Geodesic
Non-parametric approximation of non-anticipativity constraints in scenario-based multistage stochastic programming
Kybernetika, Tome 44 (2008) no. 2, pp. 171-184.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{KYB_2008__44_2_a3,
     author = {Roy, Jean-S\'ebastien and Lenoir, Arnaud},
     title = {Non-parametric approximation of non-anticipativity constraints in scenario-based multistage stochastic programming},
     journal = {Kybernetika},
     pages = {171--184},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {2008},
     mrnumber = {2428218},
     zbl = {1154.90560},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2008__44_2_a3/}
}
TY  - JOUR
AU  - Roy, Jean-Sébastien
AU  - Lenoir, Arnaud
TI  - Non-parametric approximation of non-anticipativity constraints in scenario-based multistage stochastic programming
JO  - Kybernetika
PY  - 2008
SP  - 171
EP  - 184
VL  - 44
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KYB_2008__44_2_a3/
LA  - en
ID  - KYB_2008__44_2_a3
ER  - 
%0 Journal Article
%A Roy, Jean-Sébastien
%A Lenoir, Arnaud
%T Non-parametric approximation of non-anticipativity constraints in scenario-based multistage stochastic programming
%J Kybernetika
%D 2008
%P 171-184
%V 44
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2008__44_2_a3/
%G en
%F KYB_2008__44_2_a3
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/