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

Carolin Natemeyer () and Daniel Wachsmuth ()
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Carolin Natemeyer: Universität Würzburg
Daniel Wachsmuth: Universität Würzburg

Computational Optimization and Applications, 2021, vol. 80, issue 2, No 11, 639-677

Abstract: Abstract 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 $$L^p$$ 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.

Keywords: Proximal gradient method; Non-smooth and non-convex optimization; Sparse control problems (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-021-00308-0

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