Optimal Transportation Problem by Stochastic Optimal Control

Optimal Transportation Problem by Stochastic Optimal Control

We solve optimal transportation problem using stochastic optimal control theory. Indeed, for a super linear cost at most quadratic at infinity, we prove Kantorovich duality theorem by a zero noise limit (or vanishing viscosity) argument.. We also obtain a characterization of the support of an optimal measure in Monge-Kantorovich minimization problem (MKP) as a graph. Our key tool is a duality r...

A survey of stochastic optimal transportation problem

The Monge Optimal Transportation Problem

We report here two recent developments in the theory of optimal transportation. The first is a proof for the existence of optimal mappings to the Monge mass transportation problem [16]. The other is an application of optimal transportation in geometric optics [19]. The optimal transportation problem, in general, deals with the redistribution of materials in the most economical way. The original...

Optimal Control Problem for Processes Represented by Stochastic Sequential Machine

In this paper, optimal control problem for processes represented by stochastic sequential machine is analyzed. Principle of optimality is proven for the considered problem. Then by using method of dynamical programming, solution of optimal control problem is found.

Optimal Transportation under Controlled Stochastic Dynamics

We consider an extension of the Monge–Kantorovitch optimal transportation problem. The mass is transported along a continuous semimartingale, and the cost of transportation depends on the drift and the diffusion coefficients of the continuous semimartingale. The optimal transportation problem minimizes the cost among all continuous semimartingales with given initial and terminal distributions. ...