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. Our computational 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.

翻译：我们研究的是一类双级整形程序,在上层有二级锥形限制,在下层有二次二次二次二次二次曲线目标和线性限制。我们使用二级二次线性断裂程序对双级不可行的点进行分离削减。据我们所知,这是第一次在离散双级优化背景下研究分离性削减。我们利用这些脱节削减,为我们研究的问题类建立了分流和切换算法,为问题变异设置了一个只有二进制变量的切换平面法。我们的计算研究显示,我们两种方法都超越了能够解决我们测试实例线性版本的混合内分流双级双级线性程序的最先进的通用求解器,在这种模式下,非线性线性数据以麦考利克模式线性化。