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Mathematical Problems in Engineering
Volume 2015, Article ID 310301, 16 pages
Review Article

Bilevel Programming and Applications

1Departamento de Ingeniería Industrial y de Sistemas, Tecnológico de Monterrey, Avenida Eugenio Garza Sada 2501 Sur, 64849 Monterrey, NL, Mexico
2Department of Social Modeling, Central Economics and Mathematics Institute (CEMI) of the Russian Academy of Sciences (RAS), Nakhimovsky Prospekt 17, Moscow 117418, Russia
3Department of Electronics and Computing, Sumy State University, Rimsky-Korsakov Street 2, Sumy 40007, Ukraine
4Institut für Numerische Mathematik und Optimierung, Fakultät für Mathematik und Informatik, TU Bergakademie Freiberg, Akademiestraße 6, 09596 Freiberg, Germany
5SINTEF, Box 4760, Sluppen, 7465 Trondheim, Norway
6Facultad de Ciencias Físico-Matemáticas (FCFM), Universidad Autónoma de Nuevo León (UANL), Avenida Universidad S/N, 66450 San Nicolás de los Garza, NL, Mexico

Received 25 June 2014; Accepted 23 July 2014

Academic Editor: Sergii V. Kavun

Copyright © 2015 Vyacheslav V. Kalashnikov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A great amount of new applied problems in the area of energy networks has recently arisen that can be efficiently solved only as mixed-integer bilevel programs. Among them are the natural gas cash-out problem, the deregulated electricity market equilibrium problem, biofuel problems, a problem of designing coupled energy carrier networks, and so forth, if we mention only part of such applications. Bilevel models to describe migration processes are also in the list of the most popular new themes of bilevel programming, as well as allocation, information protection, and cybersecurity problems. This survey provides a comprehensive review of some of the above-mentioned new areas including both theoretical and applied results.