On the Quadratic Convergence of Newton’s Method for Mean Field Games with Non-separable Hamiltonian

Fabio Camilli () and Qing Tang ()
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Fabio Camilli: SBAI, Sapienza Università di Roma
Qing Tang: China University of Geosciences (Wuhan)

Dynamic Games and Applications, 2025, vol. 15, issue 2, No 9, 534-557

Abstract: 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 of the Mean Field Game system by Newton’s method. We also consider the case of a nonlocal coupling, but with separable Hamiltonian, and we show a similar rate of convergence.

Keywords: Mean field games; Non-separable Hamiltonian; Newton method; Congestion model; Numerical methods; 49N70; 91A13; 35Q80; 65M12 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13235-024-00561-y

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