Equivalent Optimization Formulations and Error Bounds for Variational Inequality Problems

We investigate whether some merit functions for variational inequality problems (VIP) provide error bounds for the underlying VIP. Under the condition that the involved mapping F is strongly monotone, but not necessarily Lipschitz continuous, we prove that the so-called regularized gap function provides an error bound for the underlying VIP. We give also an example showing that the so-called D-gap function might not provide error bounds for a strongly monotone VIP.This research was supported by United College and by a direct grant of the Chinese University of Hong Kong. The authors thank the referees for helpful comments and suggestions.