A Fenchel–Lagrange Duality Approach for a Bilevel Programming Problem with Extremal‐Value Function

In this paper, for a bilevel programming problem (S) with an extremal‐value function, we first give its Fenchel–Lagrange dual problem. Under appropriate assumptions, we show that a strong duality holds between them. Then, we provide optimality conditions for (S) and its dual. Finally, we show that the resolution of the dual problem is equivalent to the resolution of a one‐level convex minimization problem.