scholarly journals Error Bounds of Generalized D-Gap Functions for Nonsmooth and Nonmonotone Variational Inequality Problems

2009 ◽  
Vol 20 (2) ◽  
pp. 667-690 ◽  
Author(s):  
Guoyin Li ◽  
Kung Fu Ng
Keyword(s):  
Variational Inequality ◽  
Error Bounds ◽  
Variational Inequality Problems ◽  
Gap Functions

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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