A Note on Scalar-Valued Gap Functions for 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...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2013-01, Vol.2013 (2013), p.677-680-584
Main Authors: Sun, Xiang-Kai, Fu, Hong-Yong, Chai, Yi
Format: Article
Language:English
Subjects:
Colleges & universities
Cybernetics
Estimates
Inequalities (Mathematics)
Mathematical programming
Mathematical research
Variational principles
Vector spaces
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Summary: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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/492103