Optimizing the Fractional Power in a Model with Stochastic PDE Constraints
We study an optimization problem with SPDE constraints, which has the peculiarity that the control parameter s is the s-th power of the diffusion operator in the state equation. Well-posedness of the state equation and differentiability properties with respect to the fractional parameter s are estab...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2018-11-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2018-2031 |
| Summary: | We study an optimization problem with SPDE constraints, which has the peculiarity that the control parameter s is the s-th power of the diffusion operator in the state equation. Well-posedness of the state equation and differentiability properties with respect to the fractional parameter s are established. We show that under certain conditions on the noise, optimality conditions for the control problem can be established. |
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| ISSN: | 1536-1365 2169-0375 |