THIBAULT, Alexis; CHIZAT, Lénaïc; DOSSAL, Charles; PAPADAKIS, Nicolas

doi:10.3390/a14050143

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THIBAULT, Alexis
Modélisation et simulation de la propagation des ondes fondées sur des mesures expérimentales pour caractériser des milieux géophysiques et héliophysiques et concevoir des objets complexes [MAKUTU]

CHIZAT, Lénaïc
Laboratoire de Mathématiques d'Orsay [LMO]

DOSSAL, Charles
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Institut National des Sciences Appliquées - Toulouse [INSA Toulouse]

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Article de revue

Ce document a été publié dans

Algorithms. 2021, vol. 14, n° 5

MDPI

Résumé en anglais

This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely used iterative Bregman projections algorithm (or Sinkhorn-Knopp algorithm). We first proposed to rely on regularized nonlinear acceleration schemes. In practice, such approaches lead to fast algorithms, but their global convergence is not ensured. Hence, we next proposed a new algorithm with convergence guarantees. The idea is to overrelax the Bregman projection operators, allowing for faster convergence. We proposed a simple method for establishing global convergence by ensuring the decrease of a Lyapunov function at each step. An adaptive choice of the overrelaxation parameter based on the Lyapunov function was constructed. We also suggested a heuristic to choose a suitable asymptotic overrelaxation parameter, based on a local convergence analysis. Our numerical experiments showed a gain in convergence speed by an order of magnitude in certain regimes.< Réduire