Stochastic Cutting Planes for Data-Driven Optimization

• Main Authors: Bertsimas, Dimitris (Author), Li, Michael Lingzhi (Author)
• Format: Article
• Language: English
• Published: Institute for Operations Research and the Management Sciences (INFORMS), 2022-07-28T14:58:15Z.
• Subjects: Article
• Online Access: Get fulltext

 <jats:p> 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. </jats:p>