A note on the c-monotonicity in optimal transport with capacity constraints

Dongwei Chen

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arXiv · 2508.20428

A note on the c-monotonicity in optimal transport with capacity constraints

Dongwei Chen

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Abstract

This paper studies the geometry of the optimizer for the optimal transport problem with capacity constraints. We introduce the concept of c-capacity monotonicity, which is a generalization of c-cyclical monotonicity in optimal transport. We show that the optimizer of the optimal transport problem with capacity constraints is c-capacity monotone.

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Dongwei Chen. 2025-08-28. A note on the c-monotonicity in optimal transport with capacity constraints. https://arxiv.org/abs/2508.20428

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