scholarly journals Gap functions and error bounds for vector inverse mixed quasi-variational inequality problems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Zhong-bao Wang ◽  
Zhang-you Chen ◽  
Zhe Chen
Keyword(s):  
Variational Inequality ◽  
Error Bounds ◽  
Variational Inequality Problems ◽  
Gap Functions ◽  
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 Gap Functions and Algorithms for Variational Inequality Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Congjun Zhang ◽  
Baoqing Liu ◽  
Jun Wei
Keyword(s):  
Variational Inequality ◽  
Error Bounds ◽  
Optimization Problem ◽  
Variational Inequality Problem ◽  
Descent Method ◽  
Variational Inequality Problems ◽  
Steepest Descent Method ◽  
Gap Functions ◽  
Constraint Optimization ◽  
Mixed Variational Inequality

We solve several kinds of variational inequality problems through gap functions, give algorithms for the corresponding problems, obtain global error bounds, and make the convergence analysis. By generalized gap functions and generalized D-gap functions, we give global bounds for the set-valued mixed variational inequality problems. And through gap function, we equivalently transform the generalized variational inequality problem into a constraint optimization problem, give the steepest descent method, and show the convergence of the method.

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