Approximations of Stochastic Optimization Problems Subject to Measurability Constraints

Abstract : Motivated by the numerical resolution of stochastic optimization problems subject to measurability constraints, we focus upon the issue of discretization. There exist indeed two components to be discretized for such problems, namely, the random variable modelling uncertainties (noise) and the $\sigma$-field modelling the knowledge (information) according to which decisions are taken. There is no reason to bind these two discretizations, which are a priori unrelated. In this setting, we present conditions under which the discretized problems converge to the original one. The focus is put on the convergence notions ensuring the quality of the approximation; we illustrate their importance by means of a counterexample based on the Monte Carlo approximation. Copyright © 2009 Society for Industrial and Applied Mathematics
Type de document :
Article dans une revue
SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2009, 19 (4), pp.1719-1734. <10.1137/070692376>
Liste complète des métadonnées

https://hal-ensta.archives-ouvertes.fr/hal-00975464
Contributeur : Aurélien Arnoux <>
Soumis le : mardi 8 avril 2014 - 16:36:24
Dernière modification le : jeudi 5 janvier 2017 - 01:53:20

Identifiants

Collections

Citation

Pierre Carpentier, Jean-Philippe Chancelier, Michel De Lara. Approximations of Stochastic Optimization Problems Subject to Measurability Constraints. SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2009, 19 (4), pp.1719-1734. <10.1137/070692376>. <hal-00975464>

Partager

Métriques

Consultations de la notice

102