Geodesic
Adaptive regularization and discretization of Bang-Bang optimal control problems
Electronic transactions on numerical analysis, Tome 40 (2013), pp. 249-267
In this article, Tikhonov regularization of control-constrained optimal control problems is investigated. Typically the solutions of such problems exhibit a so-called bang-bang structure. We develop a parameter choice rule that adaptively selects the Tikhonov regularization parameter depending on a posteriori computable quantities. We prove that this choice leads to optimal convergence rates with respect to the discretization parameter. The article is complemented by numerical results.
Classification : 49K20, 49N45, 65K15
Keywords: optimal control, bang-bang control, Tikhonov regularization, parameter choice rule 
@article{ETNA_2013__40__a13,
     author = {Wachsmuth,  Daniel},
     title = {Adaptive regularization and discretization of {Bang-Bang} optimal control problems},
     journal = {Electronic transactions on numerical analysis},
     pages = {249--267},
     year = {2013},
     volume = {40},
     zbl = {1287.49025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2013__40__a13/}
}
TY  - JOUR
AU  - Wachsmuth,  Daniel
TI  - Adaptive regularization and discretization of Bang-Bang optimal control problems
JO  - Electronic transactions on numerical analysis
PY  - 2013
SP  - 249
EP  - 267
VL  - 40
UR  - http://geodesic.mathdoc.fr/item/ETNA_2013__40__a13/
LA  - en
ID  - ETNA_2013__40__a13
ER  - 
%0 Journal Article
%A Wachsmuth,  Daniel
%T Adaptive regularization and discretization of Bang-Bang optimal control problems
%J Electronic transactions on numerical analysis
%D 2013
%P 249-267
%V 40
%U http://geodesic.mathdoc.fr/item/ETNA_2013__40__a13/
%G en
%F ETNA_2013__40__a13
Wachsmuth,  Daniel. Adaptive regularization and discretization of Bang-Bang optimal control problems. Electronic transactions on numerical analysis, Tome 40 (2013), pp. 249-267. http://geodesic.mathdoc.fr/item/ETNA_2013__40__a13/