Gap functions and error bounds for inverse quasi-variational inequality problems

This paper is dedicated to inverse quasi-variational inequalities which correspond to a mixture of quasi-variational inequalities and inverse variational inequalities. Our aim is to obtain local/global error bounds for inverse quasi-variational inequality problems in terms of different gap functions/merit functions i.e. the residual gap function, the regularized gap function and the DD-gap function. These bounds provide effective estimated distances between a specific point and the exact solution of the inverse quasi-variational inequality problem. Since the class of inverse quasi-variational inequalities includes the classes of general quasi-variational inequalities and variational inequalities, our results cover and extend similar results for these problems.