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：针对二阶平均场博弈系统的一个问题，本文构建了具有严格全局收敛性保证的凸化数值方法。该问题涉及无限多个理性参与者的博弈回溯分析。除传统的初始条件和终端条件外，假设额外已知一个终端条件。卡尔曼估计与卡尔曼权函数在此过程中起关键作用。数值实验表明，该方法对复杂函数具有良好的计算性能。该研究团队多年来一直积极运用凸化方法的多种变体，数值求解系数反问题。