November 8, 2025Open Access

Nonlinear Dynamical Unbalanced Optimal Transport: Relaxation and Duality

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This analysis introduces optimal transport addressing control input and mass dissipation, implying a more tractable problem formulation.

Non-convex optimization transforms into a convex dual formulation using techniques from dual optimal control.
A first-order algorithm based on the dual formulation aims to solve the problem numerically, enhancing tractability.
The study incorporates mass dissipation and limited control input in the framework of optimal transport.
This approach highlights the significance of HJB equations in deriving smooth sub-solutions to the transport problem.

Wu et al. (2025) studied this question.

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