Optimal Transport with Constraints: From Mirror Descent to Classical Mechanics

Author:

Ibrahim Abdullahi Adinoyi1ORCID,Muehlebach Michael1,De Bacco Caterina1ORCID

Affiliation:

1. Max Planck Institute for Intelligent Systems

Abstract

Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is limited by the lack of principled and flexible ways to incorporate realistic constraints. We propose a principled physics-based approach to impose constraints flexibly in optimal transport problems. Constraints are included in mirror descent dynamics using the D’Alembert-Lagrange principle from classical mechanics. This results in a sparse, local and linear approximation of the feasible set leading in many cases to closed-form updates. Published by the American Physical Society 2024

Funder

International Max Planck Research School for Advanced Methods in Process and Systems Engineering

Publisher

American Physical Society (APS)

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