Author:
Natemeyer Carolin,Wachsmuth Daniel
Abstract
AbstractWe 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 $$L^p$$
L
p
-type for $$p\in [0,1)$$
p
∈
[
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.
Funder
DFG
Julius-Maximilians-Universität Würzburg
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Control and Optimization
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