| Contents |
| We consider optimal control problems subject to semilinear parabolic equations.
The objective features an $L^1$-norm term, which promotes the sparsity of the optimal control.
Different types of iterated norms are considered, which give rise to different (directional) sparsity patterns.
In this presentation, we consider first-order necessary as well as second-order necessary and sufficient optimality conditions for these problems.
These constitute the basis of fast numerical solution methods and discretization error estimates. |
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