Semismooth Newton Method for Boundary Bilinear Control
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910352505044992 |
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| author | Casas, Eduardo Chrysafinos, Konstantinos Mateos, Mariano |
| author_facet | Casas, Eduardo Chrysafinos, Konstantinos Mateos, Mariano |
| contents | We study a control-constrained optimal control problem governed by a semilinear elliptic equation. The control acts in a bilinear way on the boundary, and can be interpreted as a heat transfer coefficient. A detailed study of the state equation is performed and differentiability properties of the control-to-state mapping are shown. First and second order optimality conditions are derived. Our main result is the proof of 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_2403_01135 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semismooth Newton Method for Boundary Bilinear Control Casas, Eduardo Chrysafinos, Konstantinos Mateos, Mariano Optimization and Control 35J61, 49K20, 49M15, 49M05 We study a control-constrained optimal control problem governed by a semilinear elliptic equation. The control acts in a bilinear way on the boundary, and can be interpreted as a heat transfer coefficient. A detailed study of the state equation is performed and differentiability properties of the control-to-state mapping are shown. First and second order optimality conditions are derived. Our main result is the proof of 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 | Semismooth Newton Method for Boundary Bilinear Control |
| topic | Optimization and Control 35J61, 49K20, 49M15, 49M05 |
| url | https://arxiv.org/abs/2403.01135 |