  We study the optimal transport problem for $d>2$ discrete measures. This is a
linear programming problem on $d$-tensors. It gives a way to compute a
"distance" between two sets of discrete measures. We introduce an entropic
regularization term, which gives rise to a scaling of tensors. We give a
variation of the celebrated Sinkhorn scaling algorithm. We show that this
algorithm can be viewed as a partial minimization algorithm of a strictly
convex function. Under appropriate conditions the rate of convergence is
geometric and we estimate the rate. Our results are generalizations of known
results for the classical case of two discrete measures.
