In this paper we survey some important classes of gap function for variational inequalities and also some recently introduced gap functions for generalized variational inequalities. A new gap function is proposed for generalized variational inequalities and error bound is developed. Error bounds are also developed for some particular classes of gap functions. In fact a gap function is useful in devising an error bound if its value on a feasible sequence converging to solution of the variational inequality decreases to zero. We under what conditions the gap functions discussed in this article will follow the above property.
Unpublished Indian Institute of Technology, Kanpur Kanpur, India May02, 2012. Submitted to the Vietnam Journal of Mathematics for the special issue in honour of the 65th birthday of P. Q, Khanh