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|a Bertsimas, Dimitris
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|a Li, Michael Lingzhi
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|a Stochastic Cutting Planes for Data-Driven Optimization
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|b Institute for Operations Research and the Management Sciences (INFORMS),
|c 2022-07-28T14:58:15Z.
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|z Get fulltext
|u https://hdl.handle.net/1721.1/144110
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|a <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>
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|a Article
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|t 10.1287/ijoc.2022.1205
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|t INFORMS Journal on Computing
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