Efficient preconditioners for solving dynamical optimal transport via interior point methods - Laboratoire de Mathématiques d'Orsay Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Efficient preconditioners for solving dynamical optimal transport via interior point methods

Résumé

In this paper we address the numerical solution of the quadratic optimal transport problem in its dynamical form, the so-called Benamou-Brenier formulation. When solved using interior point methods, the main computational bottleneck is the solution of large saddle point linear systems arising from the associated Newton-Raphson scheme. The main purpose of this paper is to design efficient preconditioners to solve these linear systems via iterative methods. Among the proposed preconditioners, we introduce one based on the partial commutation of the operators that compose the dual Schur complement of these saddle point linear systems, which we refer as $\boldsymbol{B}\boldsymbol{B}$-preconditioner. A series of numerical tests show that the $\boldsymbol{B}\boldsymbol{B}$-preconditioner is the most efficient among those presented, with a CPU-time scaling only slightly more than linearly with respect to the number of unknowns used to discretize the problem.
Fichier principal
Vignette du fichier
arxiv_main.pdf (525.38 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03766668 , version 1 (01-09-2022)
hal-03766668 , version 2 (04-05-2023)
hal-03766668 , version 3 (22-01-2024)

Identifiants

Citer

Enrico Facca, Gabriele Todeschi, Andrea Natale, Michele Benzi. Efficient preconditioners for solving dynamical optimal transport via interior point methods. 2022. ⟨hal-03766668v2⟩
142 Consultations
40 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More