Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.07105 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917038103986176 |
|---|---|
| author | Borchard, Nicolas Wachsmuth, Gerd |
| author_facet | Borchard, Nicolas Wachsmuth, Gerd |
| contents | We address optimal control problems on the space of measures for an objective containing a smooth functional and an optimal transport regularization. That is, the quadratic Monge-Kantorovich distance between a given prior measure and the control is penalized in the objective. We consider optimality conditions and reparametrize the problem using the celebrated structure theorem by Brenier. The optimality conditions can be formulated as a piecewise differentiable equation. This is utilized to formulate solution algorithms and to analyze their local convergence properties. We present a numerical example to illustrate the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07105 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical solution of optimal control problems using quadratic transport regularization Borchard, Nicolas Wachsmuth, Gerd Optimization and Control 49M15, 49M29, 49K20 We address optimal control problems on the space of measures for an objective containing a smooth functional and an optimal transport regularization. That is, the quadratic Monge-Kantorovich distance between a given prior measure and the control is penalized in the objective. We consider optimality conditions and reparametrize the problem using the celebrated structure theorem by Brenier. The optimality conditions can be formulated as a piecewise differentiable equation. This is utilized to formulate solution algorithms and to analyze their local convergence properties. We present a numerical example to illustrate the theoretical findings. |
| title | Numerical solution of optimal control problems using quadratic transport regularization |
| topic | Optimization and Control 49M15, 49M29, 49K20 |
| url | https://arxiv.org/abs/2503.07105 |