A canonical duality approach for the solution of affine quasi-variational inequalities

We apply a sequential dual canonical transformation on the global optimization problem resulting from the reformulation of the Karush–Kuhn– Tucker conditions of affine quasi-variational inequalities (QVIs) using the Fischer- Burmeister complementarity function. Canonical duality is generally able to provide conditions for a critical point of the dual formulation to be the corresponding point of a global optimum of the original problem. By studying the new dual formulation it is possible to obtain properties that are not evident from the original one and that can be useful to develop new methods for the solution of (not necessarily affine) QVIs. The resulting formulation is canonically dual to the original in the sense that there is no duality gap between critical points of the original problem and those of the dual one.