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arXiv · 2207.05014

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

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

We study a class of integer bilevel programs with second-order cone constraints at the upper-level and a convex-quadratic objective function and linear constraints at the lower-level. We develop disjunctive cuts (DCs) to separate bilevel-infeasible solutions using a second-order-cone-based cut-generating procedure. We propose DC separation strategies and consider several approaches for removing redundant disjunctions and normalization. Using these DCs, we propose 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 an extensive computational study on a diverse set of instances, including instances with binary and with integer variables, and instances with a single and with multiple linking constraints. Our computational study demonstrates that the proposed enhancements of our solution approaches are effective for improving the performance. Moreover, both of 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 binary instances.

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Elisabeth Gaar, Jon Lee, Ivana Ljubić, Markus Sinnl, Kübra Tanınmış. 2022-07-11. On SOCP-based disjunctive cuts for solving a class of integer bilevel nonlinear programs. https://doi.org/10.1007/s10107-023-01965-1

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