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

Author

Listed:
  • Fabio Camilli

    (SBAI, Sapienza Università di Roma)

  • Qing Tang

    (China University of Geosciences (Wuhan))

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.

Suggested Citation

  • Fabio Camilli & Qing Tang, 2025. "On the Quadratic Convergence of Newton’s Method for Mean Field Games with Non-separable Hamiltonian," Dynamic Games and Applications, Springer, vol. 15(2), pages 534-557, May.
    • Handle: RePEc:spr:dyngam:v:15:y:2025:i:2:d:10.1007_s13235-024-00561-y
    DOI: 10.1007/s13235-024-00561-y
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    References listed on IDEAS

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    1. Marco Cirant & Roberto Gianni & Paola Mannucci, 2020. "Short-Time Existence for a General Backward–Forward Parabolic System Arising from Mean-Field Games," Dynamic Games and Applications, Springer, vol. 10(1), pages 100-119, March.
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