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Journal articles
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
https://hal-ensta-paris.archives-ouvertes.fr//hal-00975464
Contributor : Aurélien Arnoux <>
Submitted on : Tuesday, April 8, 2014 - 4:36:24 PM
Last modification on : Friday, June 11, 2021 - 2:12:02 PM
Contributor : Aurélien Arnoux <>
Submitted on : Tuesday, April 8, 2014 - 4:36:24 PM
Last modification on : Friday, June 11, 2021 - 2:12:02 PM