar]
  7. J. Kennedy, Particle swarm optimization. Encyclopedia of Machine Learning. Springer (2011) 760–766. [CrossRef] [Google Scholar]
  8. P. Bak, How Nature Works: The Science of Self-organized criticality. Springer Science & Business Media (2013). [Google Scholar]
  9. M. Bongini and M. Fornasier, Sparse control of multiagent systems. Active Particles, Vol. 1. Theory, Methods, and Applications (2016). [Google Scholar]
  10. J.A. Carrillo, Y.P. Choi and S.P. Perez, A review on attractive-repulsive hydrodynamics for consensus in collective behaviour. Active Particles, Vol. 1. Springer (2017) 173–228. [Google Scholar]
  11. T. Vicsek and A. Zafeiris, Collective motion. Phys. Rep. 517 (2012) 71–140. [CrossRef] [Google Scholar]
  12. M. Caponigro, M. Fornasier, B. Piccoli and E. Trelat, Sparse stabilization and control of the Cucker-Smale model. Math. Control Relat. Fields 4 (2013) 447–466. [CrossRef] [MathSciNet] [Google Scholar]
  13. M. Bongini and M. Fornasier, Sparse stabilization of dynamical systems driven by attraction and avoidance forces. Netw. Heterog. Media 9 (2014) 1–31. [CrossRef] [MathSciNet] [Google Scholar]
  14. M. Bongini, M. Fornasier, F. Rossi and F. Solombrino, Mean-field Pontryagin maximum principle. J. Optim. Theory Appl. 175 (2017) 1–38. [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Fornasier and F. Solombrino, Mean-field optimal control. ESAIM Control Optim. Calc. Var. 20 (2014) 1123–1152. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  16. B. Piccoli, F. Rossi and E. Trélat, Control to flocking of the kinetic Cucker–Smale model. SIAM J. Math. Anal. 47 (2015) 4685–4719. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Fornasier, S. Lisini, C. Orrieri and G. Savaré, Mean-field optimal control as gamma-limit of finite agent controls. Eur. J. Appl. Math. 30 (2019) 1153–1186. [CrossRef] [Google Scholar]
  18. M. Burger, R. Pinnau, C. Totzeck, O. Tse and A. Roth, Instantaneous control of interacting particle systems in the mean-field limit. J. Computat. Phys. 405 (2020) 109181. [Google Scholar]
  19. J.M. Lasry and P.L. Lions, Mean field games. Jpn. J. Math. 2 (2007) 229–260. [Google Scholar]
  20. M. Huang, P.E. Caines and R.P. Malhamé, Individual and mass behaviour in large population stochastic wireless power control problems: centralized and Nash equilibrium solutions. Proceedings of the 42nd IEEE Conference on Decision and Control, Vol. 1. IEEE (2003) 98–103. [Google Scholar]
  21. A. Bensoussan, J. Frehse and P. Yam, Mean Field Games and Mean Field Type Control Theory. Springer (2013). [CrossRef] [Google Scholar]
  22. M. Burger, M. Di Francesco, P. Markowich and M.-T. Wolfram, Mean field games with nonlinear mobilities in pedestrian dynamics. Discrete Contin. Dyn. Syst. Ser. B 19 (2014) 1311–1333. [MathSciNet] [Google Scholar]
  23. F. Santambrogio, A modest proposal for MFG with density constraints. Netw. Heterog. Media 7 (2012) 337–347. [CrossRef] [MathSciNet] [Google Scholar]
  24. O. Guéant, J.M. Lasry and P.L. Lions, Mean field games and applications. Paris-Princeton Lectures on Mathematical Finance 2010. Springer (2011) 205–266. [CrossRef] [Google Scholar]
  25. P.J. Graber and A. Bensoussan, Existence and uniqueness of solutions for Bertrand and Cournot mean field games. Appl. Math. Optim. (2015) 1–25. [Google Scholar]
  26. R. Ferreira, D. Gomes and T. Tada, Existence of weak solutions to first-order stationary mean-field games with Dirichlet conditions. Proc. Am. Math. Soc. 147 (2019) 4713–4731. [CrossRef] [Google Scholar]
  27. C. Bertucci, Optimal stopping in mean field games, an obstacle problem approach. J. Math. Pures Appl. 120 (2018) 165–194. [Google Scholar]
  28. D.A. Gomes, S. Patrizi and V. Voskanyan, On the existence of classical solutions for stationary extended mean field games. Nonlinear Anal. Theory Methods Appl. 99 (2014) 49–79. [CrossRef] [Google Scholar]
  29. P. Cardaliaguet and C.A. Lehalle, Mean field game of controls and an application to trade crowding. Math. Financ. Econ. 12 (2018) 335–363. [CrossRef] [MathSciNet] [Google Scholar]
  30. B. Acciaio, J. Backhoff-Veraguas and R. Carmona, Extended mean field control problems: stochastic maximum principle and transport perspective. SIAM J. Control Optim. 57 (2019) 3666–3693. [CrossRef] [MathSciNet] [Google Scholar]
