The Dual Gap Function and Error Bounds for Strongly Monotone Variational Inequalities

In the literature of variational inequalities, there has been a lot of studies about the role of gap functions in the development of error bounds specially for the case where the variational inequality is described by a strongly monotone mapping. However the role of the dual gap function in devising error bounds, to the best of our knowledge, has not been thoroughly investigated. In this article we focus on the dual gap function for monotone variational inequalities. We highlight some properties of the dual gap function which are not shared by the other gap functions and also show how it can be used to develop error bounds for strongly monotone variational inequalities with convex and compact feasible sets.