A numerical approach to optimization problems with variational inequality constraints. (English) Zbl 0835.90093

Summary: 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.


90C30 Nonlinear programming
49J40 Variational inequalities
49J52 Nonsmooth analysis
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C31 Sensitivity, stability, parametric optimization


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