TY - JOUR
T1 - UPPER ERROR BOUNDS OF DG-FUNCTIONS FOR HISTORY-DEPENDENT VARIATIONAL-HEMIVARIATIONAL INEQUALITIES
AU - Tam, Vo Minh
AU - Chen, Jein Shan
N1 - Publisher Copyright:
© National Research University Higher School of Economics. All rights reserved.
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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U2 - 10.23952/asvao.5.2023.3.03
DO - 10.23952/asvao.5.2023.3.03
M3 - Article
AN - SCOPUS:85179006681
SN - 2562-7775
VL - 5
SP - 347
EP - 367
JO - Applied Set-Valued Analysis and Optimization
JF - Applied Set-Valued Analysis and Optimization
IS - 3
ER -