Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Relaxed multi-marginal costs and quantization effects

Abstract : We propose a duality theory for multi-marginal repulsive cost that appear in optimal transport problems arising in Density Functional Theory. The related optimization problems involve probabilities on the entire space and, as minimizing sequences may lose mass at infinity, it is natural to expect relaxed solutions which are sub-probabilities. We first characterize the N-marginals relaxed cost in terms of a stratification formula which takes into account all k interactions with k ≤ N. We then develop a duality framework involving continuous functions vanishing at infinity and deduce primal-dual necessary and sufficient optimality conditions Next we prove the existence and the regularity of an optimal dual potential under very mild assumptions. In the last part of the paper, we apply our results to a minimization problem involving a given continuous potential and we give evidence of a mass quantization effect for optimal solutions.
Complete list of metadata

Cited literature [26 references]  Display  Hide  Download
Contributor : Thierry Champion Connect in order to contact the contributor
Submitted on : Wednesday, November 6, 2019 - 7:35:49 PM
Last modification on : Tuesday, December 7, 2021 - 4:26:03 PM
Long-term archiving on: : Saturday, February 8, 2020 - 5:53:08 AM


Files produced by the author(s)


  • HAL Id : hal-02352469, version 1



Guy Bouchitté, Giuseppe Buttazzo, Thierry Champion, Luigi de Pascale. Relaxed multi-marginal costs and quantization effects. 2019. ⟨hal-02352469⟩



Record views


Files downloads