The convexification numerical method with the rigorously established global convergence property is constructed for a problem for the Mean Field Games System of the second order. This is the problem of the retrospective analysis of a game of infinitely many rational players. In addition to traditional initial and terminal conditions, one extra terminal condition is assumed to be known. Carleman estimates and a Carleman Weight Function play the key role. Numerical experiments demonstrate a good performance for complicated functions. Various versions of the convexification have been actively used by this research team for a number of years to numerically solve coefficient inverse problems.

翻译：为二阶平均场博弈系统的一个问题构造了具有严格全局收敛性的凸化数值方法。该问题涉及无穷多个理性参与者的博弈的反向分析。除了传统的初始条件和终端条件外，还假设已知一个额外的终端条件。卡尔曼估计与卡尔曼权函数在其中发挥了关键作用。数值实验表明该方法对复杂函数具有良好表现。本研究团队多年来一直积极运用凸化方法的各种变体来数值求解系数反问题。