A Semismooth Newton Method for Tikhonov Functionals with Sparsity Constraints

  title={A Semismooth Newton Method for Tikhonov Functionals with Sparsity Constraints},
  author={Roland Griesse and Dirk A. Lorenz},
Minimization problems in l for Tikhonov functionals with sparsity constraints are considered. Sparsity of the solution is ensured by a weighted l 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. AMS… CONTINUE READING
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