On conditional cuts for stochastic dual dynamic programming

Multistage stochastic programs arise in many applications from engineering whenever a set of inventories or stocks has to be valued. Such is the case in seasonal storage valuation of a set of cascaded reservoir chains in hydro management. A popular method is stochastic dual dynamic programming (SDDP...

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Autores principales:	W. van Ackooij, X. Warin
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2020
Materias:	90C15 65C35 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/c48db89d44434951b699b68edbd0446e
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spelling	oai:doaj.org-article:c48db89d44434951b699b68edbd0446e2021-12-02T05:01:15ZOn conditional cuts for stochastic dual dynamic programming2192-440610.1007/s13675-020-00123-yhttps://doaj.org/article/c48db89d44434951b699b68edbd0446e2020-06-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S219244062100126Xhttps://doaj.org/toc/2192-4406Multistage stochastic programs arise in many applications from engineering whenever a set of inventories or stocks has to be valued. Such is the case in seasonal storage valuation of a set of cascaded reservoir chains in hydro management. A popular method is stochastic dual dynamic programming (SDDP), especially when the dimensionality of the problem is large and dynamic programming is no longer an option. The usual assumption of SDDP is that uncertainty is stage-wise independent, which is highly restrictive from a practical viewpoint. When possible, the usual remedy is to increase the state-space to account for some degree of dependency. In applications, this may not be possible or it may increase the state-space by too much. In this paper, we present an alternative based on keeping a functional dependency in the SDDP—cuts related to the conditional expectations in the dynamic programming equations. Our method is based on popular methodology in mathematical finance, where it has progressively replaced scenario trees due to superior numerical performance. We demonstrate the interest of combining this way of handling dependency in uncertainty and SDDP on a set of numerical examples. Our method is readily available in the open-source software package StOpt.W. van AckooijX. WarinElsevierarticle90C1565C35Applied mathematics. Quantitative methodsT57-57.97Electronic computers. Computer scienceQA75.5-76.95ENEURO Journal on Computational Optimization, Vol 8, Iss 2, Pp 173-199 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	90C15 65C35 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
spellingShingle	90C15 65C35 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95 W. van Ackooij X. Warin On conditional cuts for stochastic dual dynamic programming
description	Multistage stochastic programs arise in many applications from engineering whenever a set of inventories or stocks has to be valued. Such is the case in seasonal storage valuation of a set of cascaded reservoir chains in hydro management. A popular method is stochastic dual dynamic programming (SDDP), especially when the dimensionality of the problem is large and dynamic programming is no longer an option. The usual assumption of SDDP is that uncertainty is stage-wise independent, which is highly restrictive from a practical viewpoint. When possible, the usual remedy is to increase the state-space to account for some degree of dependency. In applications, this may not be possible or it may increase the state-space by too much. In this paper, we present an alternative based on keeping a functional dependency in the SDDP—cuts related to the conditional expectations in the dynamic programming equations. Our method is based on popular methodology in mathematical finance, where it has progressively replaced scenario trees due to superior numerical performance. We demonstrate the interest of combining this way of handling dependency in uncertainty and SDDP on a set of numerical examples. Our method is readily available in the open-source software package StOpt.
format	article
author	W. van Ackooij X. Warin
author_facet	W. van Ackooij X. Warin
author_sort	W. van Ackooij
title	On conditional cuts for stochastic dual dynamic programming
title_short	On conditional cuts for stochastic dual dynamic programming
title_full	On conditional cuts for stochastic dual dynamic programming
title_fullStr	On conditional cuts for stochastic dual dynamic programming
title_full_unstemmed	On conditional cuts for stochastic dual dynamic programming
title_sort	on conditional cuts for stochastic dual dynamic programming
publisher	Elsevier
publishDate	2020
url	https://doaj.org/article/c48db89d44434951b699b68edbd0446e
work_keys_str_mv	AT wvanackooij onconditionalcutsforstochasticdualdynamicprogramming AT xwarin onconditionalcutsforstochasticdualdynamicprogramming
_version_	1718400852359643136

On conditional cuts for stochastic dual dynamic programming

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