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Differentiability of the value function in control-constrained parabolic problems

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2024

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Domínguez Corella, Alberto
Jork, Nicolai

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https://doi.org/10.48550/arXiv.2412.20310
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http://arxiv.org/abs/2412.20310

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Zusammenfassung

Along the optimal trajectory of an optimal control problem constrained by a semilinear parabolic partial differential equation, we prove the differentiability of the value function with respect to the initial condition and, under additional assumptions on the solution of the state equation, the differentiability of the value function with respect to the time variable. In our proof, we rely on local growth assumptions commonly associated with the study of second-order sufficient conditions. These assumptions are generally applicable to a wide range of problems, including, for instance, certain tracking-type problems. Finally, we discuss the differentiability of the value function in a neighborhood of the optimal trajectory when a growth condition for optimal controls is used.

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Fachgebiet (DDC)
510 Mathematik

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Semilinear parabolic equations, solution stability, value function

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ISO 690DOMÍNGUEZ CORELLA, Alberto, Nicolai JORK, Stefan VOLKWEIN, 2024. Differentiability of the value function in control-constrained parabolic problems
BibTex
@unpublished{DominguezCorella2024Diffe-75356,
  title={Differentiability of the value function in control-constrained parabolic problems},
  year={2024},
  doi={10.48550/arXiv.2412.20310},
  author={Domínguez Corella, Alberto and Jork, Nicolai and Volkwein, Stefan}
}
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