Optimality conditions for bilevel optimization with variational inequality constraints using approximations

Abstract We use first- and second-order approximations to establish necessary and suffcient optimality conditions for nonsmooth generalized bilevel optimization problems with variational inequality constraints. To transform the hierarchical problem into a single-level optimization problem, we employ two approaches: the gap function reformulation and the KKT reformulation. We compare these approaches and provide examples to illustrate the applicability of the results.