Semi-Discrete approximation of Optimal Mass Transport
Gershon Wolansky
TL;DR
This paper introduces a semi-discrete approximation method for optimal mass transport, defining optimal partitions, proposing an algorithm, and providing error estimates and numerical examples.
Contribution
It presents a novel semi-discrete approximation framework for optimal mass transport, including algorithms and error analysis.
Findings
Algorithm for computing optimal transport with general costs
Asymptotic error estimates for the approximation
Numerical examples demonstrating optimal partitions
Abstract
Optimal mass transport is described by an approximation of transport cost via semi-discrete costs. The notions of optimal partition and optimal strong partition are given as well. We also suggest an algorithm for computation of Optimal Transport for general cost functions induced by an action, an asymptotic error estimate and several numerical examples of optimal partitions.
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Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Functional Equations Stability Results · advanced mathematical theories