Bilevel Optimization: Advances and Next Challenges

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.