  In order to circumvent the difficulties in solving numerically the discrete
optimal transport problem, in which one minimizes the linear target function
$P\mapsto\langle C,P\rangle:=\sum_{i,j}C_{ij}P_{ij}$, Cuturi introduced a
variant of the problem in which the target function is altered by a convex one
$\Phi(P)=\langle C,P\rangle-\lambda\mathcal{H}(P)$, where $\mathcal{H}$ is the
Shannon entropy and $\lambda$ is a positive constant. We herein generalize
their formulation to a target function of the form $\Phi(P)=\langle
C,P\rangle+\lambda f(P)$, where $f$ is a generic strictly convex smooth
function. We also propose an iterative method for finding a numerical solution,
and clarify that the proposed method is particularly efficient when
$f(P)=\frac{1}{2}\|P\|^2$.
