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arXiv · 2007.11426

A proximal gradient method for control problems with nonsmooth and nonconvex control cost

Carolin Natemeyer·Daniel Wachsmuth
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Abstract

We investigate the convergence of an application of a proximal gradient method to control problems with nonsmooth and nonconvex 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.

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Carolin Natemeyer, Daniel Wachsmuth. 2020-07-22. A proximal gradient method for control problems with nonsmooth and nonconvex control cost. https://arxiv.org/abs/2007.11426

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