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 |
| _version_ | 1817997065431547904 |
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| author | Geldhauser Carina Valdinoci Enrico |
| author_facet | Geldhauser Carina Valdinoci Enrico |
| author_sort | Geldhauser Carina |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T02:32:34Z |
| format | Article |
| id | doaj.art-c50130168fce4234832629e0b1a69a42 |
| institution | Directory Open Access Journal |
| issn | 1536-1365 2169-0375 |
| language | English |
| last_indexed | 2024-04-14T02:32:34Z |
| publishDate | 2018-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-c50130168fce4234832629e0b1a69a422022-12-22T02:17:39ZengDe GruyterAdvanced Nonlinear Studies1536-13652169-03752018-11-0118464966910.1515/ans-2018-2031Optimizing the Fractional Power in a Model with Stochastic PDE ConstraintsGeldhauser Carina0Valdinoci Enrico1Chebyshev Laboratory, St. Petersburg State University, 14th Line V.O., 29B, Saint Petersburg199178RussiaDepartment of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, Perth, Western Australia 6009, Australia; and Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, 20133 Milan; and Istituto di Matematica Applicata e Tecnologie Informatiche, Consiglio Nazionale delle Ricerche, Via Ferrata 1, 27100 Pavia, ItalyWe 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.https://doi.org/10.1515/ans-2018-2031stochastic heat equationoptimizationoptimal controlfractional parameter65k10 35r60 35r11 |
| spellingShingle | Geldhauser Carina Valdinoci Enrico Optimizing the Fractional Power in a Model with Stochastic PDE Constraints Advanced Nonlinear Studies stochastic heat equation optimization optimal control fractional parameter 65k10 35r60 35r11 |
| title | Optimizing the Fractional Power in a Model with Stochastic PDE Constraints |
| title_full | Optimizing the Fractional Power in a Model with Stochastic PDE Constraints |
| title_fullStr | Optimizing the Fractional Power in a Model with Stochastic PDE Constraints |
| title_full_unstemmed | Optimizing the Fractional Power in a Model with Stochastic PDE Constraints |
| title_short | Optimizing the Fractional Power in a Model with Stochastic PDE Constraints |
| title_sort | optimizing the fractional power in a model with stochastic pde constraints |
| topic | stochastic heat equation optimization optimal control fractional parameter 65k10 35r60 35r11 |
| url | https://doi.org/10.1515/ans-2018-2031 |
| work_keys_str_mv | AT geldhausercarina optimizingthefractionalpowerinamodelwithstochasticpdeconstraints AT valdinocienrico optimizingthefractionalpowerinamodelwithstochasticpdeconstraints |