  The Monge-Kantorovich problem is revisited by means of a variant of the
saddle-point method without appealing to $c$-conjugates. A new abstract
characterization of the optimal plans is obtained in the case where the cost
function takes infinite values. It leads us to new explicit sufficient and
necessary optimality conditions. As by-products, we obtain a new proof of the
well-known Kantorovich dual equality and an improvement of the convergence of
the minimizing sequences.

Probability;Functional Analysis;Optimization and Control