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We propose and analyze a modified damped Newton algorithm to solve thesemi-discrete optimal transport with storage fees. We prove global linearconvergence for a wide range of storage fee functions, the main assumptionbeing that each warehouse's storage costs are independent. We show that if $F$is an arbitrary storage fee function that satisfies this independence conditionthen $F$ can be perturbed into a new storage fee function so that our algorithmconverges. We also show that the optimizers are stable under theseperturbations. Furthermore, our results come with quantitative rates.

Computational Semi-Discrete Optimal Transport with General Storage Fees