Globally Solving Unbalanced Optimal Transport and Density Control for Gaussian Distributions
In this article, we study unbalanced optimal transport (UOT) and establish a control-theoretic dynamical extension, which we call the unbalanced density control (UDC), for a class of Gaussian reference measures. In the static setting, we consider UOT with quadratic transport cost and Kullback--Leibler penalties on the marginals relative to prescribed Gaussian measures. We show that the infinite-dimensional variational problem admits an exact Gaussian reduction, yielding a finite-dimensional optimization over masses, means, and covariances, together with a closed-form expression for the optimal transported mass. We then formulate UDC for discrete-time linear systems, where the initial and ...
| Authors | Haruto Nakashima, Siddhartha Ganguly, Kenji Kashima |
|---|---|
| Primary category | math.OC |
| Published | 5 May 2026 |
| Last updated at source | 5 May 2026 |
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