A Numerical Method to Solve Multi-Marginal Optimal Transport Problems with Coulomb Cost

DOI10.1007/978-3-319-41589-5_17zbMath1372.65188arXiv1505.01136OpenAlexW2569263150MaRDI QIDQ5350489

Guillaume Carlier, Luca Nenna, Jean-David Benamou

Publication date: 1 September 2017

Published in: Splitting Methods in Communication, Imaging, Science, and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.01136

zbMATH Keywords

numerical examples Kullback-Leibler distance optimal transport problem Coulomb cost entropic regularization Kantorovich formulation iterative Bregman projections

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Existence theories for optimal control problems involving partial differential equations (49J20) Discrete approximations in optimal control (49M25)

Related Items (19)

Optimal transportation, modelling and numerical simulation ⋮ Wasserstein Barycenters Are NP-Hard to Compute ⋮ Constrained overdamped Langevin dynamics for symmetric multimarginal optimal transportation ⋮ Genetic Column Generation: Fast Computation of High-Dimensional Multimarginal Optimal Transport Problems ⋮ Multi-marginal entropy-transport with repulsive cost ⋮ Polynomial-time algorithms for multimarginal optimal transport problems with structure ⋮ Universal diagonal estimates for minimizers of the Levy-Lieb functional ⋮ A family of pairwise multi-marginal optimal transports that define a generalized metric ⋮ A Global Optimization Approach for Multimarginal Optimal Transport Problems with Coulomb Cost ⋮ The dynamical Schrödinger problem in abstract metric spaces ⋮ Unbalanced multi-marginal optimal transport ⋮ Low-Rank Tensor Approximations for Solving Multimarginal Optimal Transport Problems ⋮ Approximation of optimal transport problems with marginal moments constraints ⋮ Semidefinite Relaxation of Multimarginal Optimal Transport for Strictly Correlated Electrons in Second Quantization ⋮ Optimal transport: discretization and algorithms ⋮ Convex Relaxation Approaches for Strictly Correlated Density Functional Theory ⋮ An entropy minimization approach to second-order variational mean-field games ⋮ Hardness results for multimarginal optimal transport problems ⋮ Second-order models for optimal transport and cubic splines on the Wasserstein Space

This page was built for publication: A Numerical Method to Solve Multi-Marginal Optimal Transport Problems with Coulomb Cost