A proximal gradient method for control problems with non-smooth and non-convex control cost
Please always quote using this URN: urn:nbn:de:bvb:20-opus-269069
- We investigate the convergence of the proximal gradient method applied to control problems with non-smooth and non-convex control cost. Here, we focus on control cost functionals that promote sparsity, which includes functionals of L\(^{p}\)-type for p\in [0,1). We prove stationarity properties of weak limit points of the method. These properties are weaker than those provided by Pontryagin’s maximum principle and weaker than L-stationarity.
Author: | Carolin Natemeyer, Daniel Wachsmuth |
---|---|
URN: | urn:nbn:de:bvb:20-opus-269069 |
Document Type: | Journal article |
Faculties: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Language: | English |
Parent Title (English): | Computational Optimization and Applications |
ISSN: | 1573-2894 |
Year of Completion: | 2021 |
Volume: | 80 |
Issue: | 2 |
Pagenumber: | 639-677 |
Source: | Computational Optimization and Applications 2021, 80(2):639-677. DOI: 10.1007/s10589-021-00308-0 |
DOI: | https://doi.org/10.1007/s10589-021-00308-0 |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Tag: | non-smooth and non-convex optimization; proximal gradient method; sparse control problems |
Release Date: | 2022/06/13 |
Licence (German): | CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International |