A Semismooth Newton Method for Tikhonov Functionals with Sparsity Constraints

Details A Semismooth Newton Method for Tikhonov Functionals with Sparsity Constraints A Semismooth Newton Method for Tikhonov Functionals with Sparsity Constraints

2007-09-20

arxiv.org/abs/0709.3186v3

Inverse Problems 24:035007 (19pp), 2008

Mathematics

Optimization and Control

Scientific paper

10.1088/0266-5611/24/3/035007

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.

Affiliated with

Also associated with

No associations

Rating

A Semismooth Newton Method for Tikhonov Functionals with Sparsity Constraints does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Semismooth Newton Method for Tikhonov Functionals with Sparsity Constraints, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Semismooth Newton Method for Tikhonov Functionals with Sparsity Constraints will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-517893