Optimality conditions for pessimistic bilevel problems using convexificator

The purpose of this paper is to study the pessimistic version of bilevel programming problems in finite-dimensional spaces. Problems of this type are intrinsically nonsmooth (even for smooth initial data). By using optimal value function, we transform the initial problem into a generalized minimax optimization problem. Using convexificators, first-order necessary optimality conditions are then established. An example that illustrates our findings is also given.