On the Convergence of Continuous and Discrete Unbalanced Optimal Transport Models for 1-Wasserstein Distance

DOI10.1137/22m1520748arXiv2303.17267OpenAlexW4392489242MaRDI QIDQ6117401

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Publication date: 20 March 2024

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.17267

zbMATH Keywords

\(\Gamma\)-convergenceasymptotic preservingunbalanced optimal transportprimal-dual hybrid algorithm

Mathematics Subject Classification ID

Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) (90C08) Probabilistic measure theory (60A10) Numerical methods for variational inequalities and related problems (65K15)

Cites Work

• Unnamed Item
• Unnamed Item
• The optimal partial transport problem
• Partial \(L^1\) Monge-Kantorovich problem: variational formulation and numerical approximation
• Free boundaries in optimal transport and Monge-Ampère obstacle problems
• A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions
• Proximal-point algorithm using a linear proximal term
• Gamma-convergence and optimal control problems
• A new optimal transport distance on the space of finite Radon measures
• Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures
• An interpolating distance between optimal transport and Fisher-Rao metrics
• Unbalanced optimal transport: dynamic and Kantorovich formulations
• A parallel method for earth mover's distance
• Semi-linear second-order elliptic equations in \(L^1\)
• A first-order primal-dual algorithm for convex problems with applications to imaging
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Unnormalized optimal transport
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• Generalized Wasserstein distance and its application to transport equations with source
• On a problem of Monge
• A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science
• Multilevel Optimal Transport: A Fast Approximation of Wasserstein-1 Distances
• Regularized Discrete Optimal Transport
• A Continuous Model of Transportation

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