Geodesic
Non-parametric approximation of non-anticipativity constraints in scenario-based multistage stochastic programming
Kybernetika, Tome 44 (2008) no. 2, pp. 171-184 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We propose two methods to solve multistage stochastic programs when only a (large) finite set of scenarios is available. The usual scenario tree construction to represent non-anticipativity constraints is replaced by alternative discretization schemes coming from non-parametric estimation ideas. In the first method, a penalty term is added to the objective so as to enforce the closeness between decision variables and the Nadaraya–Watson estimation of their conditional expectation. A numerical application of this approach on an hydro-power plant management problem is developed. The second method exploits the interpretation of kernel estimators as a sum of basis functions.
We propose two methods to solve multistage stochastic programs when only a (large) finite set of scenarios is available. The usual scenario tree construction to represent non-anticipativity constraints is replaced by alternative discretization schemes coming from non-parametric estimation ideas. In the first method, a penalty term is added to the objective so as to enforce the closeness between decision variables and the Nadaraya–Watson estimation of their conditional expectation. A numerical application of this approach on an hydro-power plant management problem is developed. The second method exploits the interpretation of kernel estimators as a sum of basis functions.
Classification : 49M25, 60F25, 62G07, 90C15, 90C59, 90C90
Keywords: multistage stochastic programming; scenarios; discrete approximation 
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Roy, Jean-Sébastien; Lenoir, Arnaud. Non-parametric approximation of non-anticipativity constraints in scenario-based multistage stochastic programming. Kybernetika, Tome 44 (2008) no. 2, pp. 171-184. http://geodesic.mathdoc.fr/item/KYB_2008_44_2_a3/

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