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arXiv · 2111.06824

SOCP-based disjunctive cuts for a class of integer nonlinear bilevel programs

Elisabeth Gaar·Jon Lee·Ivana Ljubić·Markus Sinnl·Kübra Tanınmış
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Abstract

We study a class of bilevel integer programs with second-order cone constraints at the upper level and a convex quadratic objective and linear constraints at the lower level. We develop disjunctive cuts to separate bilevel infeasible points using a second-order-cone-based cut-generating procedure. To the best of our knowledge, this is the first time disjunctive cuts are studied in the context of discrete bilevel optimization. Using these disjunctive cuts, we establish a branch-and-cut algorithm for the problem class we study, and a cutting plane method for the problem variant with only binary variables. We present a preliminary computational study on instances with no second-order cone constraints at the upper level and a single linear constraint at the lower level. Our study demonstrates that both our approaches outperform a state-of-the-art generic solver for mixed-integer bilevel linear programs that is able to solve a linearized version of our test instances, where the non-linearities are linearized in a McCormick fashion.

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Elisabeth Gaar, Jon Lee, Ivana Ljubić, Markus Sinnl, Kübra Tanınmış. 2021-11-12. SOCP-based disjunctive cuts for a class of integer nonlinear bilevel programs. https://doi.org/10.1007/978-3-031-06901-7_20

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