Thursday, March 9, 2023 - 11:15 in H2
Sparse optimization problems in fractional order Sobolev spaces
A talk in the Nonlocal Equations: Analysis and Numerics 2023 series by
Daniel Wachsmuth from Würzburg
| Abstract: |
We consider optimization problems in the fractional order Sobolev spaces
with sparsity promoting objective functionals containing $L^p$-pseudonorms, $p\in (0,1)$.
Existence of solutions is proven. By means of a smoothing scheme, we obtain first-order optimality conditions,
which contain an equation with the fractional Laplace operator.
An algorithm based on this smoothing scheme is developed. Weak limit points of iterates are shown
to satisfy a stationarity system that is slightly weaker than that given by the necessary condition.
Within the CRC this talk is associated to the project(s): A7 |
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