Abstract
We consider optimization problems in the fractional order Sobolev spaces with sparsity promoting objective functionals containing L p -pseudonorms, . 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.
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