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

Review Article

Departamento de Ingeniería Industrial y de Sistemas, Tecnológico de Monterrey, Avenida Eugenio Garza Sada 2501 Sur, 64849 Monterrey, NL, Mexico

Department of Social Modeling, Central Economics and Mathematics Institute CEMI of the Russian Academy of Sciences RAS, Nakhimovsky Prospekt 17, Moscow 117418, Russia

Department of Electronics and Computing, Sumy State University, Rimsky-Korsakov Street 2, Sumy 40007, Ukraine

Institut für Numerische Mathematik und Optimierung, Fakultät für Mathematik und Informatik, TU Bergakademie Freiberg, Akademiestraße 6, 09596 Freiberg, Germany

SINTEF, Box 4760, Sluppen, 7465 Trondheim, Norway

Facultad 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.

Author: Vyacheslav V. Kalashnikov, Stephan Dempe, Gerardo A. Pérez-Valdés, Nataliya I. Kalashnykova, and José-Fernando Camacho-Vall



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