Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2207.05503 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929587821215744 |
|---|---|
| author | Marko, Jonas Wachsmuth, Gerd |
| author_facet | Marko, Jonas Wachsmuth, Gerd |
| contents | We investigate local optimality conditions of first and second order for integer optimal control problems with total variation regularization via a finite-dimensional switching point problem. We show the equivalence of local optimality for both problems, which will be used to derive conditions concerning the switching points of the control function. A non-local optimality condition treating back-and-forth switches will be formulated.
For the numerical solution, we propose a proximal-gradient method. The emerging discretized subproblems will be solved by employing Bellman's optimality principle, leading to an algorithm which is polynomial in the mesh size and in the admissible control levels. An adaption of this algorithm can be used to handle subproblems of the trust-region method proposed in Leyffer, Manns, 2021. Finally, we demonstrate computational results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_05503 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Integer optimal control problems with total variation regularization: Optimality conditions and fast solution of subproblems Marko, Jonas Wachsmuth, Gerd Optimization and Control 49K30, 49L20 49M37, 90C10 We investigate local optimality conditions of first and second order for integer optimal control problems with total variation regularization via a finite-dimensional switching point problem. We show the equivalence of local optimality for both problems, which will be used to derive conditions concerning the switching points of the control function. A non-local optimality condition treating back-and-forth switches will be formulated. For the numerical solution, we propose a proximal-gradient method. The emerging discretized subproblems will be solved by employing Bellman's optimality principle, leading to an algorithm which is polynomial in the mesh size and in the admissible control levels. An adaption of this algorithm can be used to handle subproblems of the trust-region method proposed in Leyffer, Manns, 2021. Finally, we demonstrate computational results. |
| title | Integer optimal control problems with total variation regularization: Optimality conditions and fast solution of subproblems |
| topic | Optimization and Control 49K30, 49L20 49M37, 90C10 |
| url | https://arxiv.org/abs/2207.05503 |