ИСТИНА

We discuss the Kantorovich optimal transportation problem with density constraint for measures on infinite dimensional spaces. The classical Kantorovich optimal transportation problem is a linear optimization problem on a convex domain: among all measures with fixed marginals we find an optimal one where the optimality is measured against a cost function. The modification of this problem we consider presumes a pointwise constraint on the densities of admissible measures. We have to find an optimal measure among all measures with fixed marginals and densities dominated by a given function. The talk gives a short overview of recent results in this field.