Abstract

Many engineering problems can be formulated as an optimization problem whose solution depends on the solution of another optimization problem. The main (or upper level) optimization problem can then only affect the lower level optimization problem through setting some parameters for the lower level problem. This leads naturally to so-called ‘bi-level optimization’ problems.

Bi-level optimization problems have been studied for a long time, but since they are in general very computationally demanding, they have found little application until recently.

The presentation will focus on the case when the solution of the lower level problem is uniquely given by the parameters set by the upper level problem. Reformulation to a single level problem using binary variables will be covered, and some solution heuristics will be presented. The relevance of the problem formulation will be illustrated using examples from recent publications in constrained control.

Finally, an example will be given where the usual reformulation via binary variables does not apply, but where a simple solution nevertheless can be found by exploiting the KKT conditions of the lower level problem.