Gap functions and global error bounds for set-valued variational inequalities

Authors:
Jianghua Fan;Xiaoguo Wang
Affiliations:
Guangxi Normal University, Guilin, Guangxi541004, PR China;Guangxi Normal University, Guilin, Guangxi541004, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

The set-valued variational inequality problem is very useful in economics theory and nonsmooth optimization. In this paper, we introduce some gap functions for set-valued variational inequality problems under suitable assumptions. By using these gap functions we derive global error bounds for the solution of the set-valued variational inequality problems. Our results not only generalize the previously known results for classical variational inequalities from single-valued case to set-valued, but also present a way to construct gap functions and derive global error bounds for set-valued variational inequality problems.