Optimizing the fractional power in a model with stochastic PDE constraints

Carina Geldhauser; Enrico Valdinoci

doi:10.1515/ans-2018-2031

Optimizing the fractional power in a model with stochastic PDE constraints

Carina Geldhauser, Enrico Valdinoci

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	649-669
Number of pages	21
Journal	Advanced Nonlinear Studies
Volume	18
Issue number	4
DOIs	https://doi.org/10.1515/ans-2018-2031
Publication status	Published - 2018 Nov 1
Externally published	Yes

Subject classification (UKÄ)

Computational Mathematics

Free keywords

Fractional Parameter
Optimal Control
Optimization
Stochastic Heat Equation

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10.1515/ans-2018-2031

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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.",

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AU - Valdinoci, Enrico

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N2 - 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.

AB - 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.

KW - Fractional Parameter

KW - Optimal Control

KW - Optimization

KW - Stochastic Heat Equation

U2 - 10.1515/ans-2018-2031

DO - 10.1515/ans-2018-2031

M3 - Article

AN - SCOPUS:85053700583

SN - 1536-1365

VL - 18

SP - 649

EP - 669

JO - Advanced Nonlinear Studies

JF - Advanced Nonlinear Studies

IS - 4

ER -

Optimizing the fractional power in a model with stochastic PDE constraints

Abstract

Subject classification (UKÄ)

Free keywords

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