A semismooth Newton method for Tikhonov functionals with sparsity constraints
A semismooth Newton method for Tikhonov functionals with sparsity constraints
Minimization problems in ℓ2 for Tikhonov functionals with sparsity constraints are considered. Sparsity of the solution is ensured by a weighted ℓ1 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 …