Stability of the Monge Map in Semi-Dual Optimal Transport

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.

<iframe src="https://silytics.si/embed/item/8ceae70a-06e8-49a6-a1ad-d8f87123f8c7" width="420" height="190" style="border:0" loading="lazy" title="Silytics entry"></iframe>

Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.