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- W2611684948 abstract "This paper is concerned with an optimal control problem governed by a non-smooth semilinear elliptic equation. We show that the control-to-state mapping is directionally differentiable and precisely characterize its Bouligand sub-differential. By means of a suitable regularization, first-order optimality conditions including an adjoint equation are derived and afterwards interpreted in light of the previously obtained characterization. In addition, the directional derivative of the control-to-state mapping is used to establish strong stationarity conditions. While the latter conditions are shown to be stronger, we demonstrate by numerical examples that the former conditions are amenable to numerical solution using a semi-smooth Newton method." @default.
- W2611684948 created "2017-05-12" @default.
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- W2611684948 date "2018-01-01" @default.
- W2611684948 modified "2023-10-11" @default.
- W2611684948 title "Optimal control of a non-smooth semilinear elliptic equation" @default.
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- W2611684948 doi "https://doi.org/10.3934/mcrf.2018011" @default.
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