An Algorithm for Linear Stochastic Bilevel Problems

Linear stochastic bilevel problems -although explained quickly- pose some difficulties when it comes to solving, even without the stochasticity. The aim of this work is to find a technique that allows for the use of decomposition methods known from stochastic programming in the framework of linear stochastic bilevel problems. The uncertainty is modeled as a discrete, finite distribution on some probability space. Two approaches are made, one using the optimal value function of the lower level, whereas the second technique utilizes the Karush-Kuhn-Tucker conditions of the lower level. Using the latter approach, an integer-programming based algorithm for the global resolution of these problems is presented and evaluated.

Autorentext

Dr. Charlotte Henkel began studying mathematics at the Technische Universität Dortmund in 2004. In 2009, she completed with a Diploma and started her doctor thesis in 2010 at the chair for discrete mathematics and optimization at the University Duisburg-Essen. Since 2014, she is a Consultant in the banking sector.