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Reports (Research Report) Year : 2001

An Hilbertian Framework for the Time-Continuous Monge-Kantorovich Problem

Kevin Guittet
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Abstract

In [1], a computational fluid dynamic style reformulation is introduced to solve the classical Monge-Kantorovich problem. Though the described augmented Lagrangian method involves an Hilbertian framework, the discussion was purely formal. Taking advantage of the recent progress in the optimal transport theory [4],[4],[6][10]and despite the lack of coercivity of the Hilbertian problem, we establish an existence result. Then under a reasonable assumption of positivity for the density, we prove the existence of saddle-points for both Lagrangian defined in [1], and finally prove the convergence of the numerical method.

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Other [cs.OH]
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Dates and versions

inria-00072506 , version 1 (24-05-2006)

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  • HAL Id : inria-00072506 , version 1

Cite

Kevin Guittet. An Hilbertian Framework for the Time-Continuous Monge-Kantorovich Problem. [Research Report] RR-4122, INRIA. 2001. ⟨inria-00072506⟩
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