Exact quantization of multistage stochastic linear problems
Optimization and Control
2021-07-21 v1
Abstract
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.
Cite
@article{arxiv.2107.09566,
title = {Exact quantization of multistage stochastic linear problems},
author = {Maël Forcier and Stéphane Gaubert and Vincent Leclère},
journal= {arXiv preprint arXiv:2107.09566},
year = {2021}
}