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On Linear Bilevel Optimization Problems with Complementarity-Constrained Lower Levels

Steven A. Gabriel(sgabriel***at***umd.edu)
Marina Leal(m.leal***at***umh.es)
Martin Schmidt(martin.schmidt***at***uni-trier.de)

Abstract: We consider a novel class of linear bilevel optimization models with a lower level that is a linear optimization problem 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 seen as a special case of the considered class of bilevel problems under some additional assumptions. 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.

Keywords: Bilevel optimization, Linear programs with complementarity constraints, Linear complementarity problems, Reformulations, Spatial price equilibria, Oligopoly models in energy

Category 1: Complementarity and Variational Inequalities

Category 2: Applications -- OR and Management Sciences

Citation:

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Entry Submitted: 10/21/2020
Entry Accepted: 10/21/2020
Entry Last Modified: 10/21/2020

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