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Optimal Transportation Problem by Stochastic Optimal Control

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83841

Title: Optimal Transportation Problem by Stochastic Optimal Control
Authors: Mikami, Toshio Browse this author
Thieullen, Michele Browse this author
Keywords: optimal transportation
Monge-Kantorovich problem
Monge problem
duality
stochastic control
Hamilton-Jacobi-Bellman pde
value function
vanishing viscosity
semi-convex functions.
Issue Date: 3-Feb-2005
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 690
Start Page: 1
End Page: 17
Abstract: 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: bulletin (article)
URI: http://hdl.handle.net/2115/69495
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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