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We analyze asymptotic convergence properties of Newton's method for a class of evolutive Mean Field Games systems with non-separable Hamiltonian arising in mean field type models with congestion.
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Convex optimization
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M. Huang, P. E. Caines and R. P. Malhame, Large-population cost-coupled LQG problems with non uniform agents: Individual-mass behaviour and decentralized ϵ \epsilon -Nash equilibria
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J. M. Lasry and P. L. Lions, Mean field games
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G. Metafune, D. Pallara and A. Rhandi, Global properties of transition probabilities of singular diffusions
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On the Newton–Kantorovich theorem
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Mean field games: convergence of a finite difference method
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On the system of partial differential equations arising in mean field type control
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Weak solutions for mean field games with congestion
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On the discretization of some nonlinear Fokker-Planck-Kolmogorov equations and applications
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R. Carmona and F. Delarue, Probabilistic theory of mean field games with applications I
2018
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