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Preface
Iterative strategies for solving linearized discrete mean field games systems
1. | Université Paris Diderot, UMR 7598, Laboratoire Jacques-Louis Lions, Paris, France, France |
References:
[1] |
, UMFPACK. Available from: http://www.cise.ufl.edu/research/sparse/umfpack/current/. |
[2] |
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.
doi: 10.1137/100790069. |
[3] |
Y. Achdou and I. Capuzzo-Dolcetta, Mean field games: Numerical methods, SIAM J. Numer. Anal., 48 (2010), 1136-1162.
doi: 10.1137/090758477. |
[4] |
J.-D. Benamou and Y. Brenier, Mixed $L^2$-Wasserstein optimal mapping between prescribed density functions, J. Optim. Theory Appl., 111 (2001), 255-271.
doi: 10.1023/A:1011926116573. |
[5] |
J.-D. Benamou, Y. Brenier and K. Guittet, The Monge-Kantorovitch mass transfer and its computational fluid mechanics formulation, ICFD Conference on Numerical Methods for Fluid Dynamics (Oxford, 2001), Internat. J. Numer. Methods Fluids, 40 (2002), 21-30. |
[6] |
A. Brandt, Rigorous quantitative analysis of multigrid. I. Constant coefficients two-level cycle with $L_2$-norm, SIAM J. Numer. Anal., 31 (1994), 1695-1730.
doi: 10.1137/0731087. |
[7] |
D. A. Gomes, J. Mohr and R. R. Souza, Discrete time, finite state space mean field games, J. Math. Pures Appl. (9), 93 (2010), 308-328. |
[8] |
O. Guéant, Mean field games equations with quadratic hamiltonian: A specific approach, arXiv:1106.3269, 2011. |
[9] |
O. Guéant, J.-M. Lasry and P.-L. Lions, Mean field games and applications, in "Paris-Princeton Lectures on Mathematical Finance 2010," Lecture Notes in Math., 2003, Springer, Berlin, (2011), 205-266. |
[10] |
S. Henn, A multigrid method for a fourth-order diffusion equation with application to image processing, SIAM J. Sci. Comput., 27 (2005), 831-849 (electronic).
doi: 10.1137/040611124. |
[11] |
A. Lachapelle, J. Salomon and G. Turinici, Computation of mean field equilibria in economics, Math. Models Methods Appl. Sci., 20 (2010), 567-588.
doi: 10.1142/S0218202510004349. |
[12] |
J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. I. Le cas stationnaire, C. R. Math. Acad. Sci. Paris, 343 (2006), 619-625.
doi: 10.1016/j.crma.2006.09.019. |
[13] |
J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. II. Horizon fini et contrôle optimal, C. R. Math. Acad. Sci. Paris, 343 (2006), 679-684.
doi: 10.1016/j.crma.2006.09.018. |
[14] |
J.-M. Lasry and P.-L. Lions, Mean field games, Jpn. J. Math., 2 (2007), 229-260. |
[15] |
P.-L. Lions, Cours du Collège de France, 2007-2011. Available from: http://www.college-de-france.fr/default/EN/all/equ_der/. |
[16] |
U. Trottenberg, C. W. Oosterlee and A. Schüller, "Multigrid," With contributions by A. Brandt, P. Oswald and K. Stüben, Academic Press, Inc., San Diego, CA, 2001. |
[17] |
H. A. van der Vorst, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 13 (1992), 631-644.
doi: 10.1137/0913035. |
show all references
References:
[1] |
, UMFPACK. Available from: http://www.cise.ufl.edu/research/sparse/umfpack/current/. |
[2] |
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.
doi: 10.1137/100790069. |
[3] |
Y. Achdou and I. Capuzzo-Dolcetta, Mean field games: Numerical methods, SIAM J. Numer. Anal., 48 (2010), 1136-1162.
doi: 10.1137/090758477. |
[4] |
J.-D. Benamou and Y. Brenier, Mixed $L^2$-Wasserstein optimal mapping between prescribed density functions, J. Optim. Theory Appl., 111 (2001), 255-271.
doi: 10.1023/A:1011926116573. |
[5] |
J.-D. Benamou, Y. Brenier and K. Guittet, The Monge-Kantorovitch mass transfer and its computational fluid mechanics formulation, ICFD Conference on Numerical Methods for Fluid Dynamics (Oxford, 2001), Internat. J. Numer. Methods Fluids, 40 (2002), 21-30. |
[6] |
A. Brandt, Rigorous quantitative analysis of multigrid. I. Constant coefficients two-level cycle with $L_2$-norm, SIAM J. Numer. Anal., 31 (1994), 1695-1730.
doi: 10.1137/0731087. |
[7] |
D. A. Gomes, J. Mohr and R. R. Souza, Discrete time, finite state space mean field games, J. Math. Pures Appl. (9), 93 (2010), 308-328. |
[8] |
O. Guéant, Mean field games equations with quadratic hamiltonian: A specific approach, arXiv:1106.3269, 2011. |
[9] |
O. Guéant, J.-M. Lasry and P.-L. Lions, Mean field games and applications, in "Paris-Princeton Lectures on Mathematical Finance 2010," Lecture Notes in Math., 2003, Springer, Berlin, (2011), 205-266. |
[10] |
S. Henn, A multigrid method for a fourth-order diffusion equation with application to image processing, SIAM J. Sci. Comput., 27 (2005), 831-849 (electronic).
doi: 10.1137/040611124. |
[11] |
A. Lachapelle, J. Salomon and G. Turinici, Computation of mean field equilibria in economics, Math. Models Methods Appl. Sci., 20 (2010), 567-588.
doi: 10.1142/S0218202510004349. |
[12] |
J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. I. Le cas stationnaire, C. R. Math. Acad. Sci. Paris, 343 (2006), 619-625.
doi: 10.1016/j.crma.2006.09.019. |
[13] |
J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. II. Horizon fini et contrôle optimal, C. R. Math. Acad. Sci. Paris, 343 (2006), 679-684.
doi: 10.1016/j.crma.2006.09.018. |
[14] |
J.-M. Lasry and P.-L. Lions, Mean field games, Jpn. J. Math., 2 (2007), 229-260. |
[15] |
P.-L. Lions, Cours du Collège de France, 2007-2011. Available from: http://www.college-de-france.fr/default/EN/all/equ_der/. |
[16] |
U. Trottenberg, C. W. Oosterlee and A. Schüller, "Multigrid," With contributions by A. Brandt, P. Oswald and K. Stüben, Academic Press, Inc., San Diego, CA, 2001. |
[17] |
H. A. van der Vorst, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 13 (1992), 631-644.
doi: 10.1137/0913035. |
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