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Optimal control problems with $$L^0(\Omega )$$ L 0 ( Ω ) constraints: maximum principle and proximal gradient method

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  • Daniel Wachsmuth

    (Universität Würzburg)

Abstract

We investigate optimal control problems with $$L^0$$ L 0 constraints, which restrict the measure of the support of the controls. We prove necessary optimality conditions of Pontryagin maximum principle type. Here, a special control perturbation is used that respects the $$L^0$$ L 0 constraint. First, the maximum principle is obtained in integral form, which is then turned into a pointwise form. In addition, an optimization algorithm of proximal gradient type is analyzed. Under some assumptions, the sequence of iterates contains strongly converging subsequences, whose limits are feasible and satisfy a subset of the necessary optimality conditions.

Suggested Citation

  • Daniel Wachsmuth, 2024. "Optimal control problems with $$L^0(\Omega )$$ L 0 ( Ω ) constraints: maximum principle and proximal gradient method," Computational Optimization and Applications, Springer, vol. 87(3), pages 811-833, April.
    • Handle: RePEc:spr:coopap:v:87:y:2024:i:3:d:10.1007_s10589-023-00456-5
    DOI: 10.1007/s10589-023-00456-5
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    References listed on IDEAS

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    1. Christian Kanzow & Andreas B. Raharja & Alexandra Schwartz, 2021. "An Augmented Lagrangian Method for Cardinality-Constrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 189(3), pages 793-813, June.
    2. 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.
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