Gap functions and error bounds for generalized vector variational inequalities

2013 ◽  
Vol 8 (5) ◽  
pp. 1663-1673 ◽  
Author(s):  
Xiang-Kai Sun ◽  
Yi Chai
Keyword(s):  
Variational Inequalities ◽  
Error Bounds ◽  
Vector Variational Inequalities ◽  
Gap Functions ◽  
Generalized Vector Variational Inequalities

scholarly journals A Note on Scalar-Valued Gap Functions for Generalized Vector Variational Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Xiang-Kai Sun ◽  
Hong-Yong Fu ◽  
Yi Chai
Keyword(s):  
Variational Inequalities ◽  
Vector Variational Inequalities ◽  
Gap Functions ◽  
Mild Conditions ◽  
Generalized Vector Variational Inequalities

This paper is concerned with gap functions of generalized vector variational inequalities (GVVI). By using scalarization approach, scalar-valued variational inequalities of (GVVI) are introduced. Some relationships between the solutions of (GVVI) and its scalarized versions are established. Then, by using these relationships and some mild conditions, scalar-valued gap functions for (GVVI) are established.

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