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arXiv · 2504.03301

Nonlinear Dynamical Unbalanced Optimal Transport: Relaxation and Duality

Dongjun Wu·Anders Rantzer
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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.

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Dongjun Wu, Anders Rantzer. 2025-04-04. Nonlinear Dynamical Unbalanced Optimal Transport: Relaxation and Duality. https://arxiv.org/abs/2504.03301

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