UPPER ERROR BOUNDS OF DG-FUNCTIONS FOR HISTORY-DEPENDENT VARIATIONAL-HEMIVARIATIONAL INEQUALITIES

Vo Minh Tam; Jein Shan Chen

doi:10.23952/asvao.5.2023.3.03

UPPER ERROR BOUNDS OF DG-FUNCTIONS FOR HISTORY-DEPENDENT VARIATIONAL-HEMIVARIATIONAL INEQUALITIES

Vo Minh Tam^*, Jein Shan Chen^*

^*Corresponding author for this work

Department of Mathematics

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

2 Citations (Scopus)

Abstract

The aim of this paper is to study the difference gap function (for brevity, DG-function) and upper error bounds for an abstract class of variational-hemivariational inequalities with history-dependent operators (for brevity, HDVHIs). First, we propose a new concept of gap functions to the HDVHIs and consider the regularized gap function (for brevity, RG-function) for the HDVHIs using the optimality condition for the concerning minimization problem. Then, the DG-function for the HDVHIs depending on these RG-functions is constructed. Finally, we establish upper error bounds for the HDVHIs controlled by the RG-function and the DG-function under suitable conditions.

Original language	English
Pages (from-to)	347-367
Number of pages	21
Journal	Applied Set-Valued Analysis and Optimization
Volume	5
Issue number	3
DOIs	https://doi.org/10.23952/asvao.5.2023.3.03
Publication status	Published - 2023

Keywords

Gap function
History-dependent operator
Upper error bound
Variational-hemivariational inequality

ASJC Scopus subject areas

Analysis
Numerical Analysis
Mathematics (miscellaneous)
Modelling and Simulation
Control and Optimization
Applied Mathematics

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10.23952/asvao.5.2023.3.03

Cite this

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title = "UPPER ERROR BOUNDS OF DG-FUNCTIONS FOR HISTORY-DEPENDENT VARIATIONAL-HEMIVARIATIONAL INEQUALITIES",

abstract = "The aim of this paper is to study the difference gap function (for brevity, DG-function) and upper error bounds for an abstract class of variational-hemivariational inequalities with history-dependent operators (for brevity, HDVHIs). First, we propose a new concept of gap functions to the HDVHIs and consider the regularized gap function (for brevity, RG-function) for the HDVHIs using the optimality condition for the concerning minimization problem. Then, the DG-function for the HDVHIs depending on these RG-functions is constructed. Finally, we establish upper error bounds for the HDVHIs controlled by the RG-function and the DG-function under suitable conditions.",

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author = "Tam, {Vo Minh} and Chen, {Jein Shan}",

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T1 - UPPER ERROR BOUNDS OF DG-FUNCTIONS FOR HISTORY-DEPENDENT VARIATIONAL-HEMIVARIATIONAL INEQUALITIES

AU - Tam, Vo Minh

AU - Chen, Jein Shan

PY - 2023

Y1 - 2023

N2 - The aim of this paper is to study the difference gap function (for brevity, DG-function) and upper error bounds for an abstract class of variational-hemivariational inequalities with history-dependent operators (for brevity, HDVHIs). First, we propose a new concept of gap functions to the HDVHIs and consider the regularized gap function (for brevity, RG-function) for the HDVHIs using the optimality condition for the concerning minimization problem. Then, the DG-function for the HDVHIs depending on these RG-functions is constructed. Finally, we establish upper error bounds for the HDVHIs controlled by the RG-function and the DG-function under suitable conditions.

AB - The aim of this paper is to study the difference gap function (for brevity, DG-function) and upper error bounds for an abstract class of variational-hemivariational inequalities with history-dependent operators (for brevity, HDVHIs). First, we propose a new concept of gap functions to the HDVHIs and consider the regularized gap function (for brevity, RG-function) for the HDVHIs using the optimality condition for the concerning minimization problem. Then, the DG-function for the HDVHIs depending on these RG-functions is constructed. Finally, we establish upper error bounds for the HDVHIs controlled by the RG-function and the DG-function under suitable conditions.

KW - Gap function

KW - History-dependent operator

KW - Upper error bound

KW - Variational-hemivariational inequality

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DO - 10.23952/asvao.5.2023.3.03

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UPPER ERROR BOUNDS OF DG-FUNCTIONS FOR HISTORY-DEPENDENT VARIATIONAL-HEMIVARIATIONAL INEQUALITIES

Abstract

Keywords

ASJC Scopus subject areas

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