  31. C. Alasseur, I.B. Taher and A. Matoussi, An extended mean field game for storage in smart grids. J. Optim. Theory Appl. 184 (2020) 644–670. [CrossRef] [MathSciNet] [Google Scholar]
  32. G. Fu, P. Graewe, U. Horst and A. Popier, A mean field game of optimal portfolio liquidation. Math. Oper. Res. (2021). [Google Scholar]
  33. Z. Kobeissi, On classical solutions to the mean field game system of controls. Commun. Partial Differ. Equ. (2021) 1–36. [Google Scholar]
  34. Y. Achdou and I. Capuzzo-Dolcetta, Mean field games: numerical methods. SIAM J. Numer. Anal. 48 (2010) 1136–1162. [Google Scholar]
  35. Y. Achdou, F. Camilli and I. Capuzzo-Dolcetta, Mean field games: convergence of a finite difference method. SIAM J. Numer. Anal. 51 (2013) 2585–2612. [CrossRef] [MathSciNet] [Google Scholar]
  36. Y. Achdou, F. Camilli and I. Capuzzo-Dolcetta, Mean field games: numerical methods for the planning problem. SIAM J. Control Optim. 50 (2012) 77–109. [Google Scholar]
  37. Y. Achdou and M. Laurière, Mean field type control with congestion (II): an augmented Lagrangian method. Appl. Math. Optim. 74 (2016) 535–578. [CrossRef] [MathSciNet] [Google Scholar]
  38. Y. Achdou and M. Lauriére, Mean field games and applications: numerical aspects. Lecture Notes in Mathematics. Vol. 2281 of Mean Field Games. Springer, Cham (2020) 249–307. [CrossRef] [Google Scholar]
  39. Y. Achdou and Z. Kobeissi, Mean field games of controls: finite difference approximations. Math. Eng. 3 (2021) Paper No. 024, 35. [CrossRef] [MathSciNet] [Google Scholar]
  40. M. Laurière, Numerical methods for mean field games and mean field type control. (2021). [Google Scholar]
  41. M. Laurière and L. Tangpi, Convergence of large population games to mean field games with interaction through the controls. (2020). [Google Scholar]
  42. O.A. Ladyzhenskaia, V.A. Solonnikov and N.N. Ural’tseva, Linear and Quasi-linear Equations of Parabolic Type. Vol. 23. American Mathematical Soc. (1988). [Google Scholar]
  43. F. Santambrogio, Monogr. Math. Vol. 55 of Optimal Transport for Applied Mathematicians. Birkäuser, NY (2015). [Google Scholar]
  44. R. Ferreira and D. Gomes, Existence of weak solutions to stationary mean-field games through variational inequalities. SIAM J. Math. Anal. 50 (2018) 5969–6006. [CrossRef] [MathSciNet] [Google Scholar]
  45. J.A. Carrillo, S. Martin and M.T. Wolfram, An improved version of the Hughes model for pedestrian flow. Math. Models Methods Appl. Sci. 26 (2016) 671–697. [CrossRef] [MathSciNet] [Google Scholar]
  46. U. Jermann and V. Quadrini, Macroeconomic effects of financial shocks. Am. Econ. Rev. 102 (2012) 238–271. [CrossRef] [PubMed] [Google Scholar]
  47. M. Bongini and G. Buttazzo, Optimal control problems in transport dynamics. Math. Models Methods Appl. Sci. 27 (2017) 427–451. [CrossRef] [MathSciNet] [Google Scholar]
  48. G. Albi, M. Bongini, E. Cristiani and D. Kalise, Invisible sparse control of self-organizing agents leaving unknown environments. SIAM J. Appl. Math. 76 (2016) 1683–1710. [CrossRef] [MathSciNet] [Google Scholar]
  49. F. Cucker and J.G. Dong, A conditional, collision-avoiding, model for swarming. Discrete Contin. Dynam. Syst. 34 (2014) 1009–1020. [CrossRef] [Google Scholar]
  50. F. Cucker and S. Smale, On the mathematics of emergence. Jpn. J. Math. 2 (2007) 197–227. [CrossRef] [MathSciNet] [Google Scholar]
  51. A. Blanchet and G. Carlier, From Nash to Cournot-Nash equilibria via the Monge–Kantorovich problem. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 372 (2014) 20130398. [MathSciNet] [Google Scholar]
  52. P. Cardaliaguet and S. Hadikhanloo, Learning in mean field games: the fictitious play. ESAIM Control Optim. Calc. Var. 23 (2017) 569–591. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  53. F. Salvarani and G. Turinici, Optimal individual strategies for influenza vaccines with imperfect efficacy and durability of protection. Math. Biosci. Eng. 15 (2018) 629–652. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  54. R.M. Corless, G.H. Gonnet, D.E. Hare, D. J. Jeffrey and D. E. Knuth On the lambert w function. Adv. Comput. Math. 5 (1996) 329–359. [CrossRef] [Google Scholar]

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