Global Optimisation of Pessimistic Bi-Level Problems

We study the solution of non-convex, pessimistic bi-level problems. After providing several motivating examples, we relate the problem to existing research in optimisation. We analyse key properties of the optimisation problem, such as closedness of the feasible region and computational complexity. We then present and investigate a semiinfinite solution approach that solves ǫ-approximations of the problem. To the best of our knowledge, this represents the first solution technique proposed for this problem class. We close with numerical results and a discussion on fruitful directions for future research.