https://hal.inria.fr/hal-03095139Kleinert, ThomasThomasKleinertFAU - Friedrich-Alexander Universität Erlangen-NürnbergLabbé, MartineMartineLabbéINOCS - Integrated Optimization with Complex Structure - Inria Lille - Nord Europe - Inria - Institut National de Recherche en Informatique et en Automatique - ULB - Université libre de Bruxelles - CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 - Centrale Lille - Université de Lille - CNRS - Centre National de la Recherche ScientifiqueLjubić, IvanaIvanaLjubićEssec Business SchoolSchmidt, MartinMartinSchmidtTrier UniversityA Survey on Mixed-Integer Programming Techniques in Bilevel OptimizationHAL CCSD2021[INFO.INFO-RO] Computer Science [cs]/Operations Research [cs.RO]Labbé, Martine2021-01-04 15:26:132023-03-24 14:53:202021-01-04 15:50:11enJournal articlesapplication/pdf1Bilevel optimization is a field of mathematical programming in which some variables are constrained to be the solution of another optimization problem. As a consequence, bilevel optimization is able to model hierarchical decision processes. This is appealing for modeling real-world problems, but it also makes the resulting optimization models hard to solve in theory and practice. The scientific interest in computational bilevel optimization increased a lot over the last decade and is still growing. Independent of whether the bilevel problem itself contains integer variables or not, many state-of-the-art solution approaches for bilevel optimization make use of techniques that originate from mixed-integer programming. These techniques include branch-and-bound methods, cutting planes and, thus, branch-and-cut approaches, or problemspecific decomposition methods. In this survey article, we review bilevel-tailored approaches that exploit these mixed-integer programming techniques to solve bilevel optimization problems. To this end, we first consider bilevel problems with convex or, in particular, linear lower-level problems. The discussed solution methods in this field stem from original works from the 1980's but, on the other hand, are still actively researched today. Second, we review modern algorithmic approaches to solve mixed-integer bilevel problems that contain integrality constraints in the lower level. Moreover, we also briefly discuss the area of mixed-integer nonlinear bilevel problems. Third, we devote some attention to more specific fields such as pricing or interdiction models that genuinely contain bilinear and thus nonconvex aspects. Finally, we sketch a list of open questions from the areas of algorithmic and computational bilevel optimization, which may lead to interesting future research that will further propel this fascinating and active field of research.