Approximations of Stochastic Optimization Problems Subject to Measurability Constraints

Pierre Carpentier, Jean-Philippe Chancelier and Michel De Lara
january, 2009
Publication type:
Paper in peer-reviewed journals
SIAM Journal on Optimization, vol. 19(4), pp. 1719-1734
Keywords :
Stochastic programming - Measurability constraints - Discretization
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
    author={Pierre Carpentier and Jean-Philippe Chancelier and Michel De 
           Lara },
    title={Approximations of Stochastic Optimization Problems Subject to 
           Measurability Constraints },
    doi={10.1137/070692376 },
    journal={SIAM Journal on Optimization },
    year={2009 },
    volume={19(4) },