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Mathematics > Optimization and Control

arXiv:2108.12888 (math)
[Submitted on 29 Aug 2021 (v1), last revised 18 May 2023 (this version, v5)]

Title:Differentiability of the Value Function of Semilinear Parabolic Infinite Time Horizon Optimal Control Problems on $L^2(Ω)$ under Control Constraints

Authors:Karl Kunisch, Buddhika Priyasad
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Abstract:An abstract framework guaranteeing the local continuous differentiability of the value function associated with optimal stabilization problems subject to abstract semilinear parabolic equations subject to a norm constraint on the controls is established. It guarantees that the value function satisfies the associated Hamilton-Jacobi-Bellman equation in the classical sense. The applicability of the developed framework is demonstrated for specific semilinear parabolic equations.
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:2108.12888 [math.OC]
  (or arXiv:2108.12888v5 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2108.12888
Journal reference: Appl Math Optim 85, 10 (2022)
Related DOI: https://doi.org/10.1007/s00245-022-09840-9

Submission history

From: Buddhika Priyasad Sembukutti Liyanage [view email]
[v1] Sun, 29 Aug 2021 18:18:12 UTC (42 KB)
[v2] Mon, 25 Oct 2021 23:43:29 UTC (42 KB)
[v3] Thu, 9 Feb 2023 08:24:28 UTC (43 KB)
[v4] Sat, 6 May 2023 21:31:22 UTC (44 KB)
[v5] Thu, 18 May 2023 06:34:02 UTC (44 KB)
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