Stochastic Cutting Planes for Data-Driven Optimization
<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. Numeric...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Institute for Operations Research and the Management Sciences (INFORMS),
2022-07-28T14:58:15Z.
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| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | <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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