Generalized adaptive partition-based method for two-stage stochastic linear programs: Geometric oracle and analysis

Adaptive Partition-based Methods (APM) are numerical methods that solve, in particular, two-stage stochastic linear problems (2SLP). We say that a partition of the uncertainty space is adapted to the current first stage control xˇ if we can aggregate scenarios while conserving the true value of the...

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Bibliographic Details
Published in:Operations research letters Vol. 50; no. 5; pp. 452 - 457
Main Authors: Forcier, Maël, Leclère, Vincent
Format: Journal Article
Language:English
Published: Elsevier B.V 01.09.2022
Subjects:
Adaptive partition methods
Exact method
Stochastic linear programming
Stochastic linear programming
Adaptive partition methods
Exact method
ISSN:0167-6377, 1872-7468
Online Access:Get full text
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Summary:Adaptive Partition-based Methods (APM) are numerical methods that solve, in particular, two-stage stochastic linear problems (2SLP). We say that a partition of the uncertainty space is adapted to the current first stage control xˇ if we can aggregate scenarios while conserving the true value of the expected recourse cost at xˇ. The core idea of APM is to iteratively construct an adapted partition to all past tentative first stage controls. Relying on the normal fan of the dual admissible set, we give a necessary and sufficient condition for a partition to be adapted even for non-finite distribution, and provide a geometric method to obtain an adapted partition. Further, by showing the connection between APM and the L-shaped algorithm, we prove convergence and complexity bounds of the APM methods. The paper presents the fixed recourse case and ends with elements to forgo this assumption.
ISSN:0167-6377
1872-7468
DOI:10.1016/j.orl.2022.06.004