A time-fractional optimal transport: Formulation and algorithm

Abstract

The time-fractional optimal transport (OT) models are developed to describe the anomalous transport of the agents such that their densities are transported from the initial density distribution to the terminal one with the minimal cost. The general-proximal primal-dual hybrid gradient (G-prox PDHG) algorithm is applied to solve the OT formulations, in which a preconditioner induced by the numerical approximation to the time-fractional PDE is derived to accelerate the convergence of the algorithm. Numerical experiments for OT problems between Gaussian distributions are carried out to investigate the performance of the OT formulations. Those numerical experiments also demonstrate the effectiveness and flexibility of our proposed algorithm.