Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/309937 
Year of Publication: 
2022
Citation: 
[Journal:] Journal of Global Optimization [ISSN:] 1573-2916 [Volume:] 84 [Issue:] 3 [Publisher:] Springer US [Place:] New York, NY [Year:] 2022 [Pages:] 607-650
Publisher: 
Springer US, New York, NY
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.
Subjects: 
Bilevel optimization
Mixed-integer nonlinear programming
Strong duality
Projection
Global optimization
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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