On Linear Bilevel Optimization Problems with Complementarity-Constrained Lower Levels

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  • We consider a novel class of linear bilevel optimization models with a lower level that is a linear program with complementarity constraints (LPCC). We present different single-level reformulations depending on whether the linear complementarity problem (LCP) as part of the lower-level constraint set depends on the upper-level decisions or not as well as on whether the LCP matrix is positive definite or positive semidefinite. Moreover, we illustrate the connection to linear trilevel models that can be reduced to bilevel problems with LPCC lower levels having positive (semi)definite matrices. Finally, we provide two generic and illustrative bilevel models from the fields of transportation and energy to show the practical relevance of the newly introduced class of bilevel problems and show related theoretical results.

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Author:Steven A. Gabriel, Marina Leal, Martin Schmidt
Document Type:Preprint
Date of Publication (online):2020/10/21
Release Date:2020/10/21
Tag:Bilevel optimization; Linear complementarity problems; Linear programs with complementarity constraints; Reformulations; Spatial price equilibria
Page Number:16
Institutes:Universit├Ąt Trier
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International