  This article studies problems of optimal transport, by embedding them in a
general functional analytic framework of convex optimization. This provides a
unified treatment of a large class of related problems in probability theory
and allows for generalizations of the classical problem formulations. General
results on convex duality yield dual problems and optimality conditions for
these problems. When the objective takes the form of a convex integral
functional, we obtain more explicit optimality conditions and establish the
existence of solutions for a relaxed formulation of the problem. This covers,
in particular, the mass transportation problem and its nonlinear
generalizations.
