We consider minimization problems with bisubmodular objective functions. We propose valid inequalities, namely the poly-bimatroid inequalities, and provide a complete linear description of the convex hull of the epigraph of a bisubmodular function. Furthermore, we develop a cutting plane algorithm for constrained bisubmodular minimization based on the poly-bimatroid inequalities. Our computational experiments on the minimization subproblem in robust coupled sensor placement show that our algorithm can solve highly non-linear problems that do not admit compact mixed-integer linear formulations.

中文翻译：

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双次模函数最小化的多面体方法

我们考虑双次模目标函数的最小化问题。我们提出了有效的不等式，即多双拟阵不等式，并提供了一个双次模函数的题词凸包的完整线性描述。此外，我们开发了一种基于多双拟阵不等式的用于约束双次模最小化的切割平面算法。我们对鲁棒耦合传感器放置中的最小化子问题的计算实验表明，我们的算法可以解决不允许紧凑混合整数线性公式的高度非线性问题。