Eduardo Casas, Konstantinos Chrysafinos, Mariano Mateos
Published 2024-03-02Version 1
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.
Journal: IEEE Control Systems Letters, 7 (2023) 3549--3554
Bilinear control of semilinear elliptic PDEs: Convergence of a semismooth Newton method
Convergence analysis of the semismooth Newton method for sparse control problems governed by semilinear elliptic equations
Reformulation of the M-stationarity conditions as a system of discontinuous equations and its solution by a semismooth Newton method
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