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arXiv · 2309.04727

Optimal transport with constraints: from mirror descent to classical mechanics

Abdullahi Adinoyi Ibrahim·Michael Muehlebach·Caterina De Bacco
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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 such optimal transport problems. Constraints are included in mirror descent dynamics using the principle of D'Alembert-Lagrange from classical mechanics. This leads to a sparse, local and linear approximation of the feasible set leading in many cases to closed-form updates.

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Abdullahi Adinoyi Ibrahim, Michael Muehlebach, Caterina De Bacco. 2023-09-09. Optimal transport with constraints: from mirror descent to classical mechanics. https://doi.org/10.1103/physrevlett.133.057401

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