Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/330750 
Year of Publication: 
2025
Citation: 
[Journal:] Journal of Global Optimization [ISSN:] 1573-2916 [Volume:] 93 [Issue:] 1 [Publisher:] Springer US [Place:] New York, NY [Year:] 2025 [Pages:] 1-25
Publisher: 
Springer US, New York, NY
Abstract: 
We study bilevel problems with a convex quadratic mixed-integer upper-level, integer linking variables, and a nonconvex quadratic, purely continuous lower-level problem. We prove Σ2p-hardness of this class of problems, derive an iterative lower- and upper-bounding scheme, and show its finiteness and correctness in the sense that it computes globally optimal points or proves infeasibility of the instance. To this end, we make use of the Karush–Kuhn–Tucker conditions of the lower-level problem for the lower-bounding step, since these conditions are only necessary but not sufficient in our setting. Moreover, integer no-good cuts as well as a simple optimality cut are used to obtain finiteness of the method. Finally, we illustrate the applicability of our approach by the first large-scale numerical experiment for this class of problems in the literature.
Subjects: 
Bilevel optimization
Nonconvex lower levels
Mixed-integer optimization
Complexity
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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