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Exact quantization of multistage stochastic linear problems

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Maël Forcier, Stéphane Gaubert, Vincent Leclère

Optimization and Control · Submitted 20 Jul 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that the multistage linear problem (MSLP) with an arbitrary cost distribution is equivalent to a MSLP on a finite scenario tree.

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arXiv ID2107.09566 (version 1)
Pith IDQKYYCXDV, Pith's permanent record of this paper and its review
CitationMa\"el Forcier, St\'ephane Gaubert, Vincent Lecl\`ere. "Exact quantization of multistage stochastic linear problems." arXiv:2107.09566 (2021). https://pith.science/paper/QKYYCXDV
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,545 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.07 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We show that the multistage linear problem (MSLP) with an arbitrary cost distribution is equivalent to a MSLP on a finite scenario tree. result 0.95 0.93 0.88 asserted 1.00
s1 We establish this exact quantization result by analyzing the polyhedral structure of MSLPs. method 0.97 0.93 0.08 asserted 1.00
s2 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. result 0.85 0.93 0.11 asserted 1.00
s3 This leads to new complexity results, showing that MSLP is fixed-parameter tractable. result 0.81 0.92 0.19 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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