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

Author

Listed:
  • Carolin Natemeyer

    (Universität Würzburg)

  • Daniel Wachsmuth

    (Universität Würzburg)

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.

Suggested Citation

  • Carolin Natemeyer & Daniel Wachsmuth, 2021. "A proximal gradient method for control problems with non-smooth and non-convex control cost," Computational Optimization and Applications, Springer, vol. 80(2), pages 639-677, November.
    • Handle: RePEc:spr:coopap:v:80:y:2021:i:2:d:10.1007_s10589-021-00308-0
    DOI: 10.1007/s10589-021-00308-0
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    References listed on IDEAS

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    1. Christoph Buchheim & Renke Kuhlmann & Christian Meyer, 2018. "Combinatorial optimal control of semilinear elliptic PDEs," Computational Optimization and Applications, Springer, vol. 70(3), pages 641-675, July.
    2. Caroline Geiersbach & Teresa Scarinci, 2021. "Stochastic proximal gradient methods for nonconvex problems in Hilbert spaces," Computational Optimization and Applications, Springer, vol. 78(3), pages 705-740, April.
    3. Kristian Bredies & Dirk A. Lorenz & Stefan Reiterer, 2015. "Minimization of Non-smooth, Non-convex Functionals by Iterative Thresholding," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 78-112, April.
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