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arXiv · 2410.13730

On SCD Semismooth$^*$ Newton methods for the efficient minimization of Tikhonov functionals with non-smooth and non-convex penalties

Helmut Gfrerer·Simon Hubmer·Ronny Ramlau
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Abstract

We consider the efficient numerical minimization of Tikhonov functionals with nonlinear operators and non-smooth and non-convex penalty terms, which appear for example in variational regularization. For this, we consider a new class of SCD semismooth$^*$ Newton methods, which are based on a novel concept of graphical derivatives, and exhibit locally superlinear convergence. We present a detailed description of these methods, and provide explicit algorithms in the case of sparsity and total-variation penalty terms. The numerical performance of these methods is then illustrated on a number of tomographic imaging problems.

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Helmut Gfrerer, Simon Hubmer, Ronny Ramlau. 2024-10-17. On SCD Semismooth$^*$ Newton methods for the efficient minimization of Tikhonov functionals with non-smooth and non-convex penalties. https://arxiv.org/abs/2410.13730

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