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For a bilevel program with extremal value function, a necessary and sufficient condition for global optimality is given, which reduces the bilevel program to amax-minproblem with linked constraints. Also, for the case where the extremal value function is polyhedral, this optimality condition gives the possibility of a resolution via a maximization problem of a polyhedral convex function over a convex set. Finally, this case is completed by an algorithm.doi:10.1155/ijmms.2005.419 fatcat:qhhwthp66bcxnmy4eznkaizdsy