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arXiv · 0709.3186

A Semismooth Newton Method for Tikhonov Functionals with Sparsity Constraints

Roland Griesse·Dirk A. Lorenz
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Abstract

Minimization problems in $\ell^2$ for Tikhonov functionals with sparsity constraints are considered. Sparsity of the solution is ensured by a weighted $\ell^1$ 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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Roland Griesse, Dirk A. Lorenz. 2007-09-20. A Semismooth Newton Method for Tikhonov Functionals with Sparsity Constraints. https://doi.org/10.1088/0266-5611%2F24%2F3%2F035007

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