Two Stage Algorithm for Semi-Discrete Optimal Transport on Disconnected Domains

TL;DR

This paper introduces a two-stage algorithm for semi-discrete optimal transport on disconnected domains, demonstrating global linear and local superlinear convergence, with convergence of Laguerre cells.

Contribution

The paper presents a novel two-stage algorithm specifically designed for semi-discrete optimal transport on disconnected supports, with proven convergence properties.

Findings

Global linear convergence established

Local superlinear convergence demonstrated

Convergence of Laguerre cells proven

Abstract

In this paper we present a two-stage algorithm to solve the semi-discrete Optimal Transport Problem in the case where the support of the source measure is disconnected. We establish global linear convergence and local superlinear convergence. We also find convergence of the associated Laguerre cells in the vein of \cite{BansilKitagawa19b}.