Abstract
Abstract
We consider optimization problems in the fractional order Sobolev spaces with sparsity promoting objective functionals containing L
p
-pseudonorms,
p
∈
(
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.
Funder
Division of Mathematical Sciences
Deutsche Forschungsgemeinschaft
Air Force Office of Scientific Research
Subject
Applied Mathematics,Computer Science Applications,Mathematical Physics,Signal Processing,Theoretical Computer Science
Cited by
1 articles.
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