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Stochastic Cutting Planes for Data-Driven Optimization

Author

Listed:
  • Dimitris Bertsimas

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142)

  • Michael Lingzhi Li

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

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 O ( n 3 ) appears to be sufficient for high-quality solutions.

Suggested Citation

  • Dimitris Bertsimas & Michael Lingzhi Li, 2022. "Stochastic Cutting Planes for Data-Driven Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2400-2409, September.
    • Handle: RePEc:inm:orijoc:v:34:y:2022:i:5:p:2400-2409
    DOI: 10.1287/ijoc.2022.1205
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    References listed on IDEAS

    as
    1. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 655-679.
    2. Rivers, Douglas & Vuong, Quang H., 1988. "Limited information estimators and exogeneity tests for simultaneous probit models," Journal of Econometrics, Elsevier, vol. 39(3), pages 347-366, November.
    3. Robert Bixby & Edward Rothberg, 2007. "Progress in computational mixed integer programming—A look back from the other side of the tipping point," Annals of Operations Research, Springer, vol. 149(1), pages 37-41, February.
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