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Stability of the Monge Map in Semi-Dual Optimal Transport
Anton Selits · 2026-05-08 · via cs.LG updates on arXiv.org

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Abstract:This paper shows that the semi-dual formulation of the optimal transport problem has a degenerate saddle-point structure, and that its numerical solution is equivalent to solving a constrained optimization problem. We derive necessary and sufficient conditions for the convergence of Monge maps without requiring optimality of the dual potential. This analysis helps explain why, in practice, numerical algorithms often require more iterations to update the transport map than the potential.
Subjects: Optimization and Control (math.OC); Machine Learning (cs.LG)
Cite as: arXiv:2605.05569 [math.OC]
  (or arXiv:2605.05569v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2605.05569

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Anton Selitskiy [view email]
[v1] Thu, 7 May 2026 01:22:20 UTC (3,339 KB)

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