An exact projection-based algorithm for bilevel mixed-integer problems with nonlinearities

Maximilian Merkert (), Galina Orlinskaya () and Dieter Weninger ()
Additional contact information
Maximilian Merkert: Otto von Guericke University Magdeburg
Galina Orlinskaya: Friedrich-Alexander University Erlangen-Nürnberg
Dieter Weninger: Friedrich-Alexander University Erlangen-Nürnberg

Journal of Global Optimization, 2022, vol. 84, issue 3, No 4, 607-650

Abstract: Abstract We propose an exact global solution method for bilevel mixed-integer optimization problems with lower-level integer variables and including nonlinear terms such as, e.g., products of upper-level and lower-level variables. Problems of this type are extremely challenging as a single-level reformulation suitable for off-the-shelf solvers is not available in general. In order to solve these problems to global optimality, we enhance an approximative projection-based algorithm for mixed-integer linear bilevel programming problems from the literature to become exact under one additional assumption. This assumption still allows for discrete and continuous leader and follower variables on both levels, but forbids continuous upper-level variables to appear in lower-level constraints and thus ensures that a bilevel optimum is attained. In addition, we extend our exact algorithm to make it applicable to a wider problem class. This setting allows nonlinear constraints and objective functions on both levels under certain assumptions, but still requires that the lower-level problem is convex in its continuous variables. We also discuss computational experiments on modified library instances.

Keywords: Bilevel optimization; Mixed-integer nonlinear programming; Strong duality; Projection; Global optimization; 90C11; 90C26; 90C46; 91A65 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10898-022-01172-w Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:jglopt:v:84:y:2022:i:3:d:10.1007_s10898-022-01172-w

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-022-01172-w

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().