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arXiv · 2510.10557

Optimal transport paths with capacity induced cost function

Qinglan Xia·Haotian Sun
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Abstract

This article generalizes the study of ramified optimal transport with capacity constraint in transport multi-paths by generalizing the $\mathbf{M}_{\alpha}$ cost to $\mathbf{M}_{\alpha,c}$, which incorporates capacity constraints into the cost function. Equipped with $\mathbf{M}_{\alpha,c}$ cost, we prove the existence of optimal transport path, $\mathbf{M}_{\alpha,c}$ related inequalities, decomposition of any general transport paths, and occurrence of direct line segments in an optimal transport path.

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Qinglan Xia, Haotian Sun. 2025-10-12. Optimal transport paths with capacity induced cost function. https://arxiv.org/abs/2510.10557

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