Monotone inclusion methods for a class of second-order non-potential mean-field games
<|reference_start|>Monotone inclusion methods for a class of second-order non-potential mean-field games: We propose a monotone splitting algorithm for solving a class of second-order non-potential mean-field games. Following [Achdou, Capuzzo-Dolcetta, "Mean Field Games: Numerical Methods," SINUM (2010)], we introduce a finite-difference scheme and observe that the scheme represents first-order optimality conditions for a primal-dual pair of monotone inclusions. Based on this observation, we prove that the finite-difference system obtains a solution that can be provably recovered by an extension of the celebrated primal-dual hybrid gradient (PDHG) algorithm.<|reference_end|>
@article{nurbekyan2024monotone,
    title={Monotone inclusion methods for a class of second-order non-potential
  mean-field games},
    author={Levon Nurbekyan, Siting Liu, and Yat Tin Chow},
    journal={arXiv preprint arXiv:2403.20290},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.20290},
    primaryClass={math.OC cs.NA math.NA}
}