mlsanityData to 14 Oct 2026

A fast approach to optimal transport: The back-and-forth method

arXiv 1905.12154 ↗First posted 29 May 2019math.OC cs.NA math.NAcited by 16

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Abstract (arXiv)

We present an iterative method to efficiently solve the optimal transportation problem for a class of strictly convex costs which includes quadratic and p-power costs. Given two probability measures supported on a discrete grid with n points, we compute the optimal map using O(n) storage space and O(n log(n)) operations per iteration, with an approximately exponential convergence rate. Our approach allows us to solve optimal transportation problems on spatial grids as large as 4096x4096 and 384x384x384 in a matter of minutes.

Key facts. Cited by 16 papers in the map (data through 14 Oct 2026). First posted on arXiv 29 May 2019.

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Citing papers per year: 2021: 2; 2022: 5; 2023: 1; 2024: 4; 2025: 4.

16 papers.

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  1. 2022On amortizing convex conjugates for optimal transportcited by 31
  2. 2024Neural Optimal Transport with Lagrangian Costscited by 16
  3. 2022Efficient Natural Gradient Descent Methods for Large-Scale PDE-Based Optimization Problemscited by 7
  4. 2022Tangential Wasserstein Projectionscited by 4
  5. 2021Training Wasserstein GANs without gradient penaltiescited by 3
  6. 2023Information Geometry of Wasserstein Statistics on Shapes and Affine Deformationscited by 3
  7. 2021Physics Informed Convex Artificial Neural Networks (PICANNs) for Optimal Transport based Density Estimationcited by 2
  8. 2022A new method for determining Wasserstein 1 optimal transport maps from Kantorovich potentials, with deep learning applicationscited by 2
  9. 2024A Natural Primal-Dual Hybrid Gradient Method for Adversarial Neural Network Training on Solving Partial Differential Equationscited by 2
  10. 2025Optimal Transport Barycenter via Nonconvex-Concave Minimax Optimizationcited by 2
  11. 2025Sobolev Gradient Ascent for Optimal Transport: Barycenter Optimization and Convergence Analysiscited by 2
  12. 2022Wasserstein Archetypal Analysiscited by 1
4 more
  1. 2024Collective Counterfactual Explanations: Balancing Individual Goals and Collective Dynamicscited by 1
  2. 2025Statistical Inference for Optimal Transport Maps: Recent Advances and Perspectivescited by 1
  3. 2024Sum-of-Squares Programming for Ma-Trudinger-Wang Regularity of Optimal Transport Mapscited by 0
  4. 2025Designing Algorithms for Entropic Optimal Transport from an Optimisation Perspectivecited by 0