Computational Semi-Discrete Optimal Transport with General Storage Fees

07/08/2020
by   Mohit Bansil, et al.
0

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.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

08/30/2019

A Newton algorithm for semi-discrete optimal transport with storage fees and quantitative convergence of cells

In this paper we will continue analysis of the semi-discrete optimal tra...
03/02/2020

Optimal transport: discretization and algorithms

This chapter describes techniques for the numerical resolution of optima...
07/12/2021

A stochastic Gauss-Newton algorithm for regularized semi-discrete optimal transport

We introduce a new second order stochastic algorithm to estimate the ent...
04/12/2021

Metasurfaces and Optimal transport

This paper provides a theoretical and numerical approach to show existen...
07/05/2017

An algorithm for optimal transport between a simplex soup and a point cloud

We propose a numerical method to find the optimal transport map between ...
06/24/2021

Sharp Convergence Rates for Empirical Optimal Transport with Smooth Costs

We revisit the question of characterizing the convergence rate of plug-i...
04/08/2019

Consensus-based Distributed Discrete Optimal Transport for Decentralized Resource Matching

Optimal transport has been used extensively in resource matching to prom...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.