Bilevel 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.

• Part I: Bilevel optimization, game theory, and applications.- Interactions between bilevel optimization and Nash games.- On Stackelberg-Nash equilibria in bilevel optimization games.- A short state of the art on Multi-Leader-Follower games.- Regularization and approximation methods in Stackelberg games and bilevel optimization.- Applications of bilevel optimization in energy and electricity markets.- Bilevel optimization of regularization hyperparameters in machine Learning.- Part II: Theory and methods for linear and nonlinear bilevel optimization.- Bilevel optimization and variational analysis.- Constraint qualifications and optimality conditions in bilevel optimization.- Algorithms for simple bilevel programming.- Algorithms for linear bilevel optimization.- Global search for bilevel optimization with quadratic data.- MPEC methods for bilevel optimization problems.- Approximate bilevel optimization with population-based evolutionary algorithms.- Methods for pessimistic bilevel optimization.- Part III: Extensions and uncertainty in bilevel optimization.- Methods for multiobjective bilevel optimization.- Bilevel optimal control: existence results and stationarity conditions.- Bilevel linear optimization under uncertainty.- A unified framework for multistage mixed integer linear optimization.- Part IV: Numerical and research tools for bilevel optimization.- BOLIB: Bilevel Optimization LIBrary of test problems.- Bilevel optimization: theory, algorithms and applications.- Appendix: Bilevel optimization: bibliography.