We study an optimal control problem for a simple transportation model on path graph. give closed form solution the controller, which can also account planned disturbances using feed-forward. The controller is highly structured, allows to be implemented only local communication, conducted through two sweeps

The Strictly Correlated Electrons (SCE) limit of the Levy–Lieb functional in Density Functional Theory (DFT) gives rise to a symmetric multi-marginal optimal transport problem with Coulomb cost, where number marginal laws is equal electrons system, which can be very large relevant applications. In this work, we design numerical method, built upon constrained overdamped Langevin processes solve ...

This text is an expanded version of the lectures given by the first author in the 2009 CIME summer school of Cetraro. It provides a quick and reasonably account of the classical theory of optimal mass transportation and of its more recent developments, including the metric theory of gradient flows, geometric and functional inequalities related to optimal transportation, the first and second ord...