Abstract
We present and analyze the solution of nonsmooth optimization problems by a quadratic overestimation method in a function space setting. Under certain assumptions on a suitable local model, we show convergence to first-order minimal points. Subsequently, we discuss an approach to generate such a local model using the so-called abs-linearization. Finally, we discuss a class of PDE-constrained optimization problems incorporating the -penalty term that fits into the considered class of nonsmooth optimization problems.
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Acknowledgements
We would like to thank Johannes Lankeit and Gerd Wachsmuth for the helpful comments and useful suggestions that greatly improved the manuscript.
Disclosure statement
No potential conflict of interest was reported by the author(s).