New branch-and-bound rules for linear bilevel programming
SIAM Journal on Scientific and Statistical Computing
Discrete linear bilevel programming problem
Journal of Optimization Theory and Applications
Combinatorial optimization
Practical Bilevel Optimization: Algorithms and Applications (Nonconvex Optimization and Its Applications)
Optimality conditions for a bilevel matroid problem
Journal of Combinatorial Optimization
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In bilevel programming there are two decision makers, the leader and the follower, who act in a hierarchy. In this paper we deal with a bilevel problem where the follower maximizes a supermodular function. The payoff for the leader is given by the weighted set that is chosen by the follower. To increase his payoff the leader can increase the supermodular function of the follower by a modular one, thus influencing the follower's decision, but he has to pay a penalty for this. We want to find an optimum strategy for the leader. This is a bilevel programming problem with continuous variables in the upper level and a parametric supermodular maximization problem in the lower level. We analyze the structure of the bilevel problem. This we use to provide an equivalent one-level combinatorial problem. Finally, we investigate the properties of the new problem.