2023/10/05 by Xia, Qinglan, Sun, Haotian · 1 citation
#49Q22 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2310.03825
In the Monge-Kantorovich transport problem, the transport cost is expressed in terms of transport maps or transport plans, which play crucial roles there. A variant of the Monge-Kantorovich problem is the ramified (branching) transport problem that models branching transport systems via transport paths. In this article, we showed that any cycle-free transport path between two atomic measures can be decomposed into the sum of a map-compatible path and a plan-compatible path. Moreover, we showed that each stair-shaped transport path can be decomposed into the difference of two map-compatible transport paths.