Bilinear control of semilinear elliptic PDEs: Convergence of a semismooth Newton method
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915356451274752 |
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| author | Casas, Eduardo Chrysafinos, Konstantinos Mateos, Mariano |
| author_facet | Casas, Eduardo Chrysafinos, Konstantinos Mateos, Mariano |
| contents | In this paper, we carry out the analysis of the semismooth Newton method for bilinear control problems related to semilinear elliptic PDEs. We prove existence, uniqueness and regularity for the solution of the state equation, as well as differentiability properties of the control to state mapping. Then, first and second order optimality conditions are obtained. Finally, we prove the superlinear convergence of the semismooth Newton method to local solutions satisfying no-gap second order sufficient optimality conditions as well as a strict complementarity condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_07554 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bilinear control of semilinear elliptic PDEs: Convergence of a semismooth Newton method Casas, Eduardo Chrysafinos, Konstantinos Mateos, Mariano Optimization and Control 35J61, 49K20, 49M15, 49M05 In this paper, we carry out the analysis of the semismooth Newton method for bilinear control problems related to semilinear elliptic PDEs. We prove existence, uniqueness and regularity for the solution of the state equation, as well as differentiability properties of the control to state mapping. Then, first and second order optimality conditions are obtained. Finally, we prove the superlinear convergence of the semismooth Newton method to local solutions satisfying no-gap second order sufficient optimality conditions as well as a strict complementarity condition. |
| title | Bilinear control of semilinear elliptic PDEs: Convergence of a semismooth Newton method |
| topic | Optimization and Control 35J61, 49K20, 49M15, 49M05 |
| url | https://arxiv.org/abs/2309.07554 |