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Vector Variational Inequalities and Vector Equilibria
Volume 38 of the series Nonconvex Optimization and Its Applications pp 5572
On Gap Functions for Vector Variational Inequalities
 Guangya ChenAffiliated withInstitute of Systems Science, Chinese Academy of Sciences
 , ChuenJin GohAffiliated withDepartment of Mathematics and Statistics, University of Western Australia
 , Xiao Qi YangAffiliated withDepartment of Applied Mathematics, The Hong Kong Polytechnic University
Abstract
We extend the theory of gap functions for scalar variational inequality problems (see [1,8]) to the case of vector variational inequality. The gap functions for vector variational inequality are defined as setvalued mappings. The significance of the gap function is interpreted in terms of the inverse vector variational inequality. Convexity properties of these setvalued mappings are studied under different assumptions.
Key Words
Vector variational inequality gap functions duality Fenchel conjugate Title
 On Gap Functions for Vector Variational Inequalities
 Book Title
 Vector Variational Inequalities and Vector Equilibria
 Book Subtitle
 Mathematical Theories
 Pages
 pp 5572
 Copyright
 2000
 DOI
 10.1007/9781461302995_4
 Print ISBN
 9781461379850
 Online ISBN
 9781461302995
 Series Title
 Nonconvex Optimization and Its Applications
 Series Volume
 38
 Series ISSN
 1571568X
 Publisher
 Springer US
 Copyright Holder
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Vector variational inequality
 gap functions
 duality
 Fenchel conjugate
 Industry Sectors
 eBook Packages
 Editors

 Franco Giannessi ^{(3)}
 Editor Affiliations

 3. Department of Mathematics, University of Pisa
 Authors

 Guangya Chen ^{(4)}
 ChuenJin Goh ^{(5)}
 Xiao Qi Yang ^{(6)}
 Author Affiliations

 4. Institute of Systems Science, Chinese Academy of Sciences, Beijing, P.R. China
 5. Department of Mathematics and Statistics, University of Western Australia, Nedland, WA, Australia
 6. Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China
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