A proximal gradient method for control problems with non-smooth and non-convex control cost

Please always quote using this URN: urn:nbn:de:bvb:20-opus-269069
• 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.