Artikel
A proximal gradient method for control problems with non-smooth and non-convex control cost
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 Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}-type for p∈[0,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\in [0,1)$$\end{document}. 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.
- Sprache
-
Englisch
- Erschienen in
-
Journal: Computational Optimization and Applications ; ISSN: 1573-2894 ; Volume: 80 ; Year: 2021 ; Issue: 2 ; Pages: 639-677 ; New York, NY: Springer US
- Klassifikation
-
Mathematik
- Thema
-
Proximal gradient method
Non-smooth and non-convex optimization
Sparse control problems
- Ereignis
-
Geistige Schöpfung
- (wer)
-
Natemeyer, Carolin
Wachsmuth, Daniel
- Ereignis
-
Veröffentlichung
- (wer)
-
Springer US
- (wo)
-
New York, NY
- (wann)
-
2021
- DOI
-
doi:10.1007/s10589-021-00308-0
- Letzte Aktualisierung
-
10.03.2025, 11:42 MEZ
Datenpartner
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Objekttyp
- Artikel
Beteiligte
- Natemeyer, Carolin
- Wachsmuth, Daniel
- Springer US
Entstanden
- 2021
Ähnliche Objekte (12)
Control constrained optimal control problems in non-convex three dimensional polyhedral domains
A Nonsmooth Nonconvex Descent Algorithm
Exact and non-smooth control of quantum spin systems
Exact and non-smooth control of quantum spin systems
A computational method for non-convex reachable sets using optimal control
Nonsmooth analysis and control theory
Proximal methods in medical image reconstruction and in nonsmooth optimal control of partial differential equations
Proximal methods in medical image reconstruction and in nonsmooth optimal control of partial differential equations
Non-smooth thermomechanics
On the SQH scheme to solve non-smooth PDE optimal control problems
Adjoint sensitivity analysis for optimal control of non-smooth differential-algebraic equations
Optimal control, stabilization and nonsmooth analysis
Control constrained optimal control problems in non-convex three dimensional polyhedral domains
A Nonsmooth Nonconvex Descent Algorithm
Exact and non-smooth control of quantum spin systems
Exact and non-smooth control of quantum spin systems
A computational method for non-convex reachable sets using optimal control
Nonsmooth analysis and control theory
Proximal methods in medical image reconstruction and in nonsmooth optimal control of partial differential equations
Proximal methods in medical image reconstruction and in nonsmooth optimal control of partial differential equations
Non-smooth thermomechanics
On the SQH scheme to solve non-smooth PDE optimal control problems
Adjoint sensitivity analysis for optimal control of non-smooth differential-algebraic equations
Optimal control, stabilization and nonsmooth analysis
Control constrained optimal control problems in non-convex three dimensional polyhedral domains
A Nonsmooth Nonconvex Descent Algorithm
Exact and non-smooth control of quantum spin systems
Exact and non-smooth control of quantum spin systems
A computational method for non-convex reachable sets using optimal control
Nonsmooth analysis and control theory
Proximal methods in medical image reconstruction and in nonsmooth optimal control of partial differential equations
Proximal methods in medical image reconstruction and in nonsmooth optimal control of partial differential equations
Non-smooth thermomechanics
On the SQH scheme to solve non-smooth PDE optimal control problems
Adjoint sensitivity analysis for optimal control of non-smooth differential-algebraic equations