Optimal transport paths with capacity induced cost function

2025/10/12 by Xia, Qinglan, Sun, Haotian
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2510.10557

Abstract

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

Citations

• Map-compatible decomposition of transport paths

Related

• Transport multi-paths with capacity constraints
• Optimal transport through a toll
• Ramified optimal transportation with payoff on the boundary
• Optimal Transportation with Capacity Constraints
• A note on the c-monotonicity in optimal transport with capacity constraints