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

Abstract We investigate the convergence of proximal gradient method applied to control problems with non-smooth and non-convex cost. Here, we focus on cost functionals that promote sparsity, which includes $$L^p$$ L p -type for $$p\in [0,1)$$ ∈ [ 0 , 1 ) . prove stationarity properties weak limit points method. These are weaker than those provided by Pontryagin’s maximum principle L -stationarity.