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

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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Submitted on : Wednesday, May 24, 2006 - 10:09:01 AM
Last modification on : Thursday, February 3, 2022 - 11:17:51 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:10:50 PM

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  • HAL Id : inria-00072506, version 1

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

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