Stochastic Cutting Planes for Data-Driven Optimization
针对数据驱动的混合整数非线性优化问题，提出随机割平面法，在弱假设下能以高概率收敛到ϵ最优解，数值实验显示相比标准方法有多个数量级的加速。
We introduce a stochastic version of the cutting plane method for a large class of data-driven mixed-integer nonlinear optimization (MINLO) problems. We show that under very weak assumptions, the stochastic algorithm can converge to an ϵ-optimal solution with high probability. Numerical experiments on several problems show that stochastic cutting planes is able to deliver a multiple order-of-magnitude speedup compared with the standard cutting plane method. We further experimentally explore the lower limits of sampling for stochastic cutting planes and show that, for many problems, a sampling size of [Formula: see text] appears to be sufficient for high-quality solutions.