A variational inequality for the derivative of the scalar play operator

Martin Brokate; Pavel Krejčí

doi:10.23952/jano.3.2021.2.03

A variational inequality for the derivative of the scalar play operator

Martin Brokate
, Pavel Krejčí

Chair of Numerical Mathematics and Control Theory (2008 — 2025)

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

1 Scopus citations

Abstract

We show that the directional derivative of the scalar play operator is the unique solution of a certain variational inequality. Due to the nature of the discontinuities involved, the variational inequality has an integral form based on the Kurzweil-Stieltjes integral.

Original language	English
Pages (from-to)	263-283
Number of pages	21
Journal	Journal of Applied and Numerical Optimization
Volume	3
Issue number	2
DOIs	https://doi.org/10.23952/jano.3.2021.2.03
State	Published - Aug 2021

Keywords

Energetic solution
Rate independence
Regulated function
Sweeping process
Variational inequality

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title = "A variational inequality for the derivative of the scalar play operator",

abstract = "We show that the directional derivative of the scalar play operator is the unique solution of a certain variational inequality. Due to the nature of the discontinuities involved, the variational inequality has an integral form based on the Kurzweil-Stieltjes integral.",

keywords = "Energetic solution, Rate independence, Regulated function, Sweeping process, Variational inequality",

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AB - We show that the directional derivative of the scalar play operator is the unique solution of a certain variational inequality. Due to the nature of the discontinuities involved, the variational inequality has an integral form based on the Kurzweil-Stieltjes integral.

KW - Energetic solution

KW - Rate independence

KW - Regulated function

KW - Sweeping process

KW - Variational inequality

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A variational inequality for the derivative of the scalar play operator

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Keywords

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