Exact quantization of multistage stochastic linear problems
Published in SIAM journal on Optimization, 2023
Recommended citation: https://leclere.github.io/files/papers/2023-Exact-Quantization.pdf
Best student paper at ECSO-CMS 2022.
We show that the multistage linear problem (MSLP) with an arbitrary cost distribution is equivalent to a MSLP on a finite scenario tree. We establish this exact quantization result by analyzing the polyhedral structure of MSLPs. In particular, we show that the expected cost-to-go functions are polyhedral and affine on the cells of a chamber complex, which is independent of the cost distribution. This leads to new complexity results, showing that MSLP is fixed-parameter tractable.