On linear bilevel optimization problems with complementarity-constrained lower levels

Steven A. Gabriel, Marina Leal and Martin Schmidt

Journal of the Operational Research Society, 2022, vol. 73, issue 12, 2706-2716

Abstract: 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.

Date: 2022
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://hdl.handle.net/10.1080/01605682.2021.2015254 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:tjorxx:v:73:y:2022:i:12:p:2706-2716

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/tjor20

DOI: 10.1080/01605682.2021.2015254

Access Statistics for this article

Journal of the Operational Research Society is currently edited by Tom Archibald

More articles in Journal of the Operational Research Society from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().