Stochastic Cutting Planes for Data-Driven Optimization
This provides faster optimization for data-driven MINLO problems, though it appears incremental as an adaptation of existing cutting-plane methods.
The authors tackled data-driven Mixed-Integer Nonlinear Optimization problems by introducing a stochastic cutting-plane method, achieving multiple order-of-magnitude speedups compared to the standard method and showing that a sampling size of O(∛n) suffices for high-quality solutions.
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 is able to 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 to 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 $O(\sqrt[3]{n})$ appears to be sufficient for high quality solutions.