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Journal Articles SIAM Journal on Optimization Year : 2024

Exact quantization of multistage stochastic linear problems

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.

Dates and versions

hal-03504876 , version 1 (30-12-2021)

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Maël Forcier, Stéphane Gaubert, Vincent Leclère. Exact quantization of multistage stochastic linear problems. SIAM Journal on Optimization, 2024, 34 (1), pp.533-562. ⟨10.1137/22M1508005⟩. ⟨hal-03504876⟩
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