Nonlinear Dynamical Unbalanced Optimal Transport: Relaxation and Duality
Optimization and Control
2025-04-07 v1
Abstract
In this paper, we introduce a generalized dynamical unbalanced optimal transport framework by incorporating limited control input and mass dissipation, addressing limitations in conventional optimal transport for control applications. We derive a convex dual of the problem using dual optimal control techniques developed before and during the 1990s, transforming the non-convex optimization into a more tractable form.At the core of this formulation is the smooth sub-solutions to an HJB equation. A first-order algorithm based on the dual formulation is proposed to solve the problem numerically.
Cite
@article{arxiv.2504.03301,
title = {Nonlinear Dynamical Unbalanced Optimal Transport: Relaxation and Duality},
author = {Dongjun Wu and Anders Rantzer},
journal= {arXiv preprint arXiv:2504.03301},
year = {2025}
}