Gap functions and global error bounds for set-valued variational inequalities |
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Authors: | Jianghua Fan Xiaoguo Wang |
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Institution: | Guangxi Normal University, Guilin, Guangxi 541004, PR China |
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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. |
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Keywords: | Set-valued variational inequality problem Unconstrained optimization problem Gap functions Global error bounds |
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