A saddle-point approach to the Monge-Kantorovich optimal transport problem

Overview & Synopsis

The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to cyclical $c$-monotonicity and $c$-conjugates. One gives new proofs of the well-known Kantorovich dual equality and a sufficient optimality condition which has recently been proved by W. Schachermayer and J. Teichman. A new necessary optimality condition is obtained in the case where the cost function takes infinite values.