Stochastic Cutting Planes for Data-Driven Optimization
Name
2021-Stochastic Cutting Planes.pdf
Description
Accepted version
Size
447.28 KB
Format
Adobe PDF
Checksum (MD5)
584df0d26c0a2b1c2366750c89516efc
Author(s)
Bertsimas, Dimitris
Li, Michael Lingzhi
Date Issued
June 6, 2022
Journal
INFORMS Journal on Computing
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Bertsimas, Dimitris and Li, Michael Lingzhi. 2022. "Stochastic Cutting Planes for Data-Driven Optimization." INFORMS Journal on Computing.
Version
Author's final manuscript
Abstract
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.
MIT Department
Sloan School of Management
Massachusetts Institute of Technology. Operations Research Center
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1287/ijoc.2022.1205
