Relaxed multi-marginal costs and quantization effects - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

Relaxed multi-marginal costs and quantization effects

(1) , (2) , (1) , (3)
1
2
3

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.
Fichier principal
Vignette du fichier
1907.08425.pdf (419.66 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02352469 , version 1 (06-11-2019)

Identifiers

  • HAL Id : hal-02352469 , version 1

Cite

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

Share

Gmail Facebook Twitter LinkedIn More