Differentiability of the value function in control-constrained parabolic problems
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916955278016512 |
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| author | Corella, Alberto Domínguez Jork, Nicolai Volkwein, Stefan |
| author_facet | Corella, Alberto Domínguez Jork, Nicolai Volkwein, Stefan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20310 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differentiability of the value function in control-constrained parabolic problems Corella, Alberto Domínguez Jork, Nicolai Volkwein, Stefan Optimization and Control 49L99, 35K58, 49K40 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. |
| title | Differentiability of the value function in control-constrained parabolic problems |
| topic | Optimization and Control 49L99, 35K58, 49K40 |
| url | https://arxiv.org/abs/2412.20310 |