A numerical approach to optimization problems with variational inequality constraints

Optimization problems with variational inequality constraints are converted to constrained minimization of a local Lipschitz function. To this minimization a non-differentiable optimization method is used; the required subgradients of the objective are computed by means of a special adjoint equation. Besides tests with some academic examples, the approach is applied to the computation of the Stackelberg-Cournot-Nash equilibria and to the numerical solution of a class of quasi-variational inequalities.