Nonlinear Dynamical Unbalanced Optimal Transport: Relaxation and Duality
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916673981775872 |
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| author | Wu, Dongjun Rantzer, Anders |
| author_facet | Wu, Dongjun Rantzer, Anders |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_03301 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear Dynamical Unbalanced Optimal Transport: Relaxation and Duality Wu, Dongjun Rantzer, Anders Optimization and Control 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. |
| title | Nonlinear Dynamical Unbalanced Optimal Transport: Relaxation and Duality |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.03301 |