Outer approximation for global optimization of mixed-integer quadratic bilevel problems

Abstract Bilevel optimization problems have received a lot of attention in the last years and decades. Besides numerous theoretical developments there also evolved novel solution algorithms for mixed-integer linear bilevel most recent use branch-and-cut techniques from programming that are especially tailored context. In this paper, we consider MIQP-QP problems, i.e., models with convex-quadratic upper level continuous lower level. This setting allows strong-duality-based transformation which yields, general, an equivalent nonconvex single-level reformulation original problem. Under reasonable assumptions, can derive both multi- single-tree outer-approximation-based cutting-plane algorithm. We show finite termination correctness methods present extensive numerical results illustrate applicability approaches. It turns out proposed capable solving instances several thousand variables constraints significantly outperform classical