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Thomas Kleinert (thomas.kleinertfau.de) Abstract: Bilevel 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 realworld 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 stateoftheart solution approaches for bilevel optimization make use of techniques that originate from mixedinteger programming. These techniques include branchandbound methods, cutting planes and, thus, branchandcut approaches, or problemspecific decomposition methods. In this survey article, we review bileveltailored approaches that exploit these mixedinteger programming techniques to solve bilevel optimization problems. To this end, we first consider bilevel problems with convex or, in particular, linear lowerlevel 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 mixedinteger bilevel problems that contain integrality constraints in the lower level. Moreover, we also briefly discuss the area of mixedinteger 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. Keywords: Bilevel optimization, Mixedinteger programming, Applications, Branchandbound, Branchandcut, Survey Category 1: Integer Programming ((Mixed) Integer Linear Programming ) Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming ) Citation: Download: [PDF] Entry Submitted: 01/01/2021 Modify/Update this entry  
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