我们从Nurbekyan，Saude“傅立叶近似方法的一阶非局部平均场游戏”[端口。Math. 75（2018），no. 3-4]和Liu，Jacobs，Li，Nurbekyan，Osher“Computational methods for nonlocal mean field games with applications”[arXiv：2004.12210]，用于一类具有混合耦合的非势平均场博弈（MFG）系统。到目前为止，分裂方法已被应用到潜在的MFG系统，可以投凹凸鞍点问题。在这里，我们表明，一类非潜在的MFG可以铸造的原始-对偶对单调包含和解决通过扩展的凸优化算法，如原始-对偶混合梯度（PDHG）算法。我们的方法的一个重要特点是在考虑对偶变量的傅立叶或特征空间中的非局部耦合。
英文摘要：
We extend the methods from Nurbekyan, Saude "Fourier approximation methods for first-order nonlocal mean-field games" [Port. Math. 75 (2018), no. 3-4] and Liu, Jacobs, Li, Nurbekyan, Osher "Computational methods for nonlocal mean field games with applications" [arXiv:2004.12210] to a class of non-potential mean-field game (MFG) systems with mixed couplings. Up to now, splitting methods have been applied to potential MFG systems that can be cast as convex-concave saddle-point problems. Here, we show that a class of non-potential MFG can be cast as primal-dual pairs of monotone inclusions and solved via extensions of convex optimization algorithms such as the primal-dual hybrid gradient (PDHG) algorithm. A critical feature of our approach is in considering dual variables of nonlocal couplings in Fourier or feature spaces.
A Splitting Method For Overcoming the Curse of Dimensionality in Hamilton-Jacobi Equations Arising from Nonlinear Optimal Control and Differential Games with Applications to Trajectory Generation
A Douglas-Rachford Splitting Method for Solving Monotone Variational Inequalities in Linear-quadratic Dynamic Games
Rotterdam School of Management, Erasmus University（鹿特丹管理学院，伊拉斯姆斯大学）；Division of Decision and Control Systems, KTH Royal Institute of Technology（决策与控制系，皇家理工学院）；Delft Center for Systems and Control, Delft University of Technology（系统与控制中心，代尔夫特理工大学）
Accelerated Primal-Dual Proximal Gradient Splitting Methods for Convex-Concave Saddle-Point Problems
National Center for Applied Mathematics in Chongqing, Chongqing Normal University（重庆师范大学应用数学中心）；Chongqing Research Institute of Big Data, Peking University（北京大学重庆大数据研究院）
A distributed primal-dual algorithm for computation of generalized Nash equilibria with shared affine coupling constraints via operator splitting methods
