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.

Autorentext

Stephan Dempe studied mathematics at the Technische Hochschule Karl-Marx-Stadt and got a PhD from the same university. Today he is professor for mathematical optimization at the TU Bergakademie Freiberg, Germany. Focus of his work is on parametric and nonconvex optimization.

Vyacheslav Kalashnikov studied mathematics at Novosibirsk State University, he got his PhD in Operations Research from the Siberian Division of the Academy of Sciences of the USSR and his Dr.Sc. (Habilitation degree) from the Central Economics and Mathematics Institute (CEMI), Moscow, Russia. Today he is Professor at Tecnológico de Monterrey, Mexico, at the CEMI, and at Sumy State University, Ukraine. The main areas of his work are bilevel programming, hierarchical games and their applications in engineering and economics.

Gerardo Alfredo Perez Valdes studied mathematics at the Universidad Autónoma de Nuevo León and got his PhDs in Engineering from Tecnológico de Monterrey, Mexico, and from Texas Tech University, Lubbock, USA. Today he is Professor at University of Science and Technology in Trondheim (NTNU), Norway. The focus of his work is on solution algorithms in mathematical optimization.

Nataliya Kalashnykova studied mathematics at Novosibirsk State University and got her PhD in Operations Research from the Siberian Division of the Academy of Sciences of the USSR. Today she is Professor at the Universidad Autónoma de Nuevo León, Mexico, and at Sumy State University, Ukraine. Her expertise lies in stochastic optimal control and mathematical models of optimization.

Inhalt
Introduction.- Linear Bilevel Optimization Problem.- Reduction of Bilevel Programming to a Single Level Problem.- Convex Bilevel Programs.- Mixed-Integer Bilevel Programming Problems.- Applications to Natural Gas Cash-Out Problem.- Applications to Other Energy Systems.- Reduction of the Dimension of the Upper Level Problem in a Bilevel Optimization Model.