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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Vydané v:	Operations research letters Ročník 50; číslo 5; s. 452 - 457
Hlavní autori:	Forcier, Maël, Leclère, Vincent
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier B.V 01.09.2022
Predmet:	Adaptive partition methods Exact method Stochastic linear programming Stochastic linear programming Adaptive partition methods Exact method
ISSN:	0167-6377, 1872-7468
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Popis
Shrnutí:	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