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A simplified approach to semismooth Newton methods in function space

Title data

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

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Official URL: Volltext

Project information

Project title:
Project's official titleProject's id
DFG Research Center Matheon "Mathematics for key technologies"FZT 86

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: continuity of Nemyckii operators; Newton methods in function space; optimal control
Subject classification: Mathematics Subject Classification Code: 49K20 (47H30 47J25 49M15 65K10)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics) > Professorship Applied Mathematics (Applied Mathematics) - Univ.-Prof. Dr. Anton Schiela
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 29 May 2015 07:39
Last Modified: 26 Aug 2015 11:41
URI: https://eref.uni-bayreuth.de/id/eprint/11848