Optimal Transportation Problem by Stochastic Optimal Control

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2008 Japan, France English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Control and Optimization, volume 47, pages 1,127-1,139 (issn: 0363-0129, eissn: 1095-7138,

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Authors: Mikami, Toshio; Thieullen, Michele;

doi: 10.1137/050631264

handle: 2115/69495

Optimal Transportation Problem by Stochastic Optimal Control

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Abstract

We address an optimal mass transportation problem by means of optimal stochastic control. We consider a stochastic control problem which is a natural extension of the Monge-Kantorovich problem. Using a vanishing viscosity argument we provide a probabilistic proof of two fundamental results in mass transportation: the Kantorovich duality and the graph property for the support of an optimal measure for the Monge-Kantorovich problem. Our key tool is a stochastic duality result involving solutions of the Hamilton-Jacobi-Bellman PDE.

Countries

Japan, France

Related Organizations

University of Paris
France
Sorbonne Paris Cité
France
Hokkaido Bunkyo University
Japan
French National Centre for Scientific Research
France
Sorbonne University
France

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Keywords

vanishing viscosity, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Monge-Kantorovich problem, 410, value function, Monge problem, Hamilton-Jacobi-Bellman pde, duality, stochastic control, optimal transportation, semi-convex functions

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