On the Quadratic Convergence of Newton’s Method for Mean Field Games with Non-separable Hamiltonian
Fabio Camilli,
Qing Tang
Abstract: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. We prove the well posedness of the Mean Field Game system with non-separable Hamiltonian and of the linear system giving the Newton iterations. Then, by forward induction and assuming that the initial guess is sufficiently close to the solution of problem, we show a quadratic rate of convergence for the approximation … Show more
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