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 (2008 — 2025)

Weierstrass Institute for Applied Analysis and Stochastics

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

6 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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10.1051/mmnp/2020013

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title = "Newton and Bouligand derivatives of the scalar play and stop operator",

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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N1 - Publisher Copyright: © The authors. Published by EDP Sciences, 2020.

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N2 - 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.

AB - 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.

KW - Bouligand derivative

KW - Chain rule

KW - Hysteresis operator

KW - Maximum functional

KW - Measurable selector

KW - Newton derivative

KW - Play, stop

KW - Rate independence

KW - Semismooth

KW - Sensitivity

KW - Variational inequality

UR - https://www.scopus.com/pages/publications/85096242668

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DO - 10.1051/mmnp/2020013

M3 - Article

AN - SCOPUS:85096242668

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VL - 15

JO - Mathematical Modelling of Natural Phenomena

JF - Mathematical Modelling of Natural Phenomena

M1 - 51

ER -

Newton and Bouligand derivatives of the scalar play and stop operator

Abstract

Keywords

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