A Semismooth Newton Method for Tikhonov Functionals with Sparsity Constraints
Optimization and Control
2010-10-26 v3 Numerical Analysis
Abstract
Minimization problems in for Tikhonov functionals with sparsity constraints are considered. Sparsity of the solution is ensured by a weighted 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.
Cite
@article{arxiv.0709.3186,
title = {A Semismooth Newton Method for Tikhonov Functionals with Sparsity Constraints},
author = {Roland Griesse and Dirk A. Lorenz},
journal= {arXiv preprint arXiv:0709.3186},
year = {2010}
}