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Pré-publication, Document de travail

Generalized adaptive partition-based method for two-stage stochastic linear programs : convergence and generalization

Maël Forcier 1, 2 Vincent Leclère 1 
2 TROPICAL - TROPICAL
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : Adaptive Partition-based Methods (APM) are numerical methods to solve two-stage stochastic linear problems (2SLP). The core idea is to iteratively construct an adapted partition of the space of alea in order to aggregate scenarios while conserving the true value of the cost-to-go for the current first-stage control. Relying on the normal fan of the dual admissible set, we extend the classical and generalized APM method by i) extending the method to almost arbitrary 2SLP, ii) giving a necessary and sufficient condition for a partition to be adapted even for non-finite distribution, and iii) proving the convergence of the method. We give some additional insights by linking APM to the L-shaped algorithm.
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Pré-publication, Document de travail
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https://hal-enpc.archives-ouvertes.fr/hal-03542218
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Soumis le : mardi 25 janvier 2022 - 11:15:04
Dernière modification le : jeudi 12 mai 2022 - 10:37:25

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  • HAL Id : hal-03542218, version 1
  • ARXIV : 2109.04818

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Maël Forcier, Vincent Leclère. Generalized adaptive partition-based method for two-stage stochastic linear programs : convergence and generalization. 2022. ⟨hal-03542218⟩

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