Special issue on bilevel optimization

Luce Brotcorne, Bernard Fortz, Martine Labbé
2020 EURO Journal on Computational Optimization  
Bilevel programming is a fairly recent branch of optimization that deals with programs whose constraints embed an auxiliary optimization problem. Bilevel programs are pervasive and are commonly found in a number of real-world problems. This includes problems in the domains of transportation, energy, economics, decision science, environmental economics, security, etc. Bilevel programming problems, being generically difficult to solve due to their nonconvexity and non-differentiability, it is not
more » ... surprising that a large body of research to date has focused on problems having nice properties such as linear, quadratic or convex objective and/or constraint functions. Despite their apparent simplicity, these bilevel problems have been proved to be strongly NP-hard and even checking strict and local optimality is also NP-hard. The research in bilevel programming can be classified into two parts: the design of algorithmic approaches to solve specific types of bilevel problems (e.g. linear or convex) and the definition of necessary and/or sufficient conditions of existence of equilibrium for more general bilevel programs. In the last decade, one has observed a growing interest in bilevel programming, mainly due to its adequacy to model real situations involving competing agents. Motivated by this intense development of the research domain, the first International Workshop on Bilevel Programming (IWOBIP) was organised in Monterrey, Mexico, in 2016. This workshop demonstrated the interest in gathering researchers from different optimization fields, game theory, and computer science but all presenting a central focus on bilevel optimization problems. As a consequence, the second edition of IWOBIP was organised in Lille, France, from 18 to 22 June 2018.
doi:10.1007/s13675-020-00122-z fatcat:q4jirplzrrcg7ee3tdufzjxdme