  We propose an efficient implementation of the numerical tensor-train (TT)
based algorithm solving the multicomponent coagulation equation preserving the
nonnegativeness of solution. Unnatural negative elements in the constructed
approximation arise due to the errors of the low-rank decomposition and
discretization scheme. In this work, we propose to apply the rank-one
corrections in the TT-format proportional to the minimal negative element. Such
an element can be found via application of the global optimization methods that
can be fully implemented within efficient operations in the tensor train
format. We incorporate this trick into the time-integration scheme for the
multicomponent coagulation equation and also use it for post-processing of the
stationary solution for the problem with the source of particles.
