Existence of Solutions to Generalized Bilevel Programming Problem

In this paper a generalization of mathematical programs with equilibrium constraints or variational inequality constraints is considered, that is a mathematical program with constraints defined by an implicit variational problem (which generalizes a large number of problems like variational inequalities, quasi-variational inequalities and Nash equilibria). General results on closedness of the solution map for a parametric implicit variationl problem are given with existence results for the generalized bilevel programming problem.

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