On the Choice of the Penalty Parameter for Discrete-Continuous Linear Bilevel Problems Reformulation

In this paper we focus on linear bi-level problems in which the variables controlled by the leader are discrete. It is known that such problems are equivalent to continuous linear bi-level problems in which the integrality requirements are relaxed and the leader's objective function is modified including a concave penalty function weighted by a parameter µ. The equivalence holds for a sufficiently large value of µ. A valid lower bound for µ is known in the literature. In the following, we provide an improvement of this lower bound and experiment the new lower bound on a set of test problems.