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An efficient linear programming method for Optimal Transportation

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arxiv 1509.03668 v1 pith:UU23FYGP submitted 2015-09-11 math.NA cs.NA

Adam M. Oberman , Yuanlong Ruan This is my paper · ORCID
classification math.NAcs.NA
keywords methodoptimalaccuracylinearsolutionstransportationcostefficient
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An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for moderate grid sizes. A grid refinement method results in a linear cost algorithm. Weak convergence of solutions is stablished. Barycentric projection of transference plans is used to improve the accuracy of solutions. The method is applied to more general problems, including partial optimal transportation, and barycenter problems. Computational examples validate the accuracy and efficiency of the method. Optimal maps between nonconvex domains, partial OT free boundaries, and high accuracy barycenters are presented.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. FINOM: Fast Sinkhorn on Non-uniform Meshes

    math.NA 2026-05 unverdicted novelty 7.0 of 10

    FINOM extends fast Sinkhorn to non-uniform meshes via a dividing index that creates quasi-collinear kernel blocks, reducing per-iteration cost from O(N^2) to O(N) with supporting 1D/2D experiments.

  2. A Multiscale Primal-Dual Interior-Point Relaxation Method for Large-Scale Optimal Transport Problems

    math.OC 2026-08 conditional novelty 6.0 of 10

    MSIPRM integrates a multiscale OT hierarchy with an interior-point relaxation method, solving large OT problems through sparse adaptive active sets.

  3. The Monge optimal transport barycenter problem

    math.OC 2025-07 conditional novelty 6.0 of 10

    A new flow-based algorithm solves the data-driven Monge optimal transport barycenter problem by recasting the independence constraint as a singular-value penalty, yielding linear per-iteration cost and a closed-form m...

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