Error Bounds of Regularized Gap Functions for Nonsmooth Variational Inequality Problems

2006 ◽  
Vol 110 (2) ◽  
pp. 405-429 ◽  
Author(s):  
Kung Fu Ng ◽  
Lu Lin Tan
Keyword(s):  
Variational Inequality ◽  
Error Bounds ◽  
Variational Inequality Problems ◽  
Gap Functions ◽  
Regularized Gap Functions

scholarly journals Continuity Results and Error Bounds on Pseudomonotone Vector Variational Inequalities via Scalarization

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Xin Zuo ◽  
Hong-Zhi Wei ◽  
Chun-Rong Chen
Keyword(s):  
Variational Inequality ◽  
Error Bounds ◽  
Vector Variational Inequality ◽  
Gap Functions ◽  
Strong Pseudomonotonicity ◽  
Solution Mapping ◽  
Constraint Set ◽  
Regularized Gap Functions ◽  
Lower And Upper Semicontinuities ◽  
Weak Vector

Continuity (both lower and upper semicontinuities) results of the Pareto/efficient solution mapping for a parametric vector variational inequality with a polyhedral constraint set are established via scalarization approaches, within the framework of strict pseudomonotonicity assumptions. As a direct application, the continuity of the solution mapping to a parametric weak Minty vector variational inequality is also discussed. Furthermore, error bounds for the weak vector variational inequality in terms of two known regularized gap functions are also obtained, under strong pseudomonotonicity assumptions.

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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