scholarly journals Gap Function and Global Error Bounds for Generalized Mixed Quasi-variational Inequality

2017 ◽  
Author(s):  
C. Wang ◽  
Y.L. Zhao ◽  
L. Shen
Keyword(s):  
Variational Inequality ◽  
Error Bounds ◽  
Gap Function ◽  
Global Error ◽  
Quasi Variational Inequality

scholarly journals Error bounds for generalized vector inverse quasi-variational inequality Problems with point to set mappings

2021 ◽  
Vol 6 (2) ◽  
pp. 1800-1815
Author(s):  
S. S. Chang ◽  
◽  
Salahuddin ◽  
M. Liu ◽  
X. R. Wang ◽  
...  
Keyword(s):  
Variational Inequality ◽  
Error Bounds ◽  
Variational Inequality Problems ◽  
Quasi Variational Inequality ◽  
Set Mappings

Error Bounds for Inverse Mixed Quasi-Variational Inequality via Generalized Residual Gap Functions

2021 ◽  
pp. 2150017
Author(s):  
Yinfeng Zhang ◽  
Guolin Yu
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Error Bounds ◽  
Feasible Solution ◽  
Variational Inequality Problem ◽  
Gap Functions ◽  
Strong Monotonicity ◽  
Mixed Variational Inequality ◽  
Related Literature ◽  
Quasi Variational Inequality

In this paper, we investigate error bounds of an inverse mixed quasi variational inequality problem in Hilbert spaces. Under the assumptions of strong monotonicity of function couple, we obtain some results related to error bounds using generalized residual gap functions. Each presented error bound is an effective estimation of the distance between a feasible solution and the exact solution. Because the inverse mixed quasi-variational inequality covers several kinds of variational inequalities, such as quasi-variational inequality, inverse mixed variational inequality and inverse quasi-variational inequality, the results obtained in this paper can be viewed as an extension of the corresponding results in the related literature.

scholarly journals On Gap Functions for Quasi-Variational Inequalities

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
Kouichi Taji
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Gap Function ◽  
Gap Functions ◽  
Merit Functions ◽  
Regularized Gap Function ◽  
Generalized Equilibrium ◽  
Quasi Variational Inequality

For variational inequalities, various merit functions, such as the gap function, the regularized gap function, the D-gap function and so on, have been proposed. These functions lead to equivalent optimization formulations and are used to optimization-based methods for solving variational inequalities. In this paper, we extend the regularized gap function and the D-gap functions for a quasi-variational inequality, which is a generalization of the variational inequality and is used to formulate generalized equilibrium problems. These extensions are shown to formulate equivalent optimization problems for quasi-variational inequalities and are shown to be continuous and directionally differentiable.

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