Key points are not available for this paper at this time.
We consider optimal transport problems where the cost for transporting a given probability measure ₀ to another one (₁) consists of two parts: the first one measures the transportation from ₀ to an intermediate (pivot) measure to be determined (and subject to various constraints), and the second one measures the transportation from to ₁. This leads to Monge–Kantorovich interpolation problems under constraints for which we establish various properties of the optimal pivot measures. Considering the more general situation where only some part of the mass uses the intermediate stop leads to a mathematical model for the optimal location of a parking region around a city. Numerical simulations, based on entropic regularization, are presented both for the optimal parking regions and for Monge–Kantorovich constrained interpolation problems.
Buttazzo et al. (Wed,) studied this question.