Bilevel Optimization: Advances and Next Challenges

2019 marked the 85th anniversary of Heinrich Freiherr von Stackelberg’s habilitation thesis “Marktform und Gleichgewicht,” which formed the roots of bilevel optimization. Research on the topic has grown tremendously since its introduction in the field of mathematical optimization. Besides the substantial advances that have been made from the perspective of game theory, many sub-fields of bilevel optimization have emerged concerning optimal control, multiobjective optimization, energy and electricity markets, management science, security and many more. Each chapter of this book covers a specific aspect of bilevel optimization that has grown significantly or holds great potential to grow, and was written by top experts in the corresponding area. In other words, unlike other works on the subject, this book consists of surveys of different topics on bilevel optimization. Hence, it can serve as a point of departure for students and researchers beginning their research journey or pursuing related projects. It also provides a unique opportunity for experienced researchers in the field to learn about the progress made so far and directions that warrant further investigation. All chapters have been peer-reviewed by experts on mathematical optimization.

Stephan Dempe is a Professor of Mathematical Optimization at the Technical University Bergakademie Freiberg, Germany. He is one of the world’s leading experts on bilevel optimization and has published four books and more than 50 articles on the subject.

 Alain Zemkoho is an Associate Professor of Operational Research at the School of Mathematical Sciences, University of Southampton, United Kingdom. His main research focus is on bilevel optimization, an area in which he has published many papers on the theory and numerical solution methods.