Journal
INVERSE PROBLEMS
Volume 24, Issue 3, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0266-5611/24/3/035007
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Minimization problems in l(2) for Tikhonov functionals with sparsity constraints are considered. Sparsity of the solution is ensured by a weighted l(1) penalty term. The necessary and sufficient condition for optimality is shown to be slantly differentiable (Newton differentiable), hence a semismooth Newton method is applicable. Local superlinear convergence of this method is proved. Numerical examples are provided which show that our method compares favorably with existing approaches.
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