Semismooth newton method for boundary bilinear control

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URI: https://hdl.handle.net/10902/30939
ISSN: 2475-1456
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Autoría
Casas Rentería, EduardoAutoridad Unican; Chrysafinos, Konstantinos; Mateos Alberdi, MarianoAutoridad Unican
Fecha
2023-11-29
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© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Publicado en
IEEE Control Systems Letters, 2023, 7, 3549-3554
Editorial
Institute of Electrical and Electronics Engineers, Inc.
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Palabras clave
Optimal control
Bilinear control
Semismooth Newton method
Convergence analysis
Resumen/Abstract
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.
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