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.
Optimizing the fractional power in a model with stochastic PDE constraints
E Valdinoci
2018
Abstract
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.File in questo prodotto:
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Descrizione: Optimizing the fractional power in a model with stochastic PDE constraints
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Descrizione: Optimizing the fractional power in a model with stochastic PDE constraints
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