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.

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Author: Carolin Natemeyer, Daniel Wachsmuth
Document Type:Journal article
Faculties:Fakultät für Mathematik und Informatik / Institut für Mathematik
Parent Title (English):Computational Optimization and Applications
Year of Completion:2021
Source:Computational Optimization and Applications 2021, 80(2):639-677. DOI: 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):License LogoCC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International