TY  - JOUR
A1  - Karl, Veronika
A1  - Neitzel, Ira
A1  - Wachsmuth, Daniel
T1  - A Lagrange multiplier method for semilinear elliptic state constrained optimal control problems
JF  - Computational Optimization and Applications
N2  - In this paper we apply an augmented Lagrange method to a class of semilinear ellip-tic optimal control problems with pointwise state constraints. We show strong con-vergence of subsequences of the primal variables to a local solution of the original problem as well as weak convergence of the adjoint states and weak-* convergence of the multipliers associated to the state constraint. Moreover, we show existence of stationary points in arbitrary small neighborhoods of local solutions of the original problem. Additionally, various numerical results are presented.
KW  - optimal control
KW  - semilinear elliptic operators
KW  - state constraints
KW  - augmented Lagrange method
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-232811
SN  - 0926-6003
VL  - 77
ER  - 
TY  - JOUR
A1  - Natemeyer, Carolin
A1  - Wachsmuth, Daniel
T1  - A proximal gradient method for control problems with non-smooth and non-convex control cost
JF  - Computational Optimization and Applications
N2  - 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.
KW  - sparse control problems
KW  - proximal gradient method
KW  - non-smooth and non-convex optimization
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-269069
SN  - 1573-2894
VL  - 80
IS  - 2
ER  -