Groupe d’études et de recherche en analyse des décisions


On the Pareto-optimality of Solutions to the Linear Bilevel Programming Problem


In this note it is shown that no general hypothesis on the cost functions can guarantee that a Pareto optimal solution to a linear bilevel programming problem exists. Indeed, whatever the leader's and follower's objectives, it is always possible to design constraints such that the resulting linear bilevel problem's solution is not Pareto optimal.

, 8 pages