TY  - JOUR
A1  - Schindele, Andreas
A1  - Borzì, Alfio
T1  - Proximal Methods for Elliptic Optimal Control Problems with Sparsity Cost Functional
JF  - Applied Mathematics
N2  - First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking purposes, inexact proximal schemes are compared to an inexact semismooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectiveness of proximal schemes applied to infinite-dimensional elliptic optimal control problems and to validate the theoretical estimates.
KW  - semismooth Newton method
KW  - optimal control
KW  - elliptic PDE
KW  - nonsmooth optimization
KW  - proximal method
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-145850
VL  - 7
IS  - 9
ER  -