Stephan Dempe Livres

Bilevel programming problems involve hierarchical optimization, where the upper level's constraints depend on a lower level's parametric optimization. This book focuses on scenarios with non-unique lower level solutions, exploring both optimistic and pessimistic approaches. It begins with foundational concepts in parametric nonlinear optimization and progresses to key theoretical results, including optimality conditions and solution algorithms. The text also examines stationarity conditions, stability properties, numerical complexity, and integrality constraints, providing a comprehensive overview of bilevel programming challenges.

This book describes recent theoretical findings relevant to bilevel programming in general, and in mixed-integer bilevel programming in particular. It describes recent applications in energy problems, such as the stochastic bilevel optimization approaches used in the natural gas industry. New algorithms for solving linear and mixed-integer bilevel programming problems are presented and explained.

In Theorie, Beispiel und Übung werden Aufgaben der linearen, diskreten und kontinuierlichen Optimierung vorgestellt. Darüber hinaus wird der Leser in verständlicher und anschaulicher Form in die Themengebiete Optimierung über Graphen und Netzwerke, Transportoptimierung und Logistik sowie Spieltheorie eingeführt.