SOCP-based disjunctive cuts for a class of integer nonlinear bilevel programs
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.
Cite
@article{arxiv.2111.06824,
title = {SOCP-based disjunctive cuts for a class of integer nonlinear bilevel programs},
author = {Elisabeth Gaar and Jon Lee and Ivana Ljubić and Markus Sinnl and Kübra Tanınmış},
journal= {arXiv preprint arXiv:2111.06824},
year = {2022}
}