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 result for a stochastic control problem which naturally extends (MKP).

• Type: Journal
• Year: 2008
• Where: SIAMCO
• Authors: Toshio Mikami, Michèle Thieullen
• Keywords: Kantorovich Duality Theorem, Optimal Transportation Problem, SIAMCO 2008, Stochastic Optimal Control