A simplified approach to semismooth Newton methods in function space

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Schiela, Anton:
A simplified approach to semismooth Newton methods in function space.
In: SIAM Journal on Optimization. Bd. 19 (2008) Heft 3 . - S. 1417-1432.
ISSN 1095-7189
DOI: https://doi.org/10.1137/060674375

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Abstract

We present an alternative approach to the analysis of Newton's method for function space problems involving semismooth Nemyckii operators. The simple main idea is to apply a local continuity result to appropriately chosen finite differences. In this respect it runs in parallel to the theory of Fréchet differentiable Nemyckii operators. This leads to a concise proof of superlinear convergence under relaxed conditions, compared to previous results. Moreover, extensions of this technique allow one to prove sharpened bounds on the rate of convergence and study semismooth Newton methods in the presence of compactness.