  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.
