论文标题
一般存储费用的计算半差异最佳运输
Computational Semi-Discrete Optimal Transport with General Storage Fees
论文作者
论文摘要
我们提出和分析了经过修改的牛顿算法，以解决储存费的半污物最佳运输。我们证明了各种存储费功能的全球线性融合，主要假设是每个仓库的存储成本都是独立的。我们表明，如果$ f $是满足这种独立条件的任意存储费功能，那么$ f $可能会被扰动到新的存储费函数中，以使我们的算法收敛。我们还表明，在这些扰动下，优化器是稳定的。此外，我们的结果带有定量率。
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.
