We propose and analyze a modified damped Newton algorithm to solve the semi-discrete optimal transport with storage fees. We prove global linear convergence for a wide range of storage fee functions, the main assumption being that each warehouse's storage costs are independent. We show that if F is an arbitrary storage fee function that satisfies this independence condition then F can be perturbed into a new storage fee function so that our algorithm converges. We also show that the optimizers are stable under these perturbations. Furthermore, our results come with quantitative rates.

中文翻译：

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计算半离散最优运输，并收取一般仓储费

我们提出并分析了一种改进的阻尼牛顿算法，以解决带存储费用的半离散最优运输。我们证明了广泛的仓储费用函数具有全局线性收敛性，主要假设是每个仓库的仓储成本都是独立的。我们证明，如果F是满足此独立性条件的任意存储费用函数，则F可以被扰动为新的存储费用函数，从而使我们的算法收敛。我们还表明，优化器在这些扰动下是稳定的。此外，我们的结果带有定量比率。