Asymptotics for Semidiscrete Entropic Optimal Transport

Minimal Geodesics Along Volume-Preserving Maps, Through Semidiscrete Optimal Transport

We introduce a numerical method for extracting minimal geodesics along the group of volume preserving maps, equipped with the L metric, which as observed by Arnold [Arn66] solve the Euler equations of inviscid incompressible uids. The method relies on the generalized polar decomposition of Brenier [Bre91], numerically implemented through semi-discrete optimal transport. It is robust enough to e...

The Semidiscrete Filtered Backprojection Algorithm Is Optimal for Tomographic Inversion

Long time asymptotics for optimal investment

This survey reviews portfolio selection problem for long-term horizon. We consider two objectives: (i) maximize the probability for outperforming a target growth rate of wealth process (ii) minimize the probability of falling below a target growth rate. We study the asymptotic behavior of these criteria formulated as large deviations control problems, that we solve by duality method leading to ...

Optimal Control of a Semidiscrete Cahn-Hilliard-Navier-Stokes System

In this paper, the optimal boundary control of a time-discrete Cahn-Hilliard NavierStokes system is studied. A general class of free energy potentials is considered which, in particular, includes the double-obstacle potential. The latter homogeneous free energy density yields an optimal control problem for a family of coupled systems, which result from a time discretization of a variational ine...

Entropic particle transport in periodic channels

The dynamics of Brownian motion has widespread applications extending from transport in designed micro-channels up to its prominent role for inducing transport in molecular motors and Brownian motors. Here, Brownian transport is studied in micro-sized, two-dimensional periodic channels, exhibiting periodically varying cross-sections. The particles in addition are subjected to an external force ...