Work

Quantitative Convergence of a Discretization of Dynamic Optimal Transport Using the Dual Formulation

Year: 2024

Type: book-chapter

Abstract: We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence result does not require any regularity assumption on the measures, though experiments suggest that the rate is not sharp. Via an analysis of the duality gap we also obtain the convergence rates for the gradient of the optimal potentials and the velocity field under mild regularity assumptions. To obtain such rates, we discretize the dual formulation of the dynamic optimal transport problem and use the mature literature related to the error due to discretizing the Hamilton–Jacobi equation.

Source: Foundations of Computational Mathematics

DOI: 10.1007/s10208-024-09686-3

Authors: Sadashige Ishida, Hugo Lavenant

Institutions: Institute of Science and Technology Austria, Bocconi University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Institute of Science and Technology Austria, European Commission, Università Bocconi, NextGenerationEU