A Penalty Branch-and-Bound Method for Mixed-Integer Quadratic Bilevel Problems. Part I: Key Ideas and a Fixed Parameter Setting

Andreas Horländer () and Martin Schmidt ()
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Andreas Horländer: Trier University
Martin Schmidt: Trier University

Chapter Chapter 17 in Operations Research Proceedings 2022, 2023, pp 139-145 from Springer

Abstract: Abstract We propose an algorithm for solving bilevel problems with mixed-integer convex-quadratic upper level as well as convex-quadratic and continuous lower level. The method is based on a classic branch-and-bound procedure, where branching is performed on the integer constraints and on the complementarity constraints resulting from the Karush–Kuhn–Tucker reformulation of the lower-level problem. However, instead of branching on constraints as usual, suitably chosen penalty terms are added to the objective function to create new subproblems in the tree. In this first part, we consider a fixed penalty parameter, derive the main ideas, and prove the correctness of the method for this setting.

Keywords: Bilevel optimization; Branch-and-bound; Penalty methods; Mixed-integer optimization (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/978-3-031-24907-5_17

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