Linear Bilevel Optimization Problem

Abstract

The linear bilevel optimization problem is considered first. For this some surprising properties are reported: What happens if a constraint on both the upper and the lower level variables is moved from the upper to the lower level problem or one constraint is added which is not active in the lower level problem at an optimal solution? What happens if a variable is added in the lower level? The bilevel optimization problem is a \(NP\)- hard optimization problem but conditions can be formulated guaranteeing that verification of an optimal solution can be done in polynomial time. In the last part, solution algorithms for the linear bilevel optimization problem are formulated either using regions of stability for solutions of the lower level problem or the optimal value reformulation of the bilevel problem.