Newton and Bouligand derivatives of the scalar play and stop operator

Martin Brokate

doi:10.1051/mmnp/2020013

Newton and Bouligand derivatives of the scalar play and stop operator

Martin Brokate

Chair of Numerical Mathematics and Control Theory

Weierstrass Institute for Applied Analysis and Stochastics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We prove that the play and the stop operator possess Newton and Bouligand derivatives, and exhibit formulas for those derivatives. The remainder estimate is given in a strengthened form, and a corresponding chain rule is developed. The construction of the Newton derivative ensures that the mappings involved are measurable.

Original language	English
Article number	51
Journal	Mathematical Modelling of Natural Phenomena
Volume	15
DOIs	https://doi.org/10.1051/mmnp/2020013
State	Published - 2020

Keywords

Bouligand derivative
Chain rule
Hysteresis operator
Maximum functional
Measurable selector
Newton derivative
Play, stop
Rate independence
Semismooth
Sensitivity
Variational inequality

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abstract = "We prove that the play and the stop operator possess Newton and Bouligand derivatives, and exhibit formulas for those derivatives. The remainder estimate is given in a strengthened form, and a corresponding chain rule is developed. The construction of the Newton derivative ensures that the mappings involved are measurable.",

keywords = "Bouligand derivative, Chain rule, Hysteresis operator, Maximum functional, Measurable selector, Newton derivative, Play, stop, Rate independence, Semismooth, Sensitivity, Variational inequality",

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KW - Chain rule

KW - Hysteresis operator

KW - Maximum functional

KW - Measurable selector

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KW - Play, stop

KW - Rate independence

KW - Semismooth

KW - Sensitivity

KW - Variational inequality

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Newton and Bouligand derivatives of the scalar play and stop operator

Abstract

Keywords

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