论文标题
一类非电力平均现场游戏的分裂方法
Splitting methods for a class of non-potential mean field games
论文作者
论文摘要
我们扩展了从Nurbekyan（Saude）的“一阶非本地平均场游戏的傅立叶近似方法”（端口）。数学。 75（2018），没有。 3-4]和刘，雅各布斯，李，纳尔贝基扬，奥斯赫“具有应用程序的非本地平均现场游戏的计算方法” [ARXIV：2004.12210]，用于一类具有混合耦合的非电位平均野前游戏（MFG）系统。到目前为止，分裂方法已应用于潜在的MFG系统，这些系统可以用作凸孔concave鞍点问题。在这里，我们表明，一类非电位MFG可以作为单调夹杂物的原始对偶对施加，并通过凸优化算法的扩展（例如原始的偶偶有混合梯度（PDHG）算法）求解。我们方法的关键特征是考虑傅立叶或特征空间中非局部耦合的双重变量。
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.
