Paper Info
Title
On conditional cuts for stochastic dual dynamic programming
Abstract
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.
Year
DOI
Venue
2020
10.1007/s13675-020-00123-y
EURO Journal on Computational Optimization
Keywords
DocType
Volume
Stochastic programming, SDDP algorithm, Nonsmooth optimization, Conditional expectations, 90C15, 65C35
Journal
8
Issue
ISSN
Citations 
2
2192-4406
1
PageRank 
References 
Authors
0.37
0
2
Name
Order
Citations
PageRank
Wim Van-Ackooij110.37
Xavier Warin210.